Hostname: page-component-586b7cd67f-t8hqh Total loading time: 0 Render date: 2024-11-22T01:35:38.708Z Has data issue: false hasContentIssue false
  • English
  • Français

Dynamic collision risk modeling under uncertainty

Published online by Cambridge University Press:  03 October 2012

F. Belkhouche  and
B. Bendjilali
F. Belkhouche*
Affiliation:
Department of Electrical Engineering, CSU Sacramento, CA 95819, USA
B. Bendjilali
Affiliation:
Department of Mathematics, Raritan Valley Community College, Branchburg, NJ 08876, USA
*
*Corresponding author. E-mail: [email protected]
Get access Rights & Permissions [Opens in a new window]

Summary

This paper introduces a probabilistic model for collision risk assessment between moving vehicles. The uncertainties in the states and the geometric variables obtained from the sensory system are characterized by probability density functions. Given the states and their uncertainties, the goal is to determine the probability of collision in a dynamic environment. Two approaches are discussed: (1) The virtual configuration space (VCS), and (2) the rates of change of the visibility angles. The VCS is a transformation of observer that reduces collision detection with a moving object to collision detection with a stationary object. This approach allows to create simple geometric collision cones. Error propagation models are used to solve the problem when going from the VCS to the configuration space. The second approach derives the collision conditions in terms of the rate of change of the limit visibility angles. The probability of collision is then calculated. A comparison between the two methods is carried out. Results are illustrated using simulation, including Monte Carlo simulation.

Keywords

Motion planningControl of robotic systemsMobile robots, Navigation, Robot dynamics
Type
Articles
Information
Robotica , Volume 31 , Issue 4 , July 2013 , pp. 525 - 537
Copyright
Copyright © Cambridge University Press 2012 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1.Blom, H. and Bakker, G., “Conflict Probability and Incrossing Probability in Air Traffic Management,” In: Proceedings of the IEEE International Conference on Decision and Control, Las Vegas (Dec. 2002) pp. 2421–2426.Google Scholar
2.Irvine, R., “A simplified approach to conflict probability estimation,” EEC Technical/Scientific Report No. 2001-017, (EUROCONTROL Exp. Centre, Bretigny-sur-Orge, France, May 2001).Google Scholar
3.Bashllari, A., Kaciroti, N., Nace, D. and Fundo, A., “Conflict Probability Estimations Based on Geometrical and Bayesian Approaches,” In: Proceedings of the IEEE Intelligent Transportation Systems Conference, Seattle, WA (Sep. 2007) pp. 479–484.Google Scholar
4.Vela, A., Salaun, E., Solak, S., Feron, E., Singhose, W. and Clarke, J., “A Two-Stage Stochastic Optimization Model for Air Traffic Conflict Resolution Under Wind Uncertainty,” In: Proceedings of the IEEE/AIAA 28th Digital Avionics Systems Conference, Orlando, FL (Oct. 2009) pp. 2E5-1–2E5-13.Google Scholar
5.Prandini, M., Lygeros, J., Nilim, A. and Sastry, S., “Randomized Algorithms for Probabilistic Aircraft Conflict Detection,” In: Proceedings of the IEEE International Conference on Decision and Control, Phoenix, AZ (Dec. 1999) pp. 2444–2450.Google Scholar
6.Shen, J., McClamroch, N. H. and Gilbert, E. G., “A Computational Approach to Conflict Detection Problems for Air Traffic Control,” In: Proceedings of the American Control Conference, San Diego, CA (Jun. 1999) pp. 1445–1449.Google Scholar
7.Lambert, A., Gruyer, D. and Pierre, G. S., “A fast Monte Carlo algorithm for collision probability estimation,” In: Proceedings of the 10th International Conference on Control, Automation, Robotics and Vision, Hanoi, Vietnam (Dec. 2008) pp. 406–411.Google Scholar
8.Janssona, J. and Gustafssonb, F., “A framework and automotive application of collision avoidance decision-making,” Automatica 44 (9), 2347–2351 (2008).CrossRefGoogle Scholar
9.Achour, N., Msirdi, N. and Toumi, R., “Reactive Path Planning with Collision Avoidance in Dynamic Path Planning,” In: Proc.eedings of the IEEE International Workshop on Robot and Human Interactive Communication, Berlin, Germany (Sep. 2001) pp. 62–67.Google Scholar
10.Fulgenzi, C., Spalanzani, A. and Laugier, C., “Dynamic Obstacle Avoidance in Uncertain Environment Combining PVOs and Occupancy Grid,” In: Proceedings of the IEEE Intelligent Conference on Robotics and Automation, Rome (Apr. 2007) pp. 1610–1616. [Online]. Available at: http://emotion.inrialpes.fr/bibemotion/2007/FSL07.Google Scholar
11.Blackmore, L., Li, H. and Williams, B., “A Probabilistic Approach to Optimal Robust Path Planning with Obstacle,” In: Proceedings of the American Control Conference, Minneapolis, MN (Jun. 2006) pp. 2831–2837.Google Scholar
12.Burlina, P., DeMenthon, D. and Davis, L., “Navigation with Uncertainty: Reaching a Goal in a High Collision Risk Region,” In: Proceedings of the IEEE International Conference on Robotics and Automation, Nice, France (May 1992) pp. 2440–2446.Google Scholar
13.Payeur, P., “Improving Robot Path Planning Efficiency with Probabilistic Virtual Environment Models,” In: Proceedings of the IEEE International Conference on Virtual Environments, Human-Computer Interfaces and Measurement Systems, Boston, MA (Jul. 2004) pp. 13–18.Google Scholar
14.Juny, M. and D'Andrea, R., “Probability Map Building of Uncertain Dynamic Environments with Indistinguishable Obstacles,” In: Proceedings of the American Control Conference, Denver, CO (Jun. 2003) pp. 3417–3422.Google Scholar
15.Lambert, A., Gruyer, D., Pierre, G. S. and Ndjent, A., “Collision Probability Assessment for Speed Control,” In: Proceedings of IEEE International Conference on Intelligent Transportation Systems, Beijing, China (Oct. 2008) pp. 1043–1046.Google Scholar
16.Vahidi, A. and Eskandarian, A., “Research advances in intelligent collision avoidance and adaptive cruise control,” IEEE Trans. Intell. Transp. Syst. 4 (3), 143–153 (2003).CrossRefGoogle Scholar
17.Wang, F., Yang, M. and Yang, R., “Conflict-probability-estimation-based overtaking for intelligent vehicles,” IEEE Trans. Intell. Transp. Syst. 10 (2), 366–370 (2009).CrossRefGoogle Scholar
18.van Daalen, C. E. and Jones, T., “Fast conflict detection using probability flow,” Automatica 45 (8), 1903–1909 (2009).CrossRefGoogle Scholar
19.Althoff, M., Stursberg, O. and Buss, M., “Model-based probabilistic collision detection in autonomous driving,” IEEE Trans. Intell. Transp. Syst. 10 (2), 29–310 (2009).CrossRefGoogle Scholar
20.Althoff, M., Stursberg, O. and Buss, M., “Verification of Uncertain Embedded Systems by Computing Reachable Sets Based on Zonotopes,” In: Proceedings of IFAC World Congress, Coex, South Korea (Jul. 2008) pp. 5125–5130.Google Scholar
21.Schmidt, C., Oechsle, F. and Branz, W., “Research on Trajectory Planning in Emergency Situations with Multiple Objects,” In: Proceedings of IEEE Intelligent Transportation Conference, Toronto, Canada (Sep. 2006) pp. 988–992.Google Scholar
22.Yang, C., Blasch, E. and Kadar, I., “Geometric Factors in Target Positioning and Tracking,” In: Proceedings of International Conference on Information Fusion, Seattle, WA (Jul. 2009) pp. 85–92.Google Scholar
23.Edwan, E. and Fierro, R., “A Low Cost Modular Autonomous Robot Vehicle,” In: Proceedings of the 38th Southeastern Symposium on System Theory, Cookeville, TN (Mar. 2006) pp. 245–249.Google Scholar
24.Stronger, D. and Stone, P., “Maximum Likelihood Estimation of Sensor and Action Model Functions on a Mobile Robot,” In: Proceedings of IEEE International Conference on Robotics and Automation, Pasadena, CA (May 2008), pp. 2104–2109.Google Scholar
25.Fishman, G. S., Monte Carlo: Concepts, Algorithms, and Applications (Springer-Verlag, New York, 1996).CrossRefGoogle Scholar
26.Belkhouche, F. and Belkhouche, B., “Kinematics-based characterization of the collision course,” Int. J. Robot. Autom. 23 (2), 206–3123 (2008).Google Scholar
27.Chen, S. and Li, Y., “Automatic sensor placement for model-based robot vision,” IEEE Trans. Syst. Man Cybern. 34 (1), 393–408 (2004).CrossRefGoogle ScholarPubMed
28.Belkhouche, F., “Reactive path planning in a dynamic environment,” IEEE Trans. Robot. 25 (4), 902–911 (2009).CrossRefGoogle Scholar
29.Chakravarthy, A. and Ghose, D., “Obstacle avoidance in a dynamic environment: A collision cone approach,” IEEE Trans. Syst. Man. Cybern. A: Systems and Humans 28 (5), 562–574 (1998).CrossRefGoogle Scholar
30.Welch, G. and Bishop, G., “An introduction to the Kalman filter,” Technical Report TR 95–041 (University of North Carolina at Chapel Hill, NC, 2006).Google Scholar
31.Farina, A., Ristic, B. and Benvenuti, D., “Tracking a ballistic target: Comparison of several nonliear filters,” IEEE Trans. Aerosp. Electron. Syst. 38 (3), 854–867 (2002).CrossRefGoogle Scholar
32.Cedilik, A., Kosmelj, K. and Blejec, A., “The distribution of the ratio of jointly normal variables,” Metodoloski Zvezki: Adv. Methodol. Stat. 1 (1), 99–108 (2004).Google Scholar
33.Kamerud, D., “The random variable x/y, x, y normal,” Am. Math. Mon. 85, 207 (1978).Google Scholar