Abstract
In this letter, 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 a large scale, convex, unconstrained Quadratic Program (QP). Importantly, our QP structure requires us to compute the associated matrix factorization/inverse only once for a fixed number of agents. Moreover, we can do it offline and then use the same for different problem instances. This further simplifies the solution process, effectively reducing it to a few matrix-vector products. 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.
Highlights
C OORDINATING multiple agents between given start and goal positions without collision is crucial to any multiagent application
The number of pair-wise non-convex collision avoidance constraints grow by a factor n 2
We begin by rreiWteeractoinngsitdheer main assumptions. differentially flat, spheroid agents with decoupled affine motion models along the (x, y, z) axis. Such models are suitable for quadrotors [1] and even sometimes r for autonomous cars
Summary
C OORDINATING multiple agents between given start and goal positions without collision is crucial to any multiagent application. For highly agile agents like quadrotors and autonomous cars, a popular approach has been to formulate this collision-free coordination as a trajectory optimization problem. The number of variables in the optimization problem increases linearly with the number of agents n. The sequential approaches, e.g., [1], [2], follow an iterative process wherein motion plans for only one agent is computed at a time. Collision avoidance is ensured by treating agents whose motions were computed. This section introduces some necessary mathematical preliminaries and uses them to draw a contrast between existing works and our optimizer. The left superscript k will be used to indicate the iteration index in a trajectory optimizer. M to represent the number of agents and planning horizon throughout the paper
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