Abstract
One of the main challenges in solving partially observable control problems is planning in high-dimensional belief spaces. Essentially, it is necessary to plan in the parameter space of all relevant probability distributions over the state space. The literature has explored different planning technologies including trajectory optimization [8, 6] and roadmap methods [12, 4]. Unfortunately, these methods are hard to use in a receding horizon control context where it is potentially necessary to replan on every time step. Trajectory optimization is not guaranteed to find globally optimal solutions and roadmap methods can have long planning times. This paper identifies a non-trivial instance of the belief space planning problem that is convex and can therefore be solved quickly and optimally even for high dimensional problems. We prove that the resulting control strategy will ultimately reach a goal region in belief space under mild assumptions. Since the space of convex belief space planning problem is somewhat limited, we extend the approach using mixed integer programming. We propose to solve the integer part of the problem in advance so that only convex problems need be solved during receding horizon control.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Arulampalam, S., Maskell, S., Maskell, S., Gordon, N., Clapp, T.: A tutorial on particle filters for on-line non-linear/non-gaussian bayesian tracking. IEEE Transactions on Signal Processing 50, 174–188 (2001)
Bertsekas, D.: Dynamic Programming and Optimal Control, 3rd edn. Athena Scientific (2007)
Blackmore, L., Ono, M., Bektassov, A., Williams, B.: A probabilistic particle-control approximation of chance-constrained stochastic predictive control. IEEE Transactions on Robotics (June 2010)
Bry, A., Roy, N.: Rapidly-exploring random belief trees for motion planning under uncertainty. In: IEEE Int’l Conf. on Robotics and Automation (2011)
Earl, M., D’Andrea, R.: Iterative milp methods for vehicle control problems. In: IEEE Conf. on Decision and Control, pp. 4369–4374 (December 2004)
Erez, T., Smart, W.: A scalable method for solving high-dimensional continuous POMDPs using local approximation. In: Proceedings of the International Conference on Uncertainty in Artificial Intelligence (2010)
Papadimitriou, C., Tsitsiklis, J.: The complexity of Markov decision processes. Mathematics of Operations Research 12(3), 441–450 (1987)
Platt, R., Kaelbling, L., Lozano-Perez, T., Tedrake, R.: Efficient planning in non-gaussian belief spaces and its application to robot grasping. In: Int’l Symposium on Robotics Research (2011)
Platt, R., Kaelbling, L., Lozano-Perez, T., Tedrake, R.: A hypothesis-based algorithm for planning and control in non-gaussian belief spaces. Technical Report CSAIL-TR-2011-039, Massachusetts Institute of Technology (2011)
Platt, R., Kaelbling, L., Lozano-Perez, T., Tedrake, R.: Non-gaussian belief space planning: Correctness and complexity. In: IEEE Int’l Conference on Robotics and Automation (2012)
Platt, R., Tedrake, R., Kaelbling, L., Lozano-Perez, T.: Belief space planning assuming maximum likelihood observations. In: Proceedings of Robotics: Science and Systems, RSS (2010)
Prentice, S., Roy, N.: The belief roadmap: Efficient planning in linear POMDPs by factoring the covariance. In: 12th International Symposium of Robotics Research (2008)
Richards, A., How, J.: Aircraft trajectory planning with collision avoidance using mixed integer linear programming. In: American Controls Conference (2002)
Todorov, E., Li, W.: A generalized iterative lqg method for locally-optimal feedback control of constrained nonlinear stochastic systems. In: IEEE Conference on Decision and Control (2005)
van den Berg, J., Patil, S., Alterovitz, R.: Motion planning under uncertainty using differential dynamic programming in belief space. In: Int’l Symposium on Robotics Research (2011)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Platt, R. (2013). Convex Receding Horizon Control in Non-Gaussian Belief Space. In: Frazzoli, E., Lozano-Perez, T., Roy, N., Rus, D. (eds) Algorithmic Foundations of Robotics X. Springer Tracts in Advanced Robotics, vol 86. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-36279-8_27
Download citation
DOI: https://doi.org/10.1007/978-3-642-36279-8_27
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-36278-1
Online ISBN: 978-3-642-36279-8
eBook Packages: EngineeringEngineering (R0)