SoRoMoX: Fast, Differentiable, and Parallelizable Soft Robot Models

Reduced-order models based on Cosserat-rod theory are now well established, and modeling theory is no longer the primary bottleneck in soft-robot control. Their implementations, however, do not support the differentiable, GPU-parallel, and control-oriented workflows that underpin advanced rigid-robotics applications. Here, we fill this gap with SoRoMoX (Soft Robot Models in JAX), a fully numerical, JIT-compilable Python/JAX framework. SoRoMoX implements articulated, Piecewise Constant Strain, and Variable Strain models through a unified, control-ready interface that provides inertia matrices, gravitational and elastic forces, Jacobians, and their derivatives. To our knowledge, it is the first rod/strain-based soft-robot modeling framework that runs directly on GPUs and is end-to-end differentiable with respect to states, inputs, and parameters. Sequential CPU rollouts are up to 18.1x faster than state-of-the-art alternatives, while GPU-parallel rollouts increase throughput by up to 234.6x. This performance enables workflows that were previously impractical or impossible: static-equilibrium system identification with 66% lower marker RMSE; residual-force learning with a further 64% reduction; computed-torque tracking with RMSE reduced by a factor of approximately 500 relative to model-free PD; control-gain optimization with up to 62% lower loss than untuned gains; safety-constrained control using high-order control barrier functions to keep the peak contact force within a prescribed 5 N bound, compared with 33.5 N without the safety constraint; and reinforcement-learning policy training up to 7x faster than a CPU PyElastica discrete-rod baseline through massively parallel rollouts.

TurboMPC: Fast, Scalable, and Differentiable Model Predictive Control on the GPU

Robotics increasingly relies on GPUs for parallel simulation, large-scale learning, and neural-network inference. For model predictive control (MPC) to scale with this paradigm, solvers must run efficiently on this hardware while remaining fast, differentiable, and compatible with expressive MPC formulations used in robotics. We present TurboMPC, a differentiable MPC solver that runs entirely on the GPU and supports state and control inequality constraints, implicit integrators, cross-time-coupled costs, and slack variables. TurboMPC combines sequential quadratic programming (SQP), an alternating direction method of multipliers (ADMM) inner solver, implicit differentiation, and a co-designed JAX-CUDA implementation for efficiency and ease of use. In simulation, we validate TurboMPC on constrained planning, humanoid imitation learning, and reinforcement learning with neural-network cost function tasks, achieving up to $15\times$ and $58\times$ speedups over state-of-the-art CPU and GPU differentiable solvers, respectively. We deploy TurboMPC on a full-scale car for minimum-time racing and find that batched, GPU-accelerated tuning of MPC parameters via Bayesian optimization yields significantly faster driving than a hand-tuned baseline. TurboMPC also scales to planning horizons of over $8000$ knot points while maintaining control of the vehicle. We open-source TurboMPC at: https://github.com/ToyotaResearchInstitute/turbompc

RadiusFPS: Efficient Farthest Point Sampling on CPUs and GPUs via Spherical Voxel Pruning

Point clouds are a primary sensory representation for robotic perception, underpinning LiDAR-based autonomous driving, simultaneous localization and mapping (SLAM), and navigation. Within these pipelines, Farthest Point Sampling (FPS) is the most well-known downsampling operator, as its uniform coverage preserves the geometric structure on which downstream perception relies. However, the large time complexity of classical FPS scales poorly with the million-point-per-second rates of modern 3D sensors, making it a dominant latency bottleneck that conflicts with the real-time and limited onboard compute budgets of robotic systems. Therefore, we propose RadiusFPS, an FPS acceleration framework based on spherical voxel pruning that preserves the standard FPS update rule under the same initialization and tie-breaking policy. By indexing the point cloud with spherical voxels, RadiusFPS derives a conservative geometric bound that prunes redundant distance computations in each iteration, complemented by a coordinate-wise point-skip test that removes residual updates. We further introduce RadiusFPS-G, a warp-level GPU implementation that fuses voxel selection, pruning, and distance update into memory-coalesced kernels, eliminating costly global-memory round-trips. On indoor (S3DIS, ScanNet) and outdoor LiDAR (SemanticKITTI) benchmarks, RadiusFPS-G attains up to 2.5x speedup over GPU-based FPS and matches or exceeds QuickFPS among the evaluated methods while using roughly half its GPU memory, with comparable segmentation accuracy. When coupled with the learning-based FastPoint sampler, the resulting pipeline achieves the fastest End-to-End inference among all evaluated configurations. These properties make high-quality FPS-style sampling practical for latency- and memory-constrained robotic vision.