Abstract-- 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. T o 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 4000 speedup compared to existing approaches. Code and examples are available at commalab.org/papers/spasm.

This paper presents a novel concept to support physically impaired humans in daily object manipulation tasks with a robot. Given a user's manipulation sequence, we propose a predictive model that uniquely casts the user's sequential behavior as well as a robot support intervention into a hierarchical multi-objective optimization problem. A major contribution is the prediction formulation, which allows to consider several different future paths concurrently. The second contribution is the encoding of a general notion of constancy constraints, which allows to consider dependencies between consecutive or far apart keyframes (in time or space) of a sequential task. We perform numerical studies, simulations and robot experiments to analyse and evaluate the proposed method in several table top tasks where a robot supports impaired users by predicting their posture and proactively re-arranging objects.