Dynamically-Consistent Trajectory Optimization for Legged Robots via Contact Point Decomposition

TL;DR

This paper introduces a phase-based trajectory optimization method for legged robots that ensures dynamic feasibility and contact constraint satisfaction by decoupling translational dynamics and leveraging Bézier polynomial properties.

Contribution

The method uniquely combines contact point decomposition with analytical force-position relationships to improve motion reliability in legged robot trajectory planning.

Findings

Successfully generates dynamically feasible gaits for quadruped robots.

Ensures compliance with friction cone constraints throughout trajectories.

Validates approach with simulations demonstrating motion reliability.

Abstract

To generate reliable motion for legged robots through trajectory optimization, it is crucial to simultaneously compute the robot's path and contact sequence, as well as accurately consider the dynamics in the problem formulation. In this paper, we present a phase-based trajectory optimization that ensures the feasibility of translational dynamics and friction cone constraints throughout the entire trajectory. Specifically, our approach leverages the superposition properties of linear differential equations to decouple the translational dynamics for each contact point, which operates under different phase sequences. Furthermore, we utilize the differentiation matrix of B{\'e}zier polynomials to derive an analytical relationship between the robot's position and force, thereby ensuring the consistent satisfaction of translational dynamics. Additionally, by exploiting the convex closure property of B{\'e}zier polynomials, our method ensures compliance with friction cone constraints. Using the aforementioned approach, the proposed trajectory optimization framework can generate dynamically reliable motions with various gait sequences for legged robots. We validate our framework using a quadruped robot model, focusing on the feasibility of dynamics and motion generation.