Optimistic Planning for the Near-Optimal Control of General Nonlinear Systems with Continuous Transition Distributions ⋆

Optimistic planning is an optimal control approach from artificial intelligence, which can be applied in receding horizon. It works for very general nonlinear dynamics and cost functions, and its analysis establishes a tight relationship between computation invested and near-optimality. However, there is no optimistic planning algorithm that searches for closed-loop solutions in stochastic problems with continuous transition distributions. Such transitions are essential in control, where they arise e.g. due to continuous disturbances. Existing algorithms only search for open-loop input sequences, which are suboptimal. We therefore propose a closedloop algorithm that discretizes the continuous transition distribution into sigma points, and call it sigma-optimistic planning. Assuming the error introduced by sigma-point discretization is bounded, we analyze the solution returned, showing that it is near-optimal. The algorithm is evaluated in simulation experiments, where it performs better than a state-of-the-art open-loop planning technique; a certainty-equivalence approach also works well.