Sequential robot manipulation tasks require finding collision-free trajectories that satisfy geometric constraints across multiple object interactions in potentially high-dimensional configuration spaces. Solving these problems in real-time and at large scales has remained out of reach due to computational requirements. Recently, GPU-based acceleration has shown promising results, but prior methods achieve limited performance due to CPU-GPU data transfer overhead and complex logic that prevents full hardware utilization.
To this end, we present SPaSM (Sampling Particle optimization for Sequential Manipulation), a fully GPU-parallelized framework that compiles constraint evaluation, sampling, and gradient-based optimization into optimized CUDA kernels for end-to-end trajectory optimization without CPU coordination. The method consists of a two-stage particle optimization strategy: first solving placement constraints through massively parallel sampling, then lifting solutions to full trajectory optimization in joint space.
Unlike hierarchical approaches, SPaSM jointly optimizes object placements and robot trajectories to handle scenarios where motion feasibility constrains placement options. Experimental evaluation on challenging benchmarks demonstrates solution times in the realm of milliseconds with a 100% success rate; a 4000x speedup compared to existing approaches.
We perform joint object placement and trajectory optimization by using an augmented langrangian method to iteratively improve the plan. Use the slider here to move through the steps of the tower environment optimization between the initial and optimized states.
Initial State
Final State
Here is another example of the optimization process on the tetris environment.
Initial State
Final State
@article{chen2025spasm,
author={Lucas Chen and Shrutheesh Raman Iyer and Zachary Kingston},
title={Differentiable Particle Optimization for Fast Sequential Manipulation},
year={2025},
eprint={2510.07674},
archivePrefix={arXiv},
primaryClass={cs.RO},
url={https://arxiv.org/abs/2510.07674},
}