Contact-Rich Motion Planning via GPU-Parallel Mode Evaluation

Efficient synthesis of contact-rich manipulation trajectories is essential for downstream robot learning. Gradient-based planning offers a promising approach, but jointly optimizing motion and contact decisions remains challenging. Meanwhile, many existing planners run on CPUs with limited throughput. We present CQDC-Warp, a GPU-accelerated differentiable quasi-dynamic simulator for batched model predictive control (MPC). We use it to study contact-guided trajectory optimization, in which intended robot--object contacts are specified before planning and encouraged through soft costs, while the simulated dynamics determine contact geometry and frictional response without a prescribed contact-mode schedule. Across $17{,}408$ trials on the $17$-object Allegro in-hand rotation benchmark, our framework achieves $79.8\%$ success, compared with $73.7\%$ for CFree and $65.2\%$ for IMPACT, and reduces mean trajectory-generation time by factors of $27.0$ and $50.2$, respectively. On a single NVIDIA RTX 4090 with $2{,}048$ parallel worlds, forward and backward throughput reach $2.06\times10^5$ and $2.25\times10^5$ world-steps per second, respectively. Further experiments cover manipulation with LEAP and Shadow hands, environmental contact exploitation, bimanual manipulation, whole-body control, and real-world trajectory replay on a Sharpa hand.

Fast whole-body motion planning enables continuous replanning for humanoid robots in dynamic environments while satisfying collision avoidance and kinematic constraints. However, constrained motion planning incurs substantial computational cost due to repeated constraint projection in addition to collision checking and nearest-neighbor search. Recently, GPU-based massively parallel planners have been proposed to reduce computational cost. Nevertheless, these planners still steer in the ambient configuration space, so projecting candidates that deviate from the manifold remains a significant source of overhead, particularly in highly constrained, high-dimensional problems. In this work, we introduce PATACON, a GPU-parallel bidirectional planner that explores tangent space to exploit the local manifold geometry induced by known constraint functions. Experiments on dual-arm closed-chain and humanoid whole-body constrained planning tasks show that PATACON outperforms the prior work as configuration-space dimension and constraint codimension grow, achieving up to an 11.25 times speedup. These results suggest that GPU-parallel tangent-space exploration brings constrained whole-body motion planning closer to real-time performance.

Physics simulation for contact-rich robotics is often bottlenecked by contact resolution: mainstream engines enforce non-penetration and Coulomb friction via complementarity constraints or constrained optimization, requiring per-step iterative solves whose cost grows superlinearly with contact density. We present ComFree-Sim, a GPU-parallelized analytical contact physics engine built on complementarity-free contact modeling. ComFree-Sim computes contact impulses in closed form via an impedance-style prediction--correction update in the dual cone of Coulomb friction. Contact computation decouples across contact pairs and becomes separable across cone facets, mapping naturally to GPU kernels and yielding near-linear runtime scaling with the number of contacts. We further extend the formulation to a unified 6D contact model capturing tangential, torsional, and rolling friction, and introduce a practical dual-cone impedance heuristic. ComFree-Sim is implemented in Warp and exposed through a MuJoCo-compatible interface as a drop-in backend alternative to MuJoCo Warp (MJWarp). Experiments benchmark penetration, friction behaviors, stability, and simulation runtime scaling against MJWarp, demonstrating near-linear scaling and 2--3 times higher throughput in dense contact scenes with comparable physical fidelity. We deploy ComFree-Sim in real-time MPC for in-hand dexterous manipulation on a real-world multi-fingered LEAP hand and in dynamics-aware motion retargeting, demonstrating that low-latency simulation yields higher closed-loop success rates and enables practical high-frequency control in contact-rich tasks.