CusADi2: Latency-Optimized Batch Computation of Robot Kinematics, Jacobians, and Hessians on the GPU

Trajectory optimization methods, from sampling-based zero-order to gradient-based first- and second-order approaches, require many evaluations of dynamical system functions, i.e., functions derived from a robot's dynamical model, such as forward kinematics and their Jacobians and Hessians. These evaluations are largely independent, e.g., across sampled trajectories or time steps, and can thus be evaluated in parallel as a batch. When used to make decisions online, these methods require low latency, i.e., each batch must complete in as little wall-clock time as possible. Existing frameworks utilize modern GPU hardware primarily to parallelize across batch instances, thereby optimizing throughput but not latency. We present CusADi2, a software library that reduces the batch evaluation latency by additionally parallelizing computation within each batch instance. We benchmark forward kinematics, Jacobians, and Hessians for all 67~robots in the MuJoCo Menagerie, including arms, hands, quadrupeds, humanoids, and biomechanical models, against MuJoCo XLA, MuJoCo Warp, frax, CusADi, and CasADi. CusADi2 achieves lower latency than all baselines at batch sizes of 64 to 4096, while matching them at larger batch sizes. We also demonstrate the performance advantage of CusADi2 in a sampling-based control application. All code is open-source at: https://github.com/johnviljoen/cusadi2