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

As robot control shifts toward large-scale reinforcement learning with in-loop dynamics computation, the community's reliance on CPU-bound libraries such as Pinocchio creates a throughput bottleneck in GPU-based training pipelines. We present BARD (Batched Articulated Rigid-body Dynamics), a self-contained PyTorch implementation of Featherstone's rigid-body dynamics algorithms, optimized for batched GPU evaluation and automatic differentiation. Three design choices make this efficient: a tiered lazy-evaluation cache that avoids redundant tree traversals, matmul-free joint transforms via pre-computed Rodrigues constants, and level-parallel propagation that reduces sequential operations to tree-depth batched steps. On five robot models (7-23 DOFs), BARD matches Pinocchio numerically while reaching up to 64x higher throughput for Forward Kinematics and 63x for Jacobians at batch size 4096 on an NVIDIA H200. We validate differentiability through gradient-based system identification on a 7-DOF manipulator, recovering link masses to 1.24% mean error under 5% torque noise, and integrate BARD into an Isaac Lab AMP training pipeline for an 11-DOF spined quadruped with 4096 parallel environments, where it is 8.5x faster than Pinocchio and 2.0x faster than ADAM for in-loop dynamics. BARD is open-sourced at: https://github.com/YueWang996/bard-pytorch-dynamics.

Inverse Kinematics (IK) is a core problem in robotics, in which joint configurations are found to achieve a (collision-free) desired end-effector pose. Modern IK solvers face a fundamental trade-off: analytical methods are fast but lack generality, while numerical optimization-based methods are broadly applicable but prone to local minima and high computational costs. To overcome this challenge, we introduce HJCD-IK, a GPU-accelerated, sampling-based hybrid solver. By pairing a novel orientation-aware greedy coordinate descent initialization with Jacobian-based polishing and a parallel collision filter, our method achieves up to order-of-magnitude gains in speed and accuracy over state-of-the-art solvers, consistently finding collision-free solutions on the accuracy-latency Pareto frontier, while producing a diverse distribution of high-quality samples. We validate our solver on a physical Franka manipulator and release our code open-source.

Many robotics problems, including trajectory optimization, inverse kinematics, and contact-rich motion planning, reduce to nonlinear programs (NLPs). Mature NLP solvers such as IPOPT can solve these problems, offering hard constraint satisfaction, optimality guarantees, and favorable scaling with problem dimension. These solvers underpin gradient-based methods in robotics, yet remain CPU-bound and solve only one problem at a time, preventing their integration into GPU-batched learning pipelines. On the other hand, sampling-based approaches such as reinforcement learning, model predictive path integral, and imitation learning have become the core of modern robotics research due to their ability to leverage GPU-batched simulators. These simulators can generate orders of magnitude more dynamics rollouts per second than was previously possible. If a GPU-batched NLP solver existed, it would unlock similar speedups in the number of constrained, locally optimal solutions generated per second. This regime of solving many problems concurrently versus solving a single problem at a time is a key requirement for integrating NLP solvers in modern GPU-batched robotics frameworks. To this end, we introduce jaxipm, the first GPU-batched NLP solver, based on IPOPT, and implemented in JAX. We accomplish this by redesigning IPOPT's algorithm to eliminate control flow with heterogeneous iteration fusion, and by minimizing GPU idle time with iteration level batching. We evaluate jaxipm on a variety of quadrotor nonlinear model predictive control benchmarks, including reference tracking in the presence of obstacles, multi-quadrotor navigation without collision, and navigation in a cluttered environment. We demonstrate up to a $32.85\times$ increase in throughput over IPOPT. Our complete open-source codebase is available at https://github.com/johnviljoen/jaxipm.