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.

We present two real-time trajectory optimizers based on the Cross-Entropy Method for visibility-aware navigation. The two approaches differ in handling inequality constraints stemming from bounds on motion derivatives, collision avoidance, tracking error, etc. Our first optimizer augments the inequalities into the cost function, while the second one relies on a novel GPU accelerated batch projection algorithm. We adopt a learningbased approach to ensure a fast query of the occlusion cost arising from the environment. Specifically, we train a neural network to compute the occlusion directly from the point obstacles generated from LiDAR or RGB-D sensors. Our learned occlusion model can be queried up to 3x faster than the approaches based on distance computation from occupancy or voxel maps. We improve the state-of-the-art in the following aspects. First, our optimizers do not require any explicit map building and can thus adapt on the fly to the changes in the environment. Second, we outperform existing approaches in target tracking applications in maintaining target visibility and success rate while being competitive in acceleration effort and computation time.

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