Projection-based first-order constrained optimization solver for robotics

TL;DR

This paper introduces ALSPG, a fast, geometric, first-order constrained optimization method for robotics, demonstrating competitive performance with second-order methods in inverse kinematics and motion planning tasks.

Contribution

The paper presents ALSPG, a novel first-order solver that exploits geometric constraints via Euclidean projections, offering an accessible and efficient alternative to second-order methods in robotics.

Findings

Projections improve solver performance over full constraints.

ALSPG is competitive with iLQR in unconstrained scenarios.

Successful application to IK and MPC in simulated and real robot experiments.

Abstract

Robot programming tools ranging from inverse kinematics (IK) to model predictive control (MPC) are most often described as constrained optimization problems. Even though there are currently many commercially-available second-order solvers, robotics literature recently focused on efficient implementations and improvements over these solvers for real-time robotic applications. However, most often, these implementations stay problem-specific and are not easy to access or implement, or do not exploit the geometric aspect of the robotics problems. In this work, we propose to solve these problems using a fast, easy-to-implement first-order method that fully exploits the geometric constraints via Euclidean projections, called Augmented Lagrangian Spectral Projected Gradient Descent (ALSPG). We show that 1. using projections instead of full constraints and gradients improves the performance of the solver and 2. ALSPG stays competitive to the standard second-order methods such as iLQR in the unconstrained case. We showcase these results with IK and motion planning problems on simulated examples and with an MPC problem on a 7-axis manipulator experiment.