A Projection Approach to Equality Constrained Iterative Linear Quadratic Optimal Control

TL;DR

This paper introduces a constrained iterative LQR method that efficiently handles state and input constraints in discrete-time systems, with applications demonstrated on robotic arm simulations.

Contribution

It proposes a novel projection-based approach for constrained iLQR with linear time complexity and derives a Riccati-style solution for constraint-compliant control updates.

Findings

Efficient control update rule for constrained iLQR.

Validated on a 6 DoF robotic arm simulation.

Linear time complexity in the number of time steps.

Abstract

This paper presents a state and state-input constrained variant of the discrete-time iterative Linear Quadratic Regulator (iLQR) algorithm, with linear time-complexity in the number of time steps. The approach is based on a projection of the control input onto the nullspace of the linearized constraints. We derive a fully constraint-compliant feedforward-feedback control update rule, for which we can solve efficiently with Riccati-style difference equations. We assume that the relative degree of all constraints in the discrete-time system model is equal to one, which often holds for robotics problems employing rigid-body dynamic models. Simulation examples, including a 6 DoF robotic arm, are given to validate and illustrate the performance of the method.