Trajectory Generation

This paper addresses conservatism, limited numerical accuracy, and high computational effort in existing methods ensuring safety by design in online model-based motion generation. The presented method employs a novel captivity-escape zero-sum differential game to adapt the planning model's performance so that resulting reference trajectories are trackable within a prescribed safety margin by a jointly synthesized safety controller. A numerical example demonstrates orders-of-magnitude faster computation and improved numerical accuracy compared to the state of the art.

This work presents an optimization method for generating kinodynamically feasible and collision-free multi-robot trajectories that exploits an incremental denoising scheme in diffusion models. Our key insight is that high-quality trajectories can be discovered merely by denoising noisy trajectories sampled from a distribution. This approach has no learning component, relying instead on only two ingredients: a dynamical model of the robots to obtain feasible trajectories via rollout, and a fitness function to guide denoising with Monte Carlo gradient approximation. The proposed framework iteratively optimizes a deformation for the previous trajectory with the current denoising process, allows anytime refinement as time permits, supports different dynamics, and benefits from GPU acceleration. Our evaluations for differential-drive and holonomic teams with up to 16 robots in 2D and 3D worlds show its ability to discover high-quality solutions faster than other black-box optimization methods such as MPPI. In a 2D holonomic case with 16 robots, it is almost twice as fast. As evidence for feasibility, we demonstrate zero-shot deployment of the planned trajectories on eight multirotors. Code and video: https://github.com/proroklab/d4orm