GPU Accelerated Convex Approximations for Fast Multi-Agent Trajectory Optimization

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 nonconvex 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.

Real-Time Multi-Convex Model Predictive Control for Occlusion Free Target Tracking

“…In spite of this, existing literature has an abundance of examples where SB/ADMM have been empirically found to work on even non-convex problems [33], [34]. Our own prior works [22], [23] have also presented similar empirical evidence. We have also empirically validated the convergence of the proposed optimizer in Section V. We conjecture that one of the reasons behind our AM's reliable convergence is that each sub-problem in every iteration is solved exactly to its minimum.…”

GPU Accelerated Batch Multi-Convex Trajectory Optimization for a Rectangular Holonomic Mobile Robot

“…We extend the polar representation of collision avoidance constraint from [17], [18] to a rectangular robot modeled via overlapping circles. Our collision avoidance model has the form f c = 0, where ∀t, i, j, l fc(x l (t), y l (t), ψ l (t)) =…”

“…For details refer to [18]. The matrix Q is a block-diagonal stacking of PT P. The matrix F and vector g l are obtained by rewriting constraints (7c) -(7g) in the following manner.…”

Fast Joint Multi-Robot Trajectory Optimization by GPU Accelerated Batch Solution of Distributed Sub-Problems

“…A fundamental component of any multi-robot system is the coordination planning that guides individual robots between their start and goal locations while avoiding collisions with the environment and other robots. In this paper, we adopt the optimization perspective for multi-robot motion planning (Rastgar et al, 2021). In this context, the existing approaches broadly fall into two spectra.…”

“…On one end, we have the centralized approaches wherein the trajectory of all the robots are computed together. The centralized approach can be further subdivided into sequential (Chen et al, 2015), Park et al (2020) and joint optimization (Augugliaro et al, 2012;Rastgar et al, 2021) respectively depending on whether the trajectories of the robots are computed one at a time or simultaneously. On the other end of the spectrum, we have online distributed model predictive control (DMPC) (Luis et al, 2020;Soria et al, 2021) based approaches wherein each individual robot computes its trajectories in a decoupled manner based on the trajectory prediction of the other robots in the environment.…”