GPU Accelerated Convex Approximations for Fast Multi-Agent Trajectory Optimization

TL;DR

This paper introduces a GPU-accelerated convex optimization method for multi-agent trajectory planning, enabling real-time computation of trajectories for dozens of agents with improved speed and quality.

Contribution

The paper proposes a novel convex reformulation of collision avoidance constraints and leverages GPU acceleration for efficient multi-agent trajectory optimization.

Findings

Achieves trajectory computation in under a second for tens of agents.

Reduces core computation to large-scale convex quadratic programs.

Demonstrates substantial speed and quality improvements over existing methods.

Abstract

In this paper, we present a computationally efficient trajectory optimizer that can exploit GPUs to jointly compute trajectories of tens of agents in under a second. At the heart of our optimizer is a novel reformulation of the non-convex collision avoidance constraints that reduces the core computation in each iteration to that of solving a large scale, convex, unconstrained Quadratic Program (QP). We also show that the matrix factorization/inverse computation associated with the QP needs to be done only once and can be done offline for a given number of agents. This further simplifies the solution process, effectively reducing it to a problem of evaluating a few matrix-vector products. Moreover, for a large number of agents, this computation can be trivially accelerated on GPUs using existing off-the-shelf libraries. We validate our optimizer's performance on challenging benchmarks and show substantial improvement over state of the art in computation time and trajectory quality.