  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.
