Efficient and Real-Time Motion Planning for Robotics Using Projection-Based Optimization

TL;DR

This paper introduces ALSPG, a geometric projection-based optimization method for real-time robot motion planning that outperforms traditional solvers in efficiency and is validated on various robotic platforms.

Contribution

The paper presents ALSPG, a novel first-order optimization algorithm leveraging geometric projections for efficient, real-time robot motion planning, addressing limitations of existing constrained optimization methods.

Findings

ALSPG achieves significant speedups in real-time motion planning.

ALSPG performs comparably to second-order methods like iLQR in unconstrained scenarios.

Experimental validation on multiple robots demonstrates practical effectiveness.

Abstract

Generating motions for robots interacting with objects of various shapes is a complex challenge, further complicated by the robot geometry and multiple desired behaviors. While current robot programming tools (such as inverse kinematics, collision avoidance, and manipulation planning) often treat these problems as constrained optimization, many existing solvers focus on specific problem domains or do not exploit geometric constraints effectively. We propose an efficient first-order method, Augmented Lagrangian Spectral Projected Gradient Descent (ALSPG), which leverages geometric projections via Euclidean projections, Minkowski sums, and basis functions. We show that by using geometric constraints rather than full constraints and gradients, ALSPG significantly improves real-time performance. Compared to second-order methods like iLQR, ALSPG remains competitive in the unconstrained case. We validate our method through toy examples and extensive simulations, and demonstrate its effectiveness on a 7-axis Franka robot, a 6-axis P-Rob robot and a 1:10 scale car in real-world experiments. Source codes, experimental data and videos are available on the project webpage: https://sites.google.com/view/alspg-oc