Towards Solutions of Manipulation Tasks via Optimal Control of Projected Dynamical Systems

TL;DR

This paper presents a novel framework for manipulation planning using projected dynamical systems and optimal control, capable of handling complex scenarios with multiple pushers and friction efficiently.

Contribution

It introduces a new modeling approach based on projected dynamical systems and implicit signed distance functions for manipulation planning.

Findings

Successfully generates trajectories for complex manipulation tasks.

Handles multiple pushers and friction in non-convex objects.

Maintains reasonable computational effort.

Abstract

We introduce a modeling framework for manipulation planning based on the formulation of the dynamics as a projected dynamical system. This method uses implicit signed distance functions and their gradients to formulate an equivalent gradient complementarity system. The optimal control problem is then solved via a direct method, discretized using finite-elements with switch detection. An extension to this approach is provided in the form of a friction formulation commonly used in quasi-static models. We show that this approach is able to generate trajectories for problems including multiple pushers, friction, and non-convex objects modeled as unions of convex ellipsoids with reasonable computational effort.