Towards Massively Parallel Motion Planning with Inverse Dynamics
Ioannis Tsikelis, Enrico Mingo Hoffman
AI summary
Problem
GPU-parallel optimal control solvers remain scarce compared to CPU alternatives, and existing methods struggle to support inverse dynamics formulations or arbitrary equality constraints without breaking synchronous execution.
Approach
The authors implement a batched SQP solver in PyTorch that linearizes dynamics and solves the inner quadratic program using a state-control equality-constrained LQR solver with Riccati recursion, enabling efficient GPU parallelization.
Key results
- GPU-native batched SQP solver supporting arbitrary state-control equality constraints
- Inverse dynamics formulation integrated without breaking synchronous GPU execution
- Reduced solve times and VRAM usage per environment compared to CPU and forward-dynamics baselines
- Scalable performance across batch sizes up to 32,768 parallel environments
Why it matters
Enables faster, scalable stochastic optimal control and robot learning by bridging the gap between CPU-optimized solvers and GPU-parallel architectures.
Abstract
Parallel evaluation of robotic system environments is becoming increasingly popular in modern robotics applica- tions for machine learning and stochastic control. At the same time, the field of model-based control has matured enough to provide solutions that cover the needs of sophisticated robotics platforms. However, few works address the parallelization of such solvers to be combined with the above approaches and accelerate research in robot planning and control. We present preliminary results toward a novel implementa- tion of a batched SQP solver for equality-constrained optimal control. After linearizing the dynamics in the SQP step, we employ a state-control equality constrained LQR solver. The additional equality constraints yield a structured system at each stage that can be solved via a Riccati-recursion-based block elimination. We evaluate our approach on an inverse-dynamics-based optimal control problem, in contrast to the forward-dynamics formulations typical of related works. Our results demonstrate computational efficiency and structural advantages for mas- sively parallel environments. Our implementation, available here, is developed in PyTorch, taking advantage of the library’s batched linear algebra suite for parallelization.