A Topology-Guided Path Integral Approach for Stochastic Optimal Control

TL;DR

This paper introduces a topology-guided path integral method for stochastic optimal control that improves trajectory planning in cluttered environments by reducing local minima and ensuring collision-free, dynamically feasible paths.

Contribution

It proposes a novel topological motion planning algorithm integrated with a path integral control framework to enhance solution quality in complex environments.

Findings

Successfully reduces local minima issues in sampling-based control.

Generates collision-free, dynamically feasible trajectories.

Demonstrates effectiveness through numerical examples.

Abstract

This work presents an efficient method to solve a class of continuous-time, continuous-space stochastic optimal control problems of robot motion in a cluttered environment. The method builds upon a path integral representation of the stochastic optimal control problem that allows computation of the optimal solution through sampling and estimation process. As this sampling process often leads to a local minimum especially when the state space is highly non-convex due to the obstacle field, we present an efficient method to alleviate this issue by devising a proposed topological motion planning algorithm. Combined with a receding-horizon scheme in execution of the optimal control solution, the proposed method can generate a dynamically feasible and collision-free trajectory while reducing concern about local optima. Illustrative numerical examples are presented to demonstrate the applicability and validity of the proposed approach.