Inequality Constrained Trajectory Optimization with A Hybrid Multiple-shooting iLQR

TL;DR

This paper introduces a hybrid multiple-shooting iLQR method that effectively handles inequality constraints and infeasible initial states, improving convergence speed and robustness in constrained trajectory optimization for robotic systems.

Contribution

The paper presents a novel hybrid constrained iLQR with a multiple-shooting framework, enabling robust constraint handling and better initialization in trajectory optimization.

Findings

Outperforms collocation and shooting methods in various constrained problems

Achieves fast convergence of constraint satisfaction

Enhances numerical robustness through improved globalization strategy

Abstract

Trajectory optimization has been used extensively in robotic systems. In particular, iterative Linear Quadratic Regulator (iLQR) has performed well as an off-line planner and online nonlinear model predictive control solver, with a lower computational cost. However, standard iLQR cannot handle any constraints or perform reasonable initialization of a state trajectory. In this paper, we propose a hybrid constrained iLQR variant with a multiple-shooting framework to incorporate general inequality constraints and infeasible states initialization. The main technical contributions are twofold: 1) In addition to inheriting the simplicity of the initialization in multiple-shooting settings, a two-stage framework is developed to deal with state and/or control constraints robustly without loss of the linear feedback term of iLQR. Such a hybrid strategy offers fast convergence of constraint satisfaction. 2) An improved globalization strategy is proposed to exploit the coupled effects between line-searching and regularization, which is able to enhance the numerical robustness of the constrained iLQR approaches. Our approach is tested on various constrained trajectory optimization problems and outperforms the commonly-used collocation and shooting methods.