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Probabilistically safe motion planning to avoid dynamic obstacles with uncertain motion patterns

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Abstract

This paper presents a real-time path planning algorithm that guarantees probabilistic feasibility for autonomous robots with uncertain dynamics operating amidst one or more dynamic obstacles with uncertain motion patterns. Planning safe trajectories under such conditions requires both accurate prediction and proper integration of future obstacle behavior within the planner. Given that available observation data is limited, the motion model must provide generalizable predictions that satisfy dynamic and environmental constraints, a limitation of existing approaches. This work presents a novel solution, named RR-GP, which builds a learned motion pattern model by combining the flexibility of Gaussian processes (GP) with the efficiency of RRT-Reach, a sampling-based reachability computation. Obstacle trajectory GP predictions are conditioned on dynamically feasible paths identified from the reachability analysis, yielding more accurate predictions of future behavior. RR-GP predictions are integrated with a robust path planner, using chance-constrained RRT, to identify probabilistically feasible paths. Theoretical guarantees of probabilistic feasibility are shown for linear systems under Gaussian uncertainty; approximations for nonlinear dynamics and/or non-Gaussian uncertainty are also presented. Simulations demonstrate that, with this planner, an autonomous vehicle can safely navigate a complex environment in real-time while significantly reducing the risk of collisions with dynamic obstacles.

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Notes

  1. The choice of \(\Delta t\) determines the time scales on which an agent’s next position can be accurately predicted, making trajectory derivatives more useful than instantaneous velocity.

  2. Throughout the paper, a \(t\) with a superscript refers to a trajectory, while a \(t\) without a superscript refers to a time value.

  3. When the target vehicle moves from left to right, the trajectories shown in Fig. 11 are reflected across the room’s short axis.

References

  • Althoff, D., Wollherr, D., & Buss, M. (2011). Safety assessment of trajectories for navigation in uncertain and dynamic environments. In IEEE international conference on robotics and automation (ICRA).

  • Amidi, O., & Thorpe, C. (1990). Integrated mobile robot control. In SPIE mobile robots V (pp. 504–523).

  • Aoude, G., Joseph, J., Roy, N., & How, J. (2011). Mobile agent trajectory prediction using Bayesian nonparametric reachability trees. In AIAA Infotech@Aerospace conference.

  • Aoude, G. S. (2011). Threat assessment for safe navigation in environments with uncertainty in predictability. PhD thesis, Massachusetts Institute of Technology, Department of Aeronautics and Astronautics, Cambridge, MA.

  • Aoude, G. S., Luders, B. D., & How, J. P. (2010a). Sampling-based threat assessment algorithms for intersection collisions involving errant drivers. In IFAC symposium on intelligent autonomous vehicles, Lecce, Italy.

  • Aoude, G. S., Luders, B. D., Lee, K. K. H., Levine, D. S., & How, J. P. (2010b). Threat assessment design for driver assistance system at intersections. In IEEE conference on intelligent transportation systems, Maderia, Portugal.

  • Aoude, G. S., Luders, B. D., Levine, D. S., & How, J. P. (2010c). Threat-aware path planning in uncertain urban environments. In IEEE/RSJ international conference on intelligent robots and systems (IROS), Taipei, Taiwan (pp. 6058–6063).

  • Bennewitz, M., Burgard, W., Cielniak, G., & Thrun, S. (2005). Learning motion patterns of people for compliant robot motion. International Journal of Robotics Research, 24, 31–48.

    Article  Google Scholar 

  • Blackmore, L. (2006). A probabilistic particle control approach to optimal, robust predictive control. In AIAA guidance, navigation, and, control conference (GNC).

  • Blackmore, L., Li, H., & Williams, B. (2006). A probabilistic approach to optimal robust path planning with obstacles. In American control conference (ACC).

  • Blackmore, L., Ono, M., Bektassov, A., & Williams, B. C. (2010). A probabilistic particle-control approximation of chance-constrained stochastic predictive control. IEEE Transactions on Robotics, 26(3), 502–517.

    Article  Google Scholar 

  • Calafiore, G. C., & Ghaoui, L. E. (2007). Linear programming with probability constraints—part 1. In American control conference (ACC).

  • Deisenroth, M. P., Huber, M. F., & Hanebeck, U. D. (2009). Analytic moment-based Gaussian process filtering. In International conference on machine learning (ICML), Montreal, Canada (pp. 225–232).

  • Ding, H., Reißig, G., Groß, D., & Stursberg, O. (2011). Mixed-integer programming for optimal path planning of robotic manipulators. In IEEE international conference on automation science and engineering.

  • Earl, M., & D’Andrea, R. (2005). Iterative MILP methods for vehicle control problems. The IEEE Transactions on Robotics, 21, 1158–1167.

    Article  Google Scholar 

  • Frazzoli, E., Dahleh, M. A., & Feron, E. (2002). Real-time motion planning for agile autonomous vehicles. AIAA Journal of Guidance, Control, and Dynamics, 25(1), 116–129.

    Article  Google Scholar 

  • Fulgenzi, C., Tay, C., Spalanzani, A., & Laugier, C. (2008). Probabilistic navigation in dynamic environment using rapidly-exploring random trees and gaussian processes. In IEEE/RSJ international conference on intelligent robots and systems (IROS), Nice, France.

  • Garey, M. R., & Johnson, D. S. (1979). Computers and intractability: A guide to the theory of NP-completeness. San Francisco, CA, USA: Freeman.

    MATH  Google Scholar 

  • Girard, A., Rasmussen, C. E., Quintero-Candela, J., & Murray-smith, R. (2003). Gaussian process priors with uncertain inputs—application to multiple-step ahead time series forecasting. In Advances in neural information processing systems (pp. 529–536). Cambridge: MIT Press.

  • Henry, P., Vollmer, C., Ferris, B., & Fox, D. (2010). Learning to navigate through crowded environments. In IEEE international conference on robotics and automation (ICRA).

  • How, J. P., Bethke, B., Frank, A., Dale, D., & Vian, J. (2008). Real-time indoor autonomous vehicle test environment. IEEE Control Systems Magazine, 28(2), 51–64.

    Article  MathSciNet  Google Scholar 

  • iRobot. (2011). iRobot: Education & research robots. http://store.irobot.com/shop/index.jsp?categoryId=3311368. Accessed 31 July 2011.

  • Joseph, J., Doshi-Velez, F., & Roy, N. (2010). A Bayesian nonparametric approach to modeling mobility patterns.In AAAI

  • Joseph, J., Doshi-Velez, F., Huang, A. S., & Roy, N. (2011). A Bayesian nonparametric approach to modeling motion patterns. Autonomous Robots, 31(4), 383–400.

    Article  Google Scholar 

  • Karaman, S., & Frazzoli, E. (2009). Sampling-based motion planning with deterministic \(\mu \)-calculus specifications. In IEEE conference on decision and control (CDC).

  • Kuchar, J. K., & Yang, L. C. (2002). A review of conflict detection and resolution modeling methods. IEEE Transactions on Intelligent Transportation Systems, 1(4), 179–189.

    Article  Google Scholar 

  • Kuwata, Y., Teo, J., Fiore, G., Karaman, S., Frazzoli, E., & How, J. P. (2009). Real-time motion planning with applications to autonomous urban driving. IEEE Transactions on Control Systems Technology, 17(5), 1105–1118.

    Article  Google Scholar 

  • Lachner, R. (1997). Collision avoidance as a differential game: Real-time approximation of optimal strategies using higher derivatives of the value function. In IEEE international conference on systems. Man, and cybernetics (Vol. 3, pp. 2308–2313).

  • LaValle, S. M., (1998). Rapidly-exploring random trees: A new tool for path planning. Tech. Rep. 98–11, Iowa State University.

  • LaValle, S. M. (2006). Planning algorithms. Cambridge: Cambridge University Press.

    Book  MATH  Google Scholar 

  • Lavalle, S. M., & Sharma, R. (1997). On motion planning in changing, partially-predictable environments. International Journal of Robotics Research, 16, 775–805.

    Article  Google Scholar 

  • Leonard, J., How, J. P., Teller, S., Berger, M., Campbell, S., Fiore, G., et al. (2008). A perception-driven autonomous urban vehicle. Journal of Field Robotics, 25(10), 727–774.

    Article  Google Scholar 

  • Luders, B., & How, J. P. (2011). Probabilistic feasibility for nonlinear systems with non-Gaussian uncertainty using RRT. In AIAA Infotech@Aerospace conference, St. Louis, MO.

  • Luders, B., Karaman, S., Frazzoli, E., & How, J. P. (2010a). Bounds on tracking error using closed-loop rapidly-exploring random trees. In American control conference (ACC), Baltimore, MD (pp. 5406–5412).

  • Luders, B., Kothari, M., & How, J. P. (2010b). Chance constrained RRT for probabilistic robustness to environmental uncertainty. In AIAA guidance, navigation, and control conference (GNC), Toronto, Canada.

  • Maile, M., Zaid, F. A., Caminiti, L., Lundberg, J., Mudalige, P. (2008). Cooperative intersection collision avoidance system limited to stop sign and traffic signal violations. Tech. rep., midterm Phase 1 Report.

  • Mazor, E., Averbuch, A., Bar-Shalom, Y., & Dayan, J. (2002). Interacting multiple model methods in target tracking: A survey. IEEE Transactions on Aerospace and Electronic Systems, 34(1), 103–123.

    Article  Google Scholar 

  • Melchior, N. A., & Simmons, R. (2007). Particle RRT for path planning with uncertainty. In IEEE international conference on robotics and automation (ICRA)

  • Miloh, T., & Sharma, S. (1976). Maritime collision avoidance as a differential game. Institut fur Schiffbau der Universitat Hamburg.

  • Rasmussen, C. E., & Williams, C. K. I. (2005). Gaussian processes for machine learning. Cambridge: The MIT Press.

    Google Scholar 

  • Sorenson, H. (1985). Kalman filtering: Theory and application. In IEEE.

  • Tay, C., & Laugier, C. (2007). Modelling smooth paths using Gaussian processes. In International conference on field and service robotics.

  • Thrun, S., Burgard, W., & Fox, D. (2005). Probabilistic robotics. Cambridge, MA: MIT Press.

    MATH  Google Scholar 

  • Trautman, P., & Krause, A. (2010). Unfreezing the robot: Navigation in dense, interacting crowds. In IEEE/RSJ international conference on intelligent robots and systems (IROS).

  • Vasquez, D., Fraichard, T., Aycard, O., & Laugier, C. (2008). Intentional motion on-line learning and prediction. Machine Vision and Applications, 19(5), 411–425.

    Article  MATH  Google Scholar 

  • Vitus, M. P., Pradeep, V., Hoffmann, G. M., Waslander, S. L., & Tomlin, C. J. (2008). Tunnel-MILP: Path planning with sequential convex polytopes. In AIAA guidance, navigation, and control conference (GNC), Honolulu, HI.

  • Wu, A., & How, J. (2012). Guaranteed infinite horizon avoidance of unpredictable, dynamically constrained obstacles. In Autonomous robots (pp. 1–16).

  • Yepes, J., Hwang, I., & Rotea, M. (2007). New algorithms for aircraft intent inference and trajectory prediction. AIAA Journal on Guidance, Control, and Dynamics, 30(2), 370–382.

    Article  Google Scholar 

  • Zhu, Q. (2002). Hidden Markov model for dynamic obstacle avoidance of mobile robot navigation. IEEE Transactions on Robotics and Automation, 7(3), 390–397.

    Article  Google Scholar 

Download references

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Authors and Affiliations

  1. Massachusetts Institute of Technology, Room 41-105, 77 Massachusetts Avenue, Cambridge, MA, USA

    Georges S. Aoude & Brandon D. Luders

  2. Massachusetts Institute of Technology, Room 32-331, 77 Massachusetts Avenue, Cambridge, MA, USA

    Joshua M. Joseph

  3. Massachusetts Institute of Technology, Room 33-315, 77 Massachusetts Avenue, Cambridge, MA, USA

    Nicholas Roy

  4. Massachusetts Institute of Technology, Room 33-326, 77 Massachusetts Avenue, Cambridge, MA, USA

    Jonathan P. How

Authors
  1. Georges S. Aoude
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  2. Brandon D. Luders
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  3. Joshua M. Joseph
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  4. Nicholas Roy
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  5. Jonathan P. How
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Correspondence to Georges S. Aoude.

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Aoude, G.S., Luders, B.D., Joseph, J.M. et al. Probabilistically safe motion planning to avoid dynamic obstacles with uncertain motion patterns. Auton Robot 35, 51–76 (2013). https://doi.org/10.1007/s10514-013-9334-3

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