Probabilistic Homotopy Optimization for Dynamic Motion Planning

TL;DR

This paper introduces a probabilistic homotopy optimization method for dynamic motion planning that effectively navigates complex solution spaces by switching between solving and sampling, demonstrated on cart-pole and humanoid problems.

Contribution

The paper proposes a novel probabilistic homotopy optimization algorithm that addresses challenges like bifurcation and disconnectedness in dynamic motion planning.

Findings

Successfully applied to cart-pole and humanoid motion planning

Effectively handles bifurcation and disconnected solution manifolds

Outperforms traditional homotopy methods in complex scenarios

Abstract

We present a homotopic approach to solving challenging, optimization-based motion planning problems. The approach uses Homotopy Optimization, which, unlike standard continuation methods for solving homotopy problems, solves a sequence of constrained optimization problems rather than a sequence of nonlinear systems of equations. The insight behind our proposed algorithm is formulating the discovery of this sequence of optimization problems as a search problem in a multidimensional homotopy parameter space. Our proposed algorithm, the Probabilistic Homotopy Optimization algorithm, switches between solve and sample phases, using solutions to easy problems as initial guesses to more challenging problems. We analyze how our algorithm performs in the presence of common challenges to homotopy methods, such as bifurcation, folding, and disconnectedness of the homotopy solution manifold. Finally, we demonstrate its utility via a case study on two dynamic motion planning problems: the cart-pole and the MIT Humanoid.