CQDC-Warp: GPU-Accelerated Differentiable Quasi-Dynamic Simulation for Contact-Rich Manipulation

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.