Multiscale Abstraction, Planning and Control using Diffusion Wavelets for Stochastic Optimal Control Problems

TL;DR

This paper introduces a multiscale framework combining diffusion wavelets and desirability functions to efficiently solve stochastic optimal control problems for robot motion planning in complex environments.

Contribution

It presents a novel hierarchical approach that integrates diffusion wavelet representations with desirability functions for scalable stochastic control.

Findings

Effective hierarchical abstraction of state space.

Global and local planning integration.

Successful numerical demonstrations.

Abstract

This work presents a multiscale framework to solve a class of stochastic optimal control problems in the context of robot motion planning and control in a complex environment. In order to handle complications resulting from a large decision space and complex environmental geometry, two key concepts are adopted: (a) a diffusion wavelet representation of the Markov chain for hierarchical abstraction of the state space; and (b) a desirability function-based representation of the Markov decision process (MDP) to efficiently calculate the optimal policy. In the proposed framework, a global plan that compressively takes into account the long time/length-scale state transition is first obtained by approximately solving an MDP whose desirability function is represented by coarse scale bases in the hierarchical abstraction. Then, a detailed local plan is computed by solving an MDP that considers wavelet bases associated with a focused region of the state space, guided by the global plan. The resulting multiscale plan is utilized to finally compute a continuous-time optimal control policy within a receding horizon implementation. Two numerical examples are presented to demonstrate the applicability and validity of the proposed approach.