Obstacle Avoidance in a Dynamic Environment A Collision Cone Approach
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Adaptation and Survival in Natural Selection Adaptation and survival in natural selection is a fascinating and complex process that has been shaping the diversity of life on Earth for millions of years. From the smallest microorganisms to the largest mammals, every living organism has evolved through the mechanism of natural selection to better suit its environment and increase its chances of survival. This process has led to the incredible diversity of life that we see today, with each species uniquely adapted to its specific niche in the ecosystem.One of the key aspects of adaptation and survival in natural selection is the concept of genetic variation. Genetic variation refers to the diversity of genes within a population, which is essential for natural selection to occur. Without genetic variation, there would be no raw material for evolution to work with, and species would not be able to adapt to changing environmental conditions. Genetic variation can arise through a variety of mechanisms, including mutations, genetic recombination, and gene flow between different populations. These mechanisms create the diversity of traits within a population, some of which may confer a survival advantage in certain environments.Another important aspect of adaptation and survival in natural selection is the role of environmental pressures. The environment plays a crucial role in shaping the traits of a species, as individuals with traits that are better suited to their environment are more likely to survive and reproduce. For example, in a harsh desert environment, individuals with traits that allow them to conserve water and tolerate high temperatures are more likely to survive and pass on their genes to the next generation. Over time, this can lead to the evolution of specific adaptations that are well suited to the unique challenges of the desert environment.In addition to genetic variation and environmental pressures, the concept of fitness is central to understanding adaptation and survival in natural selection. Fitness refers to the ability of an individual to survive and reproduce in its environment, and is ultimately what drives the process of natural selection. Individuals with traits that increase their fitness are more likely to pass on their genes to the next generation, leading to the spread of thoseadvantageous traits within the population. As a result, the population as a whole becomes better adapted to its environment, increasing its chances of survival.It is important to note that adaptation and survival in natural selection is not a perfect or predetermined process. Evolution does not have a specific goal or endpoint, and the traits that increase an individual's fitness in one environment may be detrimental in another. Additionally, environmental conditions are constantly changing, which means that what is advantageous today may not be advantageous tomorrow. As a result, natural selection is an ongoing and dynamic process, with species constantly adapting to new challenges and opportunities in their environment.From a human perspective, the concept of adaptation and survival in natural selection can be both awe-inspiring and humbling. The incredible diversity of life on Earth, and the myriad ways in which species have adapted to their environments, is a testament to the power of natural selection. It is a reminder of the interconnectedness of all living things, and the delicate balance that exists within ecosystems. At the same time, it serves as a stark reminder of the fragility of life, and the constant struggle for survival that is inherent to all living organisms.In conclusion, adaptation and survival in natural selection is a fundamental process that has shaped the diversity of life on Earth. Through genetic variation, environmental pressures, and the concept of fitness, species have evolved and adapted to their environments over millions of years. From a human perspective, this process is both inspiring and humbling, serving as a reminder of the interconnectedness and fragility of life. As our understanding of natural selection continues to grow, so too does our appreciation for the incredible diversity and resilience of the natural world.。
COMPETITION AND CORPORATE TAX AVOIDANCE:EVIDENCE FROM CHINESE INDUSTRIAL FIRMS*Hongbin Cai and Qiao LiuThis article investigates whether market competition enhances the incentives of Chinese industrial firms to avoid corporate income tax.We estimate the effects of competition on the relationship between firms Õreported accounting profits and their imputed profits based on the national income account.To cope with measurement errors and potential endogeneity,we use instrumental variables,exogenous policy shocks and other robustness analysis.We find robust and consistent evidence that firms in more competitive environments engage in more tax avoidance activities.Moreover,all else equal,firms in relatively disadvantageous positions demonstrate stronger incentives to avoid corporate income tax.Recently tax avoidance and evasion has received increasing attention both practically and in academic research.1The literature has come to view tax avoidance and evasion as an important corporate strategy and has examined various determinants affecting tax avoidance activities;see,e.g.,Slemrod (2004);Desai and Dharmapala (2006).However,how industrial characteristics such as competitive environment affect firms Õincentives to engage in tax avoidance activities has not been analysed.Moreover,almost all empirical works in this literature focus on the US experience;for a notable exception,see Sivadasan and Slemrod (2006)on India.Using a large dataset of Chinese industrial firms,we examine empirically how product market competition affects firms Õincentives to avoid corporate income tax.We study corporate Ôtax saving Õbehaviour of Chinese firms,because it is an important economic phenomenon in an increasingly important economy in the world.2For example,the Chinese National Auditing Office uncovered 11.89billion Chinese yuan or RMB (about $1.6billion)in 2003based on a four-month,nationwide investigation of 788companies selected at random in 17provinces and cities (The Asian Wall Street Journal ,A2,September 20,2004).Fisman and Wei (2004)also identify evidence of pervasive tariff evasion in China.It is safe to say that these cases of uncovered *We are grateful to Jo ¨rn-Steffen Pischke (the editor),and three anonymous referees for numerous con-structive comments that greatly improved the article.We have also benefited from the comments of Paul Devereux,Amar Hamoudi,Joseph Fan,Huixing Huang,Ginger Jin,Sainan Jin,Jean-Laurent Rosenthal,James Vere and participants at the HKUST Finance Seminar,2006AEA annual meeting and 2006Interna-tional Conference on Corporate Governance in Asia.We thank Geng Xiao for help in the early stage of this project and Yong Wei for excellent research assistance.The first author acknowledges support from NSFC grant (Project No.70725002)and from the Chinese Education Ministry’s NCET.The second author’s research has been supported by grants from the University Grants Committee of Hong Kong (Projects No.AOE/H-05/99,HKU 7472/06H,and HKU747107H).1For example,the US Internal Revenue Service estimated that about 17%of income tax liability is not paid (Slemrod and Yitzhaki,2002).Citing the US General Accounting Office,Desai and Dharmapala (2006)state that ÔBy 2000,53%of large US corporations reported tax liabilities lower than $100,000.ÕFeldman and Slemrod (2007)find that ÔOn average reported positive self-employment,non-farm small business and fame income must be multiplied by a factor of 1.54,4.54and 3.87,respectively,in order to obtain true income.Õ2Following the literature,we do not distinguish tax avoidance (e.g.,taking advantage of loopholes in tax laws,earning management)and illegal evasion (e.g.,failing to report revenue or profit).Moreover,Ôtax avoidance and evasion Õ,Ôtax avoidance Õ,Ôtax saving Õand Ôtax efficiency Õare used interchangeably.The Economic Journal ,119(April ),764–795.ÓThe Author(s).Journal compilation ÓRoyal Economic Society 2009.Published by Blackwell Publishing,9600Garsington Road,Oxford OX42DQ,UK and 350Main Street,Malden,MA 02148,USA.tax evasion represent only a tiny fraction of tax avoidance and evasion by Chinese firms.Intuitively,firms under greater competition pressure are more motivated to avoid tax so as to have more investment money to compete in the market place.Thus,firms in more competitive industries and firms in relatively disadvantageous positions within an industry should have stronger incentives to avoid tax.In an earlier working paper (Cai and Liu,2007),we demonstrate these results in a simple theoretical model.In this article we focus on testing these conjectures empirically.The dataset we use is maintained by the National Bureau of Statistics of China (NBS)and contains firm-level information based on the annual accounting briefing reports filed by all Ôabove scale Õindustrial firms in China from 2000to 2005.On average we have about 190,000firms per year in our sample.However,a main challenge for our empirical analysis,which is common to the literature on tax avoidance and evasion,is that firms Õtrue accounting profits are not observable.To overcome this difficulty,scholars often use book incomes as a proxy for true profits and use the book–tax gap as a measure of tax avoidance,e.g.,Desai (2003;2005)and Desai and Dharmapala (2006).But this approach works only for public companies since book incomes for non-listed companies are usually unavailable.Using a similar approach,we calculate an imputed corporate profit based on the national income account –that is,by deducting intermediate inputs from gross output.For many reasons,this imputed corporate profit can legitimately differ from a firm’s true accounting profit based on the General Accepted Accounting Principles (GAAP).A main reason is the differences in the revenue and expense recognition rules of the two systems,for example,not all gross output in the current year necessarily converts into firm revenue in the same year.Asset depreciation rules can also be different.Tax credits (such as earning-reinvestment credits)and tax loss carry-overs can be other sources of the gap between the imputed profit and true accounting profit.For these reasons,the imputed corporate profit PRO based on the national income account is probably not a good proxy for true accounting profit and certainly not as good as book income.Thus,using the gap between the imputed profit and the reported accounting profit as a measure of tax avoidance is not appropriate in our context.However,for our purposes,we only need to assume that the imputed profit and the true accounting profit are positively correlated ,which is likely to hold since both reflect a firm’s economic fundamentals.The reason is that our theoretical predictions are mainly concerned with comparative statics results about the sensitivity of reported profits to true accounting profits .As long as the imputed profit and the true accounting profit are positively correlated,our comparative statics results will carry over to the sensitivity of the reported profit to the imputed profit.Therefore,our empirical strategy is to test hypotheses regarding how competition (and other variables of interest)affects the sensitivity of the reported profits to the imputed profits.Our theoretical predictions are all confirmed by our empirical results.Specifically,we find strong evidence indicating that competition in the product market enhances firms’incentives to engage in tax avoidance activities .The estimated effect on profit under-reporting has the predicted sign and is statistically significant for several measures of competition (the number of firms,concentration,or industry average profit margin)[A P R I L 2009]765E V I D E N C E F R O M C H I N E S E I N D U S T R I A L F I R M Sand alternative definitions of industries (3-digit or 4-digit industry codes)and markets (national or regional).Our main empirical results are robust to alternative specifications.Besides OLS regressions,we run 2SLS regressions instrumenting for both the imputed profit and competition.In particular,we use the number of permissions required for establishing a new firm in a four-digit industry as the instrument for competition and the average imputed profit at the four-digit industry level (excluding the firm itself)as the instrument for the imputed profit.In all model specifications,we find supporting empirical evidence.3In addition,we investigate a natural experiment on the compet-itive environment (lifting of restrictions on foreign investment)for two industries.All these investigations yield the same result that competition encourages the under-reporting of profits by firms.This means that even though endogeneity (such as competition)and measurement errors (such as the imputed profit)pose potentially serious econometric issues in our estimation,they are unlikely to be the driving forces of our main results.The competition effect is also economically significant.Take the 2SLS regression in column (4)of Table 4as an example.When all independent variables take their mean values,the reported profit will increase by 0.504if the imputed profit increases by 1.If the competition measure used in the regression (industry average profit margin in this case)increases from its mean by one standard deviation (i.e.,competition is less intensive by one standard deviation),then the responsiveness of the reported profit to the imputed profit increases to 0.584,representing a 15.7%increase from its previous level.In other words,a representative firm in an industry that is one standard deviation less competitive than the average industry reports about 16%more profit for each unit of imputed profit than an identical firm in the industry with the average degree of competition.Our analysis also yields useful results regarding other factors that may affect firms Õincentives to engage in tax avoidance activities.After controlling for other character-istics,firms facing higher tax rates or tighter financial constraints and smaller firms report lower profits for each unit of imputed profit.These are all consistent with our theoretical predictions.The estimated effects of these factors have the predicted signs and are statistically and economically significant.Based on the 2SLS estimation of the baseline model (e.g.,see model (4)in Table 4),all else equal,for each unit of imputed profit,a one-standard-deviation increase in the tax rate reduces a firm’s reported profit by 5.6%from its mean level;a one-standard-deviation increase in our measure of accessibility to capital markets leads to a 2.1%increase in the firm’s reported profits;and lastly,a one-standard-deviation increase in firm employment size causes the firm’s reported profits to increase by 27.4%.Our article builds on and contributes to the aforementioned growing literature on corporate tax avoidance and evasion.Our main contribution is to present systematic evidence from China that product market competition increases tax avoidance.Insofar as some of the tax avoidance and evasion is illegal or socially undesirable,our article is also related to papers that point out the Ôdark side Õof competition,e.g.,3In an earlier working paper Cai and Liu (2007),we also run GMM estimations on a balanced panel of a subsample and find qualitatively similar results.766[A P R I L T H E E C O N O M I C J O U R N A LCummins and Nyman (2005)and Shleifer (2004).In particular,Shleifer (2004)ar-gues that competition encourages the spread of a wide range of unethical behaviour such as employment of child labour,corruption,excessive executive pay and cor-porate earnings manipulation.The basic idea is simple:the effects of competition critically depend on the instruments firms use to compete in the product markets.If firms use socially unproductive means to gain competitive advantage,then competi-tion may not lead to socially desirable outcomes.In this regard,ours is the first article to our knowledge that provides systematic empirical evidence consistent with that claim.The rest of the article proceeds as follows.Section 1describes briefly the institutional background of corporate taxation in China.Then Section 2develops theoretical con-jectures and empirical hypotheses.We describe the dataset and our empirical strategy in Section 3,and then present the main empirical results in Section 4.Section 5examines the robustness of our empirical analysis.Concluding remarks are in Section 6.1.Institutional BackgroundIn the central planning system before economic reforms started in 1978,Chinese industrial firms were mostly state-owned (except small collective firms).They were not independent accounting units and had to send all surpluses to the government agencies controlling them.There was no corporate income tax in the planning system;for a description of China’s economic reforms,see Wu (2003).Starting in 1979and continuing in the 1980s,the Chinese government introduced a number of enterprise taxation rge state-owned enterprises (SOEs hereafter)were subject to 55%income tax,small SOEs were subject to a 10–55%tax schedule and private firms’s income tax rate was set at 35%.For large SOEs,there were also complicated and evolving sharing formulae to divide the after tax profits between SOEs and govern-ment.SOE reforms focused on Ôdelegating decision power and giving incentives Õ(fang quan yang li)in the 1980s,and then continued in the 1990s with Ômodern corporation system Õemphasising corporatisation and governance.Many small and medium-sized SOEs were quietly privatised,others were transformed into corporations.At the same time,non-state firms (private,foreign,Hong Kong/Taiwan)grew fast and became more and more important in the economy.As a part of the Ôsystematic fiscal and taxation Õreforms,in 1994China enacted the ÔCorporate Income Tax Code Õthat overhauled corporate taxation.All domestic firms,independent of ownership types,pay 33%corporate income tax,except that small firms with taxable income less than 30,000RMB pay 18%income tax.Since the reforms,SOEs have been allowed to keep the after-tax profits for re-investing and for covering Ôreform costs Õ(e.g.,paying for laidoff workers).4Most foreign invested industrial firms pay 15%corporate income tax.The Code allowed various exemptions,tax credits (e.g.,recycling,environmental protection,retained earning reinvestment)and reductions (e.g.,to high tech firms,new firms in poor areas),and foreign investment firms in general enjoy much more favourable treatments (Cui,2005).4See the World Bank policy note ÔSOE Dividends:How Much and to Whom?Õ(Kuijs et al.,2005).2009]767E V I D E N C E F R O M C H I N E S E I N D U S T R I A L F I R M SThe tax collection agencies were also reformed in 1994.Before 1994,provincial and local tax collectors collected all taxes,then the central government and provincial governments divided the total tax revenue according to some previously negotiated sharing formula.In the 1994reforms,taxes are classified into central and local taxes,and a National Taxation bureau (Guoshuiju)and provincial bureaus (Dishuiju)are responsible for collecting central taxes and local taxes separately.Both the National Taxation Bureau and provincial bureaus are under the supervision of the State Administration of Taxation.Right now,corporate income tax is classified as a Ôcentral tax Õand thus is collected by the National Taxation Bureau and its branches in all provinces.5Along with impressive economic growth in the last three decades,the economic landscape in China has changed dramatically over the reform years.Starting from a central planning economy,the Chinese economy has become a mixed economy in which the non-state sector plays an increasingly dominant role.Among all Ôabove scale Õindustrial firms in our dataset,in 2005the SOEs and collective firms account for only 10.2%and 15.1%respectively,mixed-ownership firms for 21.4%,and private firms (domestic,foreign,and Hong Kong and Taiwan)account for 53.3%.Moreover,through many years of reforms,managers of the remaining SOEs and collective firms are now given considerable decision power and relatively strong incentives that tie their compensation with firm performance,giving rise to a common concern about Ôinsider control Õin these firms (Wu,2003).The high economic growth and increasing tax collection efforts together produce impressive growth of corporate income tax revenue for the Chinese government since the reforms in 1994.In 2001,the total revenue from corporate income tax was 263billion RMB,and in 2005it increased to 534.4billion RMB (China Statistical Yearbook,2006).6However,enforcement and collection of corporate income tax are still con-sidered rather weak.For example,according to one report by a city branch of the National Taxation Bureau ,there are three main problems:(1)insufficient manpower in the collection agency to deal with the increasingnumber of firms;(2)lack of training and skills in the collection agency to collect corporate incometax (which is much more complicated than other taxes such as VAT);and(3)ineffective management system in the collection agency.7In each city,tax collection offices usually identify large firms as Ôimportant tax targets Õ(zhongdianhu)and each tax official is assigned to deal with a certain number of these5The classification of corporate income tax has changed over time since 1994.Initially the National Taxation Bureau collected corporate income tax on SOEs that belonged to the central government and on foreign firms,while provincial bureaus were responsible for collecting income tax on other SOEs,collective firms and domestic private firms.On January 1,2002,the State Council enacted the ÔIncome Tax Sharing Reform Act Õthat changed the classification.This feature will not create problems for our empirical analysis,because the location fixed effect in our regressions should reflect any enforcement difference across loca-tions.6The data on the total revenue from corporate income tax before 2001are not available.The Yearbook has information about the total revenue from corporate income tax from SOEs and Collective firms,which increased from 70.8billion RMB in 1994to 100billion RMB in 2000.7ÔCurrent Situations and Suggestions for Improvement of Corporate Income Tax Collection Õ,by Yushen Li and Xin Li,on webpage /llyj/ShowArticle.asp?ArticleID ¼104.768[A P R I L T H E E C O N O M I C J O U R N A Lfirms.Apart from this,tax collection officials do not appear to have effective systematic ways of auditing and checking firms.For example,sampling tax evasion cases reported in the industry magazine China Taxation ,one finds that the vast majority of the cases were reported by insiders to the tax authority.Given the weak enforcement of corporate income tax,one would expect tax avoid-ance and evasion to be quite pervasive.Even though there is no systematic study,this is quite evident from anecdotal evidence and numerous cases reported in the media.Among the many avoidance and evasion methods,the following seem to be among the most common:(a )mis-recording sales revenue (e.g.,under Ôaccounts receivable Õ);(b )abusing tax credits (e.g.,claiming recycling materials);(c )transfer prices with Ôaffiliated Õfirms;(d )earning management (e.g.,to smooth profit and loss);and (e )fake receipts.8Moreover,there are also numerous books of taxation planning that teach how to minimise corporate tax legally (e.g.,Cui,2005).The large demand of such knowledge indicates that firms do pay close attention to tax efficiency strategies.2.Theoretical Conjectures,Empirical Methodology and Testable Hypotheses Let p i ,t be firm i Õs true accounting profit in year t .We postulate that it reports a profit of^p i ;t ¼d i ;t p i ;t þe i ;t þf i ;t ð1Þwhere ^pi ;t is the profit firm i reports,d i ,t <1and e i ,t 0are two parameters and f i ,t is a mean zero error term.This means that firms under-report their profits.Clearly,theamount of profit under-reported,p i ;t À^pi ;t ,is decreasing in d i ,t and e i ,t .In other words,when d i ,t and e i ,t are greater,firm i reports more truthfully.In an earlier working paper (Cai and Liu,2007),we present a simple theoretical model that yields a profit-reporting decision rule as in (1).We also show that d i ,t and e i ,t depend on market competition and other firm characteristics.Intuitively,firms under greater competitive pressure are more motivated to avoid tax so as to have more investment money to compete in the market place.Thus,firms in more competitive industries and firms in relatively disadvantageous positions within an industry should have stronger incentives to avoid tax.Our theoretical predictions can be summarised into the following two conjectures;for details,see Cai and Liu (2007):Conjecture 1.All else equal,profit under-reporting becomes more severe in more competitive environments.8On the internet there is a widely circulated article without source entitled Ô60Methods to Evade Cor-porate Taxes Õ,see,for example,/k/itsp-Software/2006–9/0/530239.html.In one case that involved 39firms in three provinces in 2004,firms used fake receipts of recycling materials to evade taxes totalling 1.239billion RMB.In another case in Hunan province in 2004,one company used transfer pricing to avoid tax of 228million RMB.For details of these cases,see the webpage of the State Adminis-tration of Taxation http://fi/g/20060420/1614658846.shtml.2009]769E V I D E N C E F R O M C H I N E S E I N D U S T R I A L F I R M SConjecture 2.All else equal,profit under-reporting becomes more severe when tax rates or marginal returns of capital are larger,or when the cost of tax avoidance is smaller.Intuitively,with higher tax rates,one yuan of un-reported profit saves more tax,hence profit under-reporting is more profitable.With higher marginal returns of capital,one yuan of saved tax will generate more future profit.In either case,firms will tend to report lower profits.On the other hand,if the cost of tax avoidance is higher,firms will report more truthfully.Note that we focus on the effect of competition on tax avoidance and do not explicitly consider the possible agency problems in the tax avoidance decisions.Recently the effects of managerial incentives on firms Õtax avoidance have been emphasised by several scholars (Crocker and Slemrod,2005;Chen and Chu,2005;Desai and Dharamapala,2006).These studies clearly show that agency issues can have important implications for firms Õtax avoidance behaviour.In this article,as long as managers partially care about firm value,our qualitative results (Conjectures 1and 2)should still hold.Specifically,if managers Õpayoff functions are increasing in firm value,competition pressure will force managers to engage in more tax avoidance activities.Thus,to focus on the competition effect and also due to data limitation,we abstract from agency issues in this article.See Section 5.4for more discussion on this.Since p i ,t is not observable,we cannot estimate (1)directly.To overcome this diffi-culty,we adopt the following ing the NBS database,which we detail in Section 3,we compute firm i Õs corporate profit PRO i ,t in year t according to the national income accounting system as follows:PRO i ;t ¼Y i ;t ÀMED i ;t ÀFC i ;t ÀWAGE i ;t ÀCURRD i ;t ÀVAT i ;t ð2Þwhere Y i ,t is the firm’s gross output;MED i ,t measures its intermediate inputs excluding financial charges;FC i ,t is its financial charges (mainly interest payments);WAGE i ,t is the firm’s total wage bill;CURRD i ,t is the amount of current depreciation and VAT i ,t is the value added tax.Note that PRO i ,t defined here,as an imputed profit,can legitimately differ from firm i Õs true accounting profit p i ,t .A main reason is the differences in the revenue and expense recognition rules of the two systems,for example,not all gross output in the current year necessarily converts into firm revenue in the same year.Asset depreciation rules can also be different.Tax credits (such as earning-reinvestment credits,recycling and environmental credit)and tax loss carry-overs can be other sources of the gap between PRO i ,t and p i ,t .For these reasons,this imputed profit is at best a very noisy proxy for p i ,t .In fact,a key challenge for our empirical strategy is to address the measurement errors in PRO i ,t effectively,which we detail in later Sections.On the other hand,the imputed profit from the national income account system and the (unobservable)true profit should be positively correlated since they both reflect the firm’s fundamentals.We suppose that the imputed profit and the true profit are related in the following way:p i ;t ¼g i ;t þPRO i ;t þh i ;t ð3Þwhere g i ,t is an unknown parameter and h i ,t is a mean zero error term.The unobservable g i ,t reflects the (firm-specific)differences in profit calculation between 770[A P R I L T H E E C O N O M I C J O U R N A Lthe accounting system and the national income account system.A priori ,we do not know the sign of g i ,t :it can be positive or negative.By substituting (3)into (1),we deriveRPRO i ;t ¼d i ;t PRO i ;t þE i ;t þ i ;t ;ð4Þwhere we use RPRO i ,t to replace ^pi ;t ;E i ,t ¼d i ,t g i ,t þe i ,t ;and i ,t ¼d i ,t h i ,t þf i ,t .Further-more,we propose the following econometric specification for d i ,t (note that j denotes the industry of firm i ):d i ;t ¼b 0þb 1Compet j ;t þb 2Tax i ;t þb 3Finance i ;t þb 4Firm Size i ;t þb 5X i ;t þ i ;t ð5Þwhere Compet j ,t measures the level of competition in industry j ;Tax i ,t is firm i Õs tax rate in year t ;Finance i ,t is a measure of how easily firm i can access capital market;and X i ,t is a set of control variables that includes other firm characteristics,time fixed effect and location fixed effect.From Conjectures 1and 2,we have the following hypotheses:Hypothesis 1.b 1<0,i.e.,a firm’s incentives to engage in tax avoidance are positively correlated with the degree of product market competition.Hypothesis 2.b 2<0,i.e.,a firm’s incentives to engage in tax avoidance are positively correlated with its tax rate.Hypothesis 3.b 3>0,i.e.,a firm’s incentives to engage in tax avoidance are negatively correlated with its accessibility to capital market.The impact of firm size on firms Õtax avoidance is harder to determine.On the one hand,as mentioned earlier,tax collectors in China pay more attention to larger firms,thus making the expected cost of avoiding tax higher for larger firms.Moreover,firm size may also serve as a proxy for easier access to capital market,which again reduces larger firms Õincentives to avoid tax.On the other hand,one could argue that there are economies of scales in tax avoidance activities,thus larger firms have stronger incentives to hide profits.While it remains an empirical issue to find out in which direction the net effect goes,our prior is that the former is likely to be more important and hence we state Hypothesis 4as follows:Hypothesis 4.b 4>0,i.e.,larger firms have weaker incentives to engage in tax avoidance.We have a specification for E i ,t ,which is similar to that for d i ,t as in (5).However,since we cannot determine the sign of g i ,t in (3)a priori ,and since E i ,t ¼d i ,t g i ,t þd i ,t e i ,t ,our model has no prediction about how E i ,t will be affected by competition or other variables.Thus,we do not have predictions about the signs of the coefficients in the estimation of E i ,t .2009]771E V I D E N C E F R O M C H I N E S E I N D U S T R I A L F I R M S。
Overcoming ObstaclesOvercoming obstacles is a universal human experience that can be both challenging and rewarding. Whether it's overcoming personal struggles, professional setbacks, or societal barriers, the journey to success often involves navigating through various obstacles. In this response, I will explore the concept of overcoming obstacles from multiple perspectives, including personal, professional, and societal. On a personal level, overcoming obstacles can be a deeply emotional and transformative experience. It often requires resilience, determination, and a willingness to confront one's own fears and limitations. For example, someone struggling with mental health issues may face the obstacle of seeking help and treatment. This can be a daunting task, as it may involve confronting stigmas and seeking support from others. However, by overcoming this obstacle, the individual can experience personal growth and healing. In my own experience, I have faced personal obstacles that have tested my strength and perseverance. One particularly challenging obstacle I faced was the loss of a loved one. This experience brought about intense grief and sadness, and it took time and effort to overcome the emotional pain. Through seeking support from friends and family, as well as engaging in self-care practices such as therapy and meditation, I was able to gradually overcome this obstacle and find healing. Professionally, overcoming obstacles is often a key factor in achieving success and growth. Whether it's navigating a competitive job market, overcoming workplace challenges, or pursuing career advancement, individuals often encounter various obstacles in their professional lives. For example, someone seeking to advance in their career may face the obstacle of acquiring new skills or qualifications. This may require dedication, hard work, and a willingness to step out of one's comfort zone. In my own career, I have encountered obstacles that have pushed me to grow and develop professionally. One significant obstacle I faced was transitioning to a new role with increased responsibilities and expectations. This required me to adapt to new challenges, learn new skills, and navigate unfamiliar territory. Through perseverance and a willingness to learn, I was able to overcome this obstacle and thrive in my new role. From a societal perspective, overcoming obstacles often involves addressing systemic barriers and injustices. Marginalizedcommunities, such as people of color, LGBTQ individuals, and people with disabilities, often face significant obstacles in various aspects of their lives. These obstacles can range from discrimination and prejudice to lack of access to resources and opportunities. Overcoming these obstacles often requires collective action, advocacy, and policy changes to create a more equitable society. As a society, we must work towards dismantling the obstacles that prevent certain groups from thriving. This can involve advocating for policy changes, supporting marginalized communities, and challenging discriminatory attitudes and behaviors. By working together to address these obstacles, we can create a more inclusive and just society for all. In conclusion, overcoming obstacles is a multifaceted and deeply human experience that requires resilience, determination, and empathy. Whether it's on a personal, professional, or societal level, navigating through obstacles can be both challenging and transformative. By acknowledging and addressing these obstacles, individuals and communities can work towards creating a more equitable and supportive environment for all.。
*2016年度河南省科技攻关计划(编号:162102110134)摘要:无人机经常应用于复杂的环境之中,该环境要求无人机具有自动避障功能。
在常用的避障技术中机器视觉具有不可替代的作用,而双目全景视觉集中了双目和全景的优势,在无人机避障领域具有广阔的应用前景。
详细分析双目视觉技术、全景视觉技术及双目全景视觉技术的结构和原理,并提出基于双目全景视觉的无人机避障技术流程和该技术未来的发展方向。
关键词:无人机;双目全景视觉;避障中图分类号:V279+.2文献标识码:A文章编号:1009-9492(2019)03-0016-04Research on UAV Obstacle Avoidance Technology Based on BinocularPanoramic VisionMA Xun-ju ,ZHANG Rui-zhu ,MA Zi-ling ,YAN Da-kao(North China University of Water Resources and Electric Power ,School of Mechanical Engineering ,Zhengzhou 450045,China )Abstract:Unmanned aerial vehicle (UAV)is often used in complex environment ,which requires UAV to have automatic obstacleavoidance function.Machine vision plays an irreplaceable role in the commonly used obstacle avoidance technology ,while binocular panoramic vision concentrates the advantages of binocular and panoramic vision and has broad application prospects in the field of UAV obstacle avoidance.The structure and principle of binocular vision technology ,panoramic vision technology and binocular panoramic vision technology were analyzed in detail ,and the technical process of obstacle avoidance for UAV based on binocular panoramic vision and its future development direction were proposed.Key words:UAV ;binocular panoramic vision ;obstacle avoidance基于双目全景视觉的无人机避障技术探究*马勋举,张瑞珠,马子领,严大考(华北水利水电大学机械学院,河南郑州450045)DOI:10.3969/j.issn.1009-9492.2019.03.0040引言无人飞行器又简称无人机,是指具有自主决策能力的空中机器人系统[1]。
海绵英语作文Sponges are fascinating creatures that have been around for millions of years. They are simple yet highly efficient organisms that play a crucial role in marine ecosystems. In this essay we will explore the characteristics of sponges their habitat and their importance to the environment.Characteristics of SpongesSponges belonging to the phylum Porifera are multicellular organisms that lack true tissues and organs. They are composed of cells that are organized into a few distinct cell types but these cells are not separated by specialized tissues. The most notable features of sponges include1. Porosity Sponges have a porous structure that allows water to flow through their bodies. This is crucial for their filterfeeding mechanism.2. Chambered Body The body of a sponge is made up of a series of chambers connected by a network of canals.3. Lack of Nervous System Unlike more complex animals sponges do not have a nervous system brain or even a true digestive system.4. Reproduction Sponges reproduce both asexually and sexually. They can regenerate from small fragments which is a form of asexual reproduction.Habitat of SpongesSponges can be found in a variety of aquatic environments predominantly in marine settings. They are known to inhabit1. Shallow Waters Many species prefer shallow waters where sunlight is abundant aiding in the photosynthesis of their symbiotic algae.2. Deep Sea Some sponges can survive in the deep sea where they adapt to the high pressure and lack of light.3. Coral Reefs Sponges are often found in coral reefs where they contribute to the biodiversity and provide habitats for other marine creatures.4. Polar Regions Surprisingly some sponges can be found in the cold waters of polar regions demonstrating their adaptability.Importance of SpongesSponges are vital to the health of marine ecosystems for several reasons1. Filter Feeders By filtering water sponges help remove excess nutrients and pollutants thus contributing to water purification.2. Biodiversity As a part of the coral reef ecosystem sponges provide habitats and food for a variety of marine species.3. Bioindicators Sponges are sensitive to environmental changes and can serve as bioindicators of water quality.4. Sponge Products Some species of sponges have been used by humans for various purposes including as cleaning tools and in the medical field for their unique properties. In conclusion sponges are not just simple organisms they are complex and integral parts of marine ecosystems. Their ability to thrive in diverse environments and their contributions to the marine food web and water quality make them an essential component of our planets biodiversity. Understanding and protecting sponges is crucial for maintaining the health of our oceans.。
无人机避障方法研究进展**基金项目:民航局民航安全能力建设资金支持研究项目(编号TM2018-3-1/2)收稿日期:2019-09-04陈亚青打张智豪I,李哲2(1•中国民用航空飞行学院飞行技术与飞行安全科研基地,四川广汉618307;2.中国民用航空飞行学院空中交通管理学院,四川 广汉618307)摘要:社会的高度信息化使得无人机能应用于各个领域,任务难度的增加决定了无人机朝集群化和自主化的方向发展。
高效的避障技术是实现无人机高速飞行和智能化的重要保障。
本文首先阐述了无人机避障的概念、过程以及分类。
其次,详细介绍了超声波、单目视觉、双目视觉、激光雷达4种单无人机避障方法以及人工势场法为主的无人机编队避障方法,并分析了各种 方法的原理和优缺点。
最后,总结了无人机避障目前存在的问题和未来的发展趋势。
关键词:避障,无人机避障;无人机编队;激光雷达避障中图分类号:V279 文献标识码:A 文章编号:1003-7241(2020)012-0001-06Research Progress on Obstacle Avoidanee Methods of UAVCHEN Ya-qing *, ZHANG Zhi-hao 1, LI Zhe 2(1. Civil Aviation for Flight Technology and Safety Research Base, Civil Aviation Flight University of C hina, Guanghan 618307 China;2. College of Air Traffic Management, Civil Aviation Flight University of China, Guanghan 618307 China )Abstract: The highly infbrmationized society enables unmanned aerial vehicle (UAV) to be applied in various fields. The increasingin mission difficulty determines the development direction of unmanned aerial vehicles towards clustering and indepen ・ dence. Efficient obstacle avoidance technology is an important guarantee for high-speed flight and intelligentization ofdrones. Firstly, this paper describes the concept, process and classification of UAV obstacle avoidance. Firstly, this paper describes the concept, process and classification of UAV obstacle avoidance. Secondly, the ultrasonic, monocular vision,binocular vision, lidar, four kinds of single unmanned aircraft obstacle avoidance methods and artificial potential field method based unmanned aerial vehicle formation obstacle avoidance method are introduced in detail, and the principles,advantages and disadvantages of these methods are analyzed. Finally, it summarizes the current problems and future devel ・ opment trends of UAV obstacle avoidance.Key words: obstacle avoidance; UAV obstacle avoidance; UAV formation; lidar radar obstacle avoidance1引言近年来,随着电子产业的飞速发展和社会的高度信 息化,无人机在众多领域都有了广泛的应用,由于执行任 务难度的提升,无人机的使用规模也在不断扩张,多无人机同时执行任务的模式被广泛适用。
Perseverance Overcoming Obstacles Perseverance is a quality that is often associated with overcoming obstacles.It is the ability to persist in the face of challenges, to keep going even whenthe odds are stacked against you. Perseverance is a key trait that can help individuals overcome obstacles and achieve their goals. In this essay, we will explore the concept of perseverance and how it can help individuals overcome obstacles in various aspects of life. One of the most common areas where perseverance is needed is in the pursuit of personal goals and aspirations. Whether it is in the realm of academics, career, or personal development, individuals often face numerous obstacles that can hinder their progress. These obstacles can take the form of academic challenges, financial constraints, or even personal setbacks. However, it is through perseverance that individuals can push through these obstacles and continue to work towards their goals. For example, consider a student who is struggling with their academics. They may be facing difficulties in understanding certain subjects or keeping up with the demands of their coursework. However, through perseverance, they can continue to put in the effort and seek help when needed. By persisting through the challenges, they can eventually overcome their academic obstacles and achieve success in their studies. Similarly, in the professional realm, individuals often face obstacles in their career paths. This can range from facing rejection in job applications, dealing with difficult colleagues or superiors, or even experiencing setbacks in their professional development. However, through perseverance, individuals can continue to pursue their career goals, whether it is by seeking alternative opportunities, improving their skills, or navigating through challenging work environments. Furthermore, perseverance is also crucial in the realm of personal development. Individuals may face obstacles in their personal lives, such as dealing withmental health issues, overcoming past traumas, or even managing difficult relationships. Through perseverance, individuals can seek the necessary support, work on their personal growth, and overcome these obstacles to lead fulfilling lives. In addition to personal goals and aspirations, perseverance is alsocrucial in the face of societal and global challenges. Individuals may face obstacles in advocating for social justice, promoting environmental sustainability,or addressing systemic inequalities. These challenges can often seem daunting and insurmountable. However, through perseverance, individuals and communities can continue to push for change, raise awareness, and work towards creating a better world for future generations. For example, consider the efforts of activists who tirelessly advocate for social and environmental causes. They often face resistance, apathy, and even hostility in their pursuits. However, it is through their perseverance and unwavering commitment that they can continue to makestrides in creating positive change. Whether it is through organizing movements, raising awareness, or lobbying for policy changes, perseverance is a key driving force in overcoming societal and global obstacles. Moreover, perseverance is not only about overcoming external obstacles but also about overcoming internal struggles. Individuals may face self-doubt, fear of failure, or lack of motivation in their pursuits. However, through perseverance, individuals can work on overcoming these internal obstacles, whether it is through seeking support, practicing self-care, or developing a resilient mindset. In conclusion, perseverance is a crucial quality that can help individuals overcome obstacles in various aspects of life. Whether it is in the pursuit of personal goals, navigating professional challenges, advocating for societal change, or overcoming internal struggles, perseverance is the driving force that enables individuals to push through adversity and achieve their aspirations. By embodying perseverance, individuals can continue to strive towards their goals, no matter how daunting the obstacles may seem.。
2022年考研考博-考博英语-南开大学考试全真模拟易错、难点剖析AB卷(带答案)一.综合题(共15题)1.单选题The discussion was so prolonged and exhausting that () we had to stop for refreshments. 问题1选项A.at largeB.at easeC.at randomD.at intervals【答案】D【解析】固定搭配词组辨析。
at large“详尽的”;at ease“安逸, 舒适”;at random“随便地, 任意地”;at intervals“不时地, 间断地”。
句意:讨论时间太长, 使人精疲力竭, 我们不得不不时地停下来吃点点心。
选项D符合句意。
2.单选题The consolidation of the crumbling walls and towers has been carried out in () with a program agreed with by the Department of the Environment.问题1选项A.caseB.accordanceC.placeD.charge 【答案】B【解析】固定搭配。
in accordance with为固定搭配,表示“依照,与...一致”。
3.单选题In the last 12 years total employment in the United States grew faster than at any time in the peacetime history of any country—from 82 to 110 million between 1973 and 1985—that is, by a full one third. The entire growth, however, was in manufacturing, and especially in non-blue-collar jobs.This trend is the same in all developed countries, and is, indeed, even more pronounced in Japan. It is therefore highly probable that in 25 years developed countries such as the United States and Japan will employ no larger a proportion of the labor force in manufacturing than developed countries now employ in farming—at most, 10 percent. Today the United States employs around 18 million people in blue-collar jobs in manufacturing industries. By 2010, the number is likely to be no more than 12 million. In some major industries the drop will be even sharper. It is quite unrealistic, for instance, to expect that the American automobile industry will employ more than one-third of its present blue-collar force 25 years hence, even though production might be 50 percent higher.If a company, an industry or a country does not in the next quarter century sharply increase manufacturing production and at the same time sharply reduce the blue-collar work force, it cannot hope to remain competitive—or even to remain “developed.” The attempt to preserve such blue-collar jobs is actually a prescription for unemployment.This is not a conclusion that American politicians, labor leaders or indeed the general public can easily understand or accept. What confuses the issue even more is that the United Stales is experiencing several separate and different shifts in the manufacturing economy. One is the acceleration of the substitution of knowledge and capital for manual labor. Where we spoke of mechanization a few decades ago, we now speak of “robotization” or “automation”. This is actually m ore a change in terminology than a change in reality. When Henry Ford introduced the assembly line in 1909, he cut the number of man— hours required to produce a motor car by some 80 percent in two or three years—far more than anyone expects to result from even the most complete robotization. But there is no doubt that we are facing a new sharp acceleration in the replacement of manual workers by machines—that is, by the products of knowledge.1.According to the author, the shrinkage in the manufacturing labor force demonstrates() .2.American politicians and labor lenders tend to dislike() .3.According to the author, in the coming 25 years, a developed country or industry, in orderto remain competitive, ought to() .4.This passage may have been excerpted from() .问题1选项A.the degree to which a country's production is robotizedB.a reduction in a country’s manufacturing industriesC.a worsening relationship between labor and managementD.the difference between a developed country and a developing country问题2选项A.confusion in manufacturing economyB.an increase in blue-collar work forceC.internal competition in manufacturing productionD.a drop in the blue-collar job opportunities问题3选项A.reduce the percentage of the blue-collar work forceB.preserve blue-collar jobs for international competitionC.accelerate motor-can manufacturing in Henry Ford's styleD.solve the problem of unemployment问题4选项A.a magazine about capital investmentB.an article on automationC.a motor-car magazineD.an article on global economy【答案】第1题:A第2题:D第3题:A第4题:D【解析】1.信息推理题。
摘要植保无人机作为一种新兴的农业机械设备,具有作业效率高、机动性能好、安全稳定性高等优点,目前得到了越来越广泛的应用。
为了保证农药喷洒精准化,前期的病虫害精准定位就显得尤为重要。
因此,建立起一套快速、便捷、高效的系统来识别病虫害区域是非常有意义的,本文选择了基于Faster R-CNN 的茶叶病虫害图像检测模型,实现了病虫害的精准定位,为植保无人机的精细化作业提供了技术支撑。
本文主要完成了以下工作:(1)在以Pixhawk飞控为核心的基础上,设计了一款四旋翼植保无人机,此植保无人机能稳定的执行自主巡航、智能避障、图像采集、智能喷洒等任务。
(2)首先选用了中值滤波算法对采集的含有噪声信息的茶叶病虫害图像进行降噪处理;然后选用了基于直方图均衡化算法的茶叶病害虫图像图像增强操作。
由于深度卷积神经网络具有较强的图像特征表征能力和模型泛化能力,因此,本文又选择了基于Faster R-CNN 的茶叶病虫害图像检测算法。
(3)选择了基于Faster R-CNN 的茶叶病虫害图像检测模型训练的方法,从而训练出高鲁棒性和高特征表示能力的目标检测网络,并利用实验与其他传统目标检测算法Deformable Part Model、R-CNN、Fast R-CNN等相比较,结果证明Faster R-CNN算法最优,能达到98.7%的准确率。
该论文有图60幅,表10个,参考文献61篇。
关键词:多旋翼无人机;PID控制;机器视觉;神经网络;病虫害检测AbstractAs new agricultural machinery, eppo UA V has the advantages of high operating efficiency, good maneuverability, and high safety and stability. At present, it has been applied more and more widely. In order to ensure the precision of pesticide spraying, it is particularly important to accurately locate diseases and insect pests in the early stage. Therefore, it has great significance to establish a fast and convenient and efficient model, which identify disease and insect pest areas. In this paper, proposed a tea disease and insect pest image detection model based on Faster R-CNN, so as to realize accurate location of diseases and insect pests, providing technical support for the fine operation of plant protection UA V. The main works are in the following:1. A four-rotor plant protection UA V is designed based on the control system of Pixhawk, which can steadily perform autonomous cruise, intelligent obstacle avoidance, image acquisition, intelligent spraying, and other tasks.2. Firstly, the median filter algorithm is used to reduce the noise of the collected images containing noise information. Then the histogram equalization algorithm is used to enhance the image of tea leaf diseases and pests. Based on the deep convolution neural network's strong ability in image feature representation and learning ability in model generalization, a Faster R-CNN based image detection algorithm for tea diseases and insect pests was proposed.3. A method based on Faster R-CNN is proposed to train the image detection Model of tea plant diseases and insect pests, so as to train a target detection network with high robustness and feature representation ability, and the experiment was compared with other traditional target detection algorithms such as Deformable Part Model, R-CNN and Faster R-CNN. The results showed that Faster R-CNN algorithm was the most optimal and could achieve 98.7% accuracy.The paper has 52 pictures, 10 tables and 61 references.Keywords: multi-rotor UA V; PID controller; machine vsion; DCNN; pest detection目录摘要 (I)目录 (VIII)图清单 (XII)表清单 (XVI)变量注释表 (XVII)1 绪论 (1)1.1研究背景和意义 (1)1.2国内外研究现状 (2)1.3论文的主要研究内容与工作安排 (10)2 植保无人机系统总体方案设计 (12)2.1总体任务需求分析 (12)2.2控制系统总体设计 (13)2.3本章小结 (16)3 植保无人机飞行控制系统设计 (17)3.1多旋翼无人机飞行控制原理 (17)3.2四旋翼无人机的坐标系与姿态控制 (19)3.3四旋翼无人机控制方案设计 (25)3.4植保无人机飞行控制系统硬件设计 (26)3.5植保无人机飞行控制系统软件设计 (30)3.6本章小结 (32)4 茶叶病虫害图像信息处理与识别 (33)4.1茶叶病虫害图像采集 (34)4.2茶叶病虫害图像预处理 (35)4.3茶叶病虫害图像识别 (37)4.4本章小结 (47)5 喷洒与避障系统设计 (49)5.1植保无人机喷洒系统设计 (49)5.2植保无人机避障系统设计 (52)5.3本章小结 (56)6植保无人机飞行实验测试 (57)6.1自主巡航实验 (57)6.2避障实验 (59)6.3智能喷洒实验 (62)6.4本章小结 (64)7总结与展望 (65)7.1总结 (65)7.2展望 (66)参考文献 (68)作者简历 (72)学位论文原创性声明 (73)学位论文数据集 (72)ContentsAbstract..................................................................................................................... V II Contents .. (X)List of Figures........................................................................................................... X II List of Tables (XVI)List of Variables (XVII)1 Introduction (1)1.1 Research Background and Significance (1)1.2 Current Research Situation at Home and Abroad (2)1.3 Main research contents of this subject (10)2 Overall design scheme of plant protection UA V system (12)2.1 Overall task requirement analysis (12)2.2 Overall design of control system (13)2.3 Summary (16)3 Design flight control system of Plant protection UA V (17)3.1 Multi-rotor UA V flight control principle (17)3.2 Coordinate system and attitude control of quadrotor UA V (19)3.3 Design control scheme of quadrotor UA V (25)3.4 Hardware design of plant protection UA V flight control system (26)3.5 Software design of plant protection UA V flight control system (30)3.6 Summary (32)4 Image information processing and identification of tea pests and diseases (33)4.1 Image collection of tea pests and diseases (34)4.2 Image preprocessing of tea pests and diseases (35)4.3 Image identification of tea pests and diseases (37)4.4 Summary (47)5 Obstacle avoidance and spray system design (49)5.1 Spraying system design of plant protection UA V (49)5.2 Evadible system design of plant protection UA V (52)5.3 Summary (56)6 Flight experimental test of Plant protection UA V (57)6.1 Autonomous cruise experiment (57)6.2 Obstacle avoidance experiment (59)6.3 Intelligent spraying experiment (62)6.4 Summary (64)7 Conclusion and outlook (65)7.1 Conclusion (65)7.2 Outlook (66)References (68)Author’s Resume (72)Declaration of Thesis Originality (73)Thesis Data Collection (74)图清单表清单变量注释表θ俯仰角φ横滚角ψ偏航角(x,y,z)机体坐标系(X,Y,Z)地理坐标系Aθ绕Z轴旋转矩阵Aφ绕Y轴旋转矩阵Aψ绕X轴旋转矩阵F无人机所受外力总和V地理坐标系的速度矢量I动量矩M无人机所受合力力矩N分布常数,通常取1.1-1.25f1、f2、f3、f4四旋翼无人机四个电机产生的拉力μ1四旋翼无人机四个电机产生的拉力总和ωx四旋翼无人机在x轴上的角速度ωy四旋翼无人机在y轴上的角速度ωz四旋翼无人机在z轴上的角速度K p比例系数T i积分时间常数T d微分时间常数μ(t)PID控制器的输出e(t)系统误差r k第k个灰度级S k直方图累计分布函数W x,y k特征图对应的卷积核在K通道(i,j)位置的权值b偏值参数f(x,y)激活函数W1上一层卷积层特征图的输入图像宽H1上一层卷积层特征图的输入图像高W2卷积运算后特征图的宽H2卷积运算后特征图的高P Zero Padding参数S卷积核步长R i,j表示像素(i,j)局部邻域pool池化操作E(F(X),Y)功能输出minX∈ℛ(X i)i=1N模型输入a j l=F l(X i)计算层级输出e j=∂E d∂F j l计算传播误差a j l e j=ðE dðw j l计算层级梯度Φ(p i)特征正向量Loos reg边框回归损失函数p i i被预测为目标的概率N cls正负样本数量N reg特征图中所有特征点p’i Loss reg表示为回归只针对正样本λ分类和回归损失函数的平衡系数1 绪论1 绪论1 Introduction1.1研究背景和意义(Research Background and Significance)随着社会的发展,我国人口数量从1980年的98705(万人)增长到2018年的139538(万人),与此同时,随着城市化进程的推进和加快,我国农村人口的比例已从1980年的80.61%减少到了2018年的40.42%,城镇化率持续提高。
562IEEE TRANSACTIONS ON SYSTEMS, MAN, AND CYBERNETICS—PART A: SYSTEMS AND HUMANS, VOL. 28, NO. 5, SEPTEMBER 1998Obstacle Avoidance in a Dynamic Environment: A Collision Cone ApproachAnimesh Chakravarthy and Debasish GhoseAbstract—A novel collision cone approach is proposed as an aid to collision detection and avoidance between irregularly shaped moving objects with unknown trajectories. It is shown that the collision cone can be effectively used to determine whether collision between a robot and an obstacle (both moving in a dynamic environment) is imminent. No restrictions are placed on the shapes of either the robot or the obstacle, i.e., they can both be of any arbitrary shape. The collision cone concept is developed in a phased manner starting from existing analytical results—available in aerospace literature—that enable prediction of collision between two moving point objects. These results are extended to predict collision between a point and a circular object, between a point and an irregularly shaped object, between two circular objects, and finally between two irregularly shaped objects. Using the collision cone approach, several strategies that the robot can follow in order to avoid collision, are presented. A discussion on how the shapes of the robot and obstacles can be approximated in order to reduce computational burden is also presented. A number of examples are given to illustrate both collision prediction and avoidance strategies of the robot. Index Terms—Collision cone, dynamic environments, obstacle avoidance, path planning.I. INTRODUCTION BSTACLE avoidance is a fundamental requirement in motion planning of a mobile robot. Several papers addressing this issue have appeared in robotics literature [6], [8], [13], [23], [24]. Motion planning can be categorized [6] as static (when the obstacles are stationary in the environment) or dynamic (when the obstacles are capable of movement and may even change shape and size). The environment could be completely known (when the trajectory of the obstacles is known a priori) or partially known (when obstacle trajectory is unknown or information about it is incomplete). This classification is not universal and an alternative classification is available in [8]. To date, a major research effort in this area has been applied to analyze and solve the problem of motion planning in a completely known environment with largely static and, to some extent, moving obstacles [23]. Their primary goal was to determine a collision-free path from a starting point to a goal point while optimizing some performance criterion. Configuration space approach, Voronoi diagrams, retraction methods, potential functions, visibility graphs, accessibility graphs, tangent graphs, etc. ([6], [8],Manuscript received August 27, 1996; revised December 7, 1997. A. Chakravarthy is with the Flight Mechanics and Simulation Division, Aeronautical Development Agency, Bangalore 560 017, India. D. Ghose is with the Department of Aerospace Engineering, Indian Institute of Science, Bangalore 560 012, India (e-mail: dghose@aero.iisc.ernet.in). Publisher Item Identifier S 1083-4427(98)04346-X.O[16]) are some of the techniques which have been reasonably successful in achieving this goal. While these approaches are justifiable for a completely known environment, a partially known dynamic environment—which is a more realistic framework in situations where obstacle motion cannot be predicted—requires a different approach. In fact, dynamic motion planning is more difficult than static motion planning even when complete information about the environment is available. This is shown by several available complexity results for motion planning [21]. Recent advances in robotics technology has made possible the development of autonomous and semiautonomous robotic systems for land, air, and underwater operations. These robots use sophisticated onboard sensors to perceive their environment and use this information to plan and execute tasks [2], [3], [22], [23], [29]. Their primary use is in uncertain environments characterized by the presence of moving obstacles with unpredictable trajectories. Motion planning of robots in uncertain and unpredictable environments has attracted the attention of robotics researchers only recently [1], [7], [9]–[12], [19], [26], [25], [28]. In this paper, we present a novel approach called the collision cone approach which is ideally suited for automated guided vehicles or autonomous mobile robots. The method is new in the sense that it uses concepts which have their roots in aerospace literature rather than in robotics. The only relevant paper in the robotics literature that uses a similar concept is that by Tychonievich et al. [27]. The specific problem considered in this paper is that of a mobile robot avoiding one or more moving obstacles with unknown trajectories, based on sensor information collected by the robot. The robot and the obstacles are both assumed to move only by translation in a two-dimensional (2-D) space. Unlike previous literature, no assumptions are made on the shape of the robot or obstacles (i.e., they need not be polygons—convex, or otherwise). They can be of any arbitrary shape but with the constraint that each is a single rigid body without relative motion between points on the body. Thus, this approach is more suitable for the problem of obstacle avoidance of an automated guided vehicle or a mobile robot in a workspace consisting of moving obstacles, rather than for motion planning of robotic manipulators. This paper is motivated by the conviction that collision avoidance and collision achievement are, in principle, two aspects of the same problem. In the robotics literature, the problem of collision avoidance has attracted a considerable amount of attention. On the other hand, collision achievement1083–4427/98$10.00 © 1998 IEEECHAKRAVARTHY AND GHOSE: OBSTACLE AVOIDANCE IN A DYNAMIC ENVIRONMENT563Fig. 1. Collision geometry between two point objects.Fig. 2. A typical (V ; Vr ) trajectory.(or interception) has been of primary concern mainly in the aerospace guidance literature [14], [30]. For example, some of the problems addressed in the guidance literature involve the guidance of a missile to intercept an aircraft, guidance of a torpedo to intercept a ship, etc. The problem of achieving collision or interception is a long-standing area of research in the aerospace literature and has evolved into a reasonably complete theory, especially in the missile guidance literature, over the past five decades. Though the problem of collision avoidance in the robotics literature is of a more recent vintage, it has also witnessed intense research activity in recent years. However, to date there has been almost no cross-fertilization of ideas between the two areas. The main reason for this is the apparent dichotomy between them in terms of their objectives, operating environments, vehicle dynamics, sensor systems, performance capabilities, etc. With the present day technological advances (especially in sensor systems) and the stringent performance requirements on intelligent robotic vehicles [3], it is felt that many of the advances in the area of aerospace guidance theory has considerable relevance in robotics too. Our purpose is to show that the fundamental concepts used for achieving intercept between bodies in motion can also be used to formulate strategies for collision avoidance. In doing so we extend these fundamental concepts to situations relevant to the collision avoidance problem in robotics, and derive several results that are new not only in robotics but also in aerospace guidance. The literature on interception problems has mainly focussed upon conditions of collision between two moving point objects based on their instantaneous velocities. In the context of collision avoidance between robots it is not sufficient to consider an object as a point mass. Its physical shape and size, and its position and orientation in space, are of prime importance. We first extend the existing theory for predicting collision between point objects to obtain more general conditions to predict collision between objects of arbitrary shapes and sizes. Based on these results the collision cone is presented as a fundamental concept used for the purpose of collision avoidance. We restrict our study to the 2-D planar case in this paper. This paper is organized as follows. In Section II, we review some results well-known in the aerospace guidance literature and illustrate some basic concepts through simple examples which also show how the collision cone can be obtained for a simple initial geometry between a point robot and acircular object. In Section III, we formalize the concept of the collision cone and present analytical results to obtain the exact collision cone between a point and a circular object, between a point and an irregularly shaped object, between two circular objects, and finally, between two irregularly shaped objects. In Section IV, we discuss some simple strategies for collision avoidance based on the collision cone concept. In Section V, we examine the possibility of simplifying the computation of the collision cone by approximating irregularly shaped objects as a collection of circular objects. We conclude the paper in Section VI with a general discussion on the applicability of the collision cone approach. II. COLLISION BETWEEN POINT OBJECTS The engagement geometry for an interception problem is given in Fig. 1. Here, and are two point objects, moving and respectively. The behavior at constant velocities of the line-of-sight (LOS) is characterized by the following kinematic equations: (1) (2) and are the relative velocity components (with rewhere along, and perpendicular to, the LOS, respectively. spect to Since we consider only the instantaneous velocities of the point objects, and are assumed to be constants. Differentiating (1) and (2), we get (3) (4) Dividing (3) by (4) and cross-multiplying, we get (5) which, on integration, yields the following relation: (6) and are the relative velocity components at where Equation (6) shows that the some initial time plane is a circle with center at the trajectory on the origin and radius equal to the initial relative velocity between and This also implies that the relative velocity is a constant with respect to time. Also, from (3), (4), and (6), plane have it is evident that the trajectories in the a time history shown in Fig. 2. Next, we state the following well-known results ([14], [15], [20], [30]).564IEEE TRANSACTIONS ON SYSTEMS, MAN, AND CYBERNETICS—PART A: SYSTEMS AND HUMANS, VOL. 28, NO. 5, SEPTEMBER 1998Lemma 1: The set of points satisfying the condition (for example, point in Fig. 2) are stationary points on the plane. implies that Substituting Proof: and this in (3) and (4) yields Lemma 2: If two point objects are moving with constant and velocities (i.e., constant speed and direction), then together form a necessary and sufficient condition for collision. and implies that Proof: From Lemma 1, and for all future time. But implies that implies the LOS does not rotate in space and that distance between the two objects reduces until collision occurs, thus proving sufficiency. To prove necessity, let the two objects collide at time In the time preceding the distance between the objects was If the obviously decreasing, thus implying that positions of the objects are projected back to any time the resulting figure formed is a triangle with the LOS at as one side and the collision point as the opposite vertex so that are parallel to each successive lines of sight at times From Lemma 1, we can see that other. Thus, implies that thus proving necessity. Example 1: Consider an initial geometry between a point and a circle with object and Let be a point on at an angle with reference to Then, the circle by using (1) and (2), and the conditions indicated in Lemma is on a collision course with point 2, it can be shown that if See Fig. 3(a). then, If we now consider all the points on the circle by using (1) and (2) (and Lemma 2) for each such point, to collide we get a corresponding value of that causes with that point. The collection of all the values of defines a lies in this cone then will eventually cone such that if We refer to this cone as the collision cone. In collide with this example, it is found that the collision cone is defined by See Fig. 3(b). Example 2: Consider another initial geometry between and with and Again, is a point on the circle at Now, will collide with if or The two values of correspond to collision occurring at different points in space and at different instants of time. and each point Again, if we consider collision between and consider the collection of all such values of we on find that the collision cone is now split into two cones, and See is defined by Fig. 3(c). We call this a split collision cone. and are moving with Lemma 3: If two point objects constant velocities and (Fig. 1), and the initial position of only is fixed; then, as long as there exists a for which is on a collision course with Proof: Let Then, the collision condition (indicated in Lemma 2) is defined by(a)(b)(c) Fig. 3. (a) Collision geometry for Example 1, (b) collision cone for Example 1, and (c) collision cone for Example 2.Substituting forandfrom (1) and (2), we get (7)Therefore, (8) (9) there exists a that Thus, from (9), as long as satisfies the conditions for collision. When we get which is not a collision condition.CHAKRAVARTHY AND GHOSE: OBSTACLE AVOIDANCE IN A DYNAMIC ENVIRONMENT565Since is a periodic function with period successive that satisfy occur at intervals of The where angle is always bounded in the sense that For we have and obviously this interval is insufficient to allow for more than for which one value of We now convert the condition into an for which equivalent condition with reference to and are obtained from (10) and (11) by putting Now, consider the inequality (13) and by putting Substituting the expressions for and respectively in (10), we getFig. 4. Collision geometry between a point and a circle.III. THE COLLISION CONE In the previous section, we illustrated the concept of a collision cone with the help of two examples. The collision cone can be used to predict the possibility of collision between two objects and to design collision avoidance strategies. In this section, we shall derive the necessary and sufficient conditions that enable the determination of the collision cone. A. Collision Between a Point and a Circular Object In Fig. 4, is a point object, while is a circle of radius and with center at The velocities of and are denoted and respectively. For any point (parametrized by on the circle we can write the relative by the angle as velocity components of (10) (11) Lemma 4: The point object is headed for a collision with if and only if there exists a ray passing the circle for which is called through the collision point). Proof: Follows from Lemma 2. Now, let us define the relative velocity components of (the upper tangent to the circle from point as and and those of (the lower tangent to the circle as and These expressions from point and are obtained from (10) and (11) by substituting respectively. then Lemma 5: At any given time, if where is a point on the there exists exactly one ray that satisfies circle Proof: Consider an arbitrary point on the circle defined by the angle From (10), it is obvious that is a continuous function of Thus, implies that there exists at least one for which It remains to be shown that this point is unique. Putting in (10), we get (12) (14) Substituting and simplifying, we get, (15) in the above equation for conveWe omit the subscript and simply by nience, and henceforth denote and Thus, (15) can be written as (16) are moving Lemma 6: If a point and a circle of radius with constant velocities such that they satisfy (16) at any given instant in time, then they will continue to satisfy (16) for all future time. as Proof: Define a function (17) Differentiating (17) with respect to we get (18) Using (5), we get (19) Putting and in (19), we getThus, since remains unchanged with time, if initially, it remains so for all future time. Lemma 6 is thus a generalization of Lemma 1. and are, in fact, and Consider Fig. 2 (where Consider a trajectory starting at some initial Then, two cases are of interest. point Case 1: This implies that the collision point lies on the line (Fig. 4), i.e., is a straight line. So, is plane (Lemma 1). a stationary point on the566IEEE TRANSACTIONS ON SYSTEMS, MAN, AND CYBERNETICS—PART A: SYSTEMS AND HUMANS, VOL. 28, NO. 5, SEPTEMBER 1998Case 2: In this case, a trajectory originating from the third (fourth) quadrant moves into the second (first) quadrant, crossing the line. At the crossing point implying that is an extremum at that instant (say at time Since is negative for and positive for all is also Let We have to determine a minimum at since this implies collision. the conditions for which Multiplying both sides of (4) by we get (20) which, on integration, yields (21) where they satisfy know that even at If the initial conditions are such that then, from Lemma 6, weand we rewrite (24) as (28) We now define two more sets and as (29) (30) The collision cone is then obtained as a set defined as (31) is obtained through the following cases. The set then is null. Case 1: If then Case 2: If (32)But Therefore, These results automatically lead to the following theorem. Theorem 1: If a point and a circle are moving with constant velocities such that their initial conditions satisfy and (22)Case 3: If i.e.,thenspans the whole space,(33) To determine we rewrite as (34) Now, definingthen they are headed for a collision. The above conditions are both necessary and sufficient for a collision to occur. Proof: Follows from the analysis given above. Putting (22) reduces to and which are the conditions for collision between two point objects and from (1) and (2) in (16), (Lemma 2). Substituting we get(35) (23) Equation (23) can be interpreted as follows. Given and there exists a range of that Let us denote this range satisfy (23) and for which Now, if has a velocity vector at an angle by such that then collision is inevitable. We call and angular limits defined by this cone, with vertex at and as the collision cone. To determine the collision cone we first rewrite (16) as (24) where (25) Also, we define the following quantities: (26) The collision cone comprises of those values of We define a set as (24) and yield that satisfy (27) where (40) Case 3: If then and (39) where (38) so that is in the first quadrant, we may rewrite (34) as (36) that satisfy (36) with a strict We define the two values of and Then, can be obtained from: equality, as then is null. Case 1: If then and Case 2: If (37)CHAKRAVARTHY AND GHOSE: OBSTACLE AVOIDANCE IN A DYNAMIC ENVIRONMENT567Case 4: If i.e.,thenspans the whole space, (41)To determinewe rewriteas (42)Define(43) so that lies in the second quadrant. From (42) (44) that satisfy (44) with a strict We define the values of and Then the set is obtained from: equality, as then is null. Case 1: If then and Case 2: If (45) where (46) Case 3: If then and (47) where (48) Case 4: If The boundaries of follows. and/or 1) If 2) If both and a) If then are then determined as then and is null. then then (49) b) If and then A representation of the collision cone in the space can be obtained by rearranging the terms in (22) to yield the initial conditions that lead to collision as Example 3: Let the initial geometry be identical to that in Example 1. This corresponds to Since we use (32) to obtain From (35), and From (43), and Since and (49) Since should be used to determine from (38) we get Since from (46) Therefore, we get Thus, from (31) from which the collision cone is obtained as Example 4: Let the initial geometry be identical to that in Example 2. This corresponds to Since (33) is used to determine From (35), and From (43), and Since and (50) should be used to determine Since from (40) we get and Since from (48) we get and Therefore, . Consequently, from (31) the collision cone is obtained asFig. 5. Collision region in the (V0 ; Vr0 ) plane.(50) c) In all other cases, 3) For all other cases, and a) If b) If c) If and and is null. then then thenand(51)Equation (51) represents a sector-shaped region in the plane, and is shown in Fig. 5. Equation (31) gives the collision cone between a point and a circle Let be an open circle containing all the Then the collision cone between points in the interior of and is the open cone obtained by removing the boundaries of the collision cone given by (31).568IEEE TRANSACTIONS ON SYSTEMS, MAN, AND CYBERNETICS—PART A: SYSTEMS AND HUMANS, VOL. 28, NO. 5, SEPTEMBER 1998Fig. 6. Definition of cones E1 ; E2 ; E3 :B. Collision Between a Point and an Irregularly Shaped Object It is possible to adapt Theorem 1 [and (31)] to obtain equivalent conditions that can be used to predict collision between a point and an irregularly shaped object. Before doing so, we give a few useful definitions [17]. A set in a linear vector space is said to be a cone with vertex at the origin implies that for all Fig. 6 shows if and each with vertex three different types of cones These cones differ from one another in the following angle is convex and has is nonconvex and manner: is nonconvex and has We shall use the has and respectively, to define these three notations different types of cones. Consider Fig. 7(a) and (b), each of which shows the engageand an irregularly ment geometry between a point object We can construct a cone with vertex at shaped object such that is the smallest cone that contains the object i.e., is the intersection of all cones that contain and have The vertex angle of is denoted by and its vertices at and It can be seen that the cone in boundaries are and that in Fig. 7(b) is of type Fig. 7(a) is of the type These cases are now considered separately. . Case 1: contained in such that and We construct a circle are tangential to Let have radius and center Note that any choice of and at a distance from should satisfy This is illustrated in Fig. 7(a). Assuming that moves with a velocity identical to that of we can state the following lemma. is on a collision course with if Lemma 7: If and only if is on a collision course with Proof: From Lemma 4, for to be on a collision course it is both necessary and sufficient that there exists a with passing through that has ray It can be seen that the ray will always pass through thus implying that is on a collision course with This proves sufficiency. be on a collision The necessity is proved similarly. Let This implies that there exists a point D on course with which is the point of collision [see Fig. 7(a)]. The ray obviously must pass through As mentioned earlier, from Fig. 7(a), we can see that (52) any circle with radius and with center at For a given a distance from A satisfying (52) will satisfy Lemma 7.(a)(b)Fig. 7. Collision geometry between a point and an irregularly shaped object (a) < and (b) > :Case 2: . conSee Fig. 7(b). Here, we construct an open circle such that and tained in the complement of the cone are tangential to the closure of Note that does not or have any points in common with Lemma 8: If then is on a collision course with if and only if is not on a collision course with and Proof: To prove necessity, let be on a collision course Then there exists a ray passing through that with Obviously, can never pass has thus implying that is not on a collision course through with Sufficiency is then proved as follows. From Lemma 3, as there exists a ray that has long as If is not on a collision course with then will not pass through Since lies in the the ray therefore will have to pass through complement of It can be seen that will then some point lying in always pass through , thus implying that is on a collision course with From Fig. 7(b), we see that (53) any circle that satisfies (53) will satisfy For a given Lemma 8. Substituting (52) [or (53)] in (22), we get and (54)represents the initial value of Equation (54) where is necessary and sufficient condition for collision between and Thus (54), with the inequality replaced by a strict inequality, is the necessary and sufficient condition for These conditions can thus be used collision between and as necessary and sufficient condition for collision between and (in the manner stated by Lemmas 7 and 8). Since these conditions are invariant with respect to the choice of the circles or (so long as (52) or (53) is satisfied), we can discard or entirely, and take and to represent the initial for relative velocity components of the angular bisector of and of the angular bisector of the complement of forCHAKRAVARTHY AND GHOSE: OBSTACLE AVOIDANCE IN A DYNAMIC ENVIRONMENT569(a)Fig. 8. Collision geometry between two circles.The case when is a limiting case for both and and the corresponding collision cone can be obtained by using either Case 1 or Case 2 above with appropriate modifications for the limiting value. Theorem 2: The collision cone between a point and an irregularly shaped object, both moving at constant velocities on a plane, is obtained as follows. Let in (35) and (43) be Now replaced by then the collision cone is obtained from (31), 1) If as the initial angle of the angular bisector of the with cone 2) If then the collision cone is the complement of as the initial angle the cone obtained from (31) with formed by the angular bisector of the complement of the cone Proof: Follows from Lemmas 7 and 8, and the arguments given above. Example 5: Let the values of and be the same now be replaced by some as in Example 2, but let the Then from irregularly shaped object such that is headed for a collision (31) and Theorem 2, we see that if its velocity vector lies inside the angular bounds with If then the collision cone is If then the collision defined by cone is defined by C. Collision Between Two Circular Objects Theorem 2 can be extended to enable detection of collision between two circular objects. Consider the engagement geomand are two circles of radii etry in Fig. 8, where and moving with velocities and respectively. The and are the common tangents to the circles, lines Note that these tangents form a cone of the intersecting at type Theorem 3: The collision cone between two circles moving with constant velocities on a plane is given by (31) with in and as the initial angle (35) and (43) equal to of the line joining the centers of the two circles.(b) Fig. 9. Collision geometry between two irregularly shaped objects (a) and (b) > :<Proof: Superposing onto the problem reduces to one of collision prediction between a point and a circle of It is easy to see that the angle subtended radius at the reduced point [i.e., as by the enlarged circle defined in Fig. 7(a)] is equal to defined in Fig. 8. The proof then follows from 1) in Theorem 2. D. Collision Between Two Irregularly Shaped Objects We now extend Theorem 3 to predict collision between two and moving with constant irregularly shaped objects and are both velocities on a plane. Note that when irregularly shaped, it is difficult to superpose the shape of onto that of We therefore adopt a different approach. Consider the irregularly shaped objects as given in Fig. 9. Several possibilities then arise. Case 1: Refer Fig. 9(a). Here, the objects are well separated and we with the smallest vertex can construct a cone of the type angle such that and are each contained on opposite sides denote the vertex angle, and and of the vertex. Let be the boundaries that intersect at vertex We can then and the draw two circles, one contained in the cone Let and be these other contained in the cone。