Estimation and Control Using Sampling-Based Bayesian Reinforcement Learning

Real-world autonomous systems operate under uncertainty about both their pose and dynamics. Autonomous control systems must simultaneously perform estimation and control tasks to maintain robustness to changing dynamics or modeling errors. However, information gathering actions often conflict with optimal actions for reaching control objectives, requiring a trade-off between exploration and exploitation. The specific problem setting considered here is for discrete-time nonlinear systems, with process noise, input-constraints, and parameter uncertainty. This article frames this problem as a Bayes-adaptive Markov decision process and solves it online using Monte Carlo tree search with an unscented Kalman filter to account for process noise and parameter uncertainty. This method is compared with certainty equivalent model predictive control and a tree search method that approximates the QMDP solution, providing insight into when information gathering is useful. Discrete time simulations characterize performance over a range of process noise and bounds on unknown parameters. An offline optimization method is used to select the Monte Carlo tree search parameters without hand-tuning. In lieu of recursive feasibility guarantees, a probabilistic bounding heuristic is offered that increases the probability of keeping the state within a desired region.