Contact-Implicit Trajectory Optimization using an Analytically Solvable Contact Model for Locomotion on Variable Ground

TL;DR

This paper introduces a new trajectory optimization method with an analytically solvable contact model that simplifies planning for robots interacting with various ground types, improving efficiency and versatility.

Contribution

The paper proposes a novel contact model with a closed-form solution that integrates into trajectory optimization without complementarity constraints, enabling unified multi-ground interaction planning.

Findings

Successfully planned trotting and jumping motions for quadruped robots.

Demonstrated advantages over rigid contact models and complementarity-based methods.

Enabled physics-based optimization across diverse ground types with only two parameters.

Abstract

This paper presents a novel contact-implicit trajectory optimization method using an analytically solvable contact model to enable planning of interactions with hard, soft, and slippery environments. Specifically, we propose a novel contact model that can be computed in closed-form, satisfies friction cone constraints and can be embedded into direct trajectory optimization frameworks without complementarity constraints. The closed-form solution decouples the computation of the contact forces from other actuation forces and this property is used to formulate a minimal direct optimization problem expressed with configuration variables only. Our simulation study demonstrates the advantages over the rigid contact model and a trajectory optimization approach based on complementarity constraints. The proposed model enables physics-based optimization for a wide range of interactions with hard, slippery, and soft grounds in a unified manner expressed by two parameters only. By computing trotting and jumping motions for a quadruped robot, the proposed optimization demonstrates the versatility for multi-contact motion planning on surfaces with different physical properties.