# Batched Differentiable Rigid Body Dynamics in PyTorch for GPU-Accelerated Robot Learning

arXiv: https://arxiv.org/abs/2605.31481 · HTML: https://mlsanity.com/paper/2605.31481/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in RL for robot locomotion and manipulation, one of 15 directions in Deep reinforcement learning methods.
- Builds on 18 of its 31 references that are in the map.
- First posted on arXiv 29 May 2026.

## Placed in

- Deep reinforcement learning methods / [RL for robot locomotion and manipulation](https://mlsanity.com/deeprl/rl-for-robot-locomotion-and-manipulation/)

## Builds on (most cited first, 18 of 18)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Isaac Gym: High Performance GPU-Based Physics Simulation For Robot Learning](https://mlsanity.com/paper/2108.10470/) (2021)
- [Learning to Walk in Minutes Using Massively Parallel Deep Reinforcement Learning](https://mlsanity.com/paper/2109.11978/) (2021)
- [Learning agile and dynamic motor skills for legged robots](https://mlsanity.com/paper/1901.08652/) (2019)
- [Brax -- A Differentiable Physics Engine for Large Scale Rigid Body Simulation](https://mlsanity.com/paper/2106.13281/) (2021)
- [DiffTaichi: Differentiable Programming for Physical Simulation](https://mlsanity.com/paper/1910.00935/) (2019)
- [A Differentiable Physics Engine for Deep Learning in Robotics](https://mlsanity.com/paper/1611.01652/) (2016)
- [Humanoid Parkour Learning](https://mlsanity.com/paper/2406.10759/) (2024)
- [MuJoCo Playground](https://mlsanity.com/paper/2502.08844/) (2025)
- [Fast and Feature-Complete Differentiable Physics for Articulated Rigid Bodies with Contact](https://mlsanity.com/paper/2103.16021/) (2021)
- [Crocoddyl: An Efficient and Versatile Framework for Multi-Contact Optimal Control](https://mlsanity.com/paper/1909.04947/) (2019)
- [Wild Visual Navigation: Fast Traversability Learning via Pre-Trained Models and Online Self-Supervision](https://mlsanity.com/paper/2404.07110/) (2024)
- [VERN: Vegetation-aware Robot Navigation in Dense Unstructured Outdoor Environments](https://mlsanity.com/paper/2303.14502/) (2023)
- [HMCF: A Human-in-the-loop Multi-Robot Collaboration Framework Based on Large Language Models](https://mlsanity.com/paper/2505.00820/) (2025)
- [GRiD: GPU-Accelerated Rigid Body Dynamics with Analytical Gradients](https://mlsanity.com/paper/2109.06976/) (2021)
- [Differentiable and Learnable Robot Models](https://mlsanity.com/paper/2202.11217/) (2022)
- [Blind-Wayfarer: A Minimalist, Probing-Driven Framework for Resilient Navigation in Perception-Degraded Environments](https://mlsanity.com/paper/2503.07492/) (2025)
- [Quattro: Transformer-Accelerated Iterative Linear Quadratic Regulator Framework for Fast Trajectory Optimization](https://mlsanity.com/paper/2504.01806/) (2025)

## Abstract (arXiv)

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.