Behavior Cloning of MPC for 3-DOF Robotic Manipulators

Sampling-based model predictive control methods, such as Model Predictive Path Integral (MPPI), offer derivative-free optimization and robustness in complex robotic systems. However, standard MPPI relies on cost-based soft penalties that cannot guarantee hard-constraint satisfaction, severely limiting its applicability to highly constrained tasks such as closed-chain manipulation. To address this, we propose Manifold-Constrained MPPI (MC-MPPI), a real-time sampling-based control framework that enforces manifold-based equality constraints while preserving the computational advantages of MPPI. The key idea is to decouple the constrained optimal control problem into latent-space planning and execution-level correction. At the planning stage, a Variational Autoencoder (VAE) learns a low-dimensional latent representation of the constraint manifold, enabling MPPI to efficiently generate near-feasible candidate trajectories without per-sample modification. Since this reference enables accurate linearization of the equality constraints, an execution-level Quadratic Programming (QP) controller resolves the residual manifold mismatch in a single solve rather than through iterative projection. Experiments on a 14-DoF closed-chain dual-arm system in both simulation and real-world settings demonstrate that MC-MPPI operates stably at 100 Hz, reliably navigates dynamic environments while effectively maintaining hard equality constraints, and significantly outperforms baseline methods in tracking accuracy. Supplementary videos and implementation details are available at https://rcilab.github.io/mcmppi.

In the literature, actor-critic model predictive control (AC-MPC) integrates MPC with reinforcement learning to enable high-performance control of complex dynamical systems. However, its differentiable MPC layer requires repeatedly solving an optimization problem in both the forward and backward passes, leading to substantial training and inference latency. This paper tackles this bottleneck introducing a CUDA-accelerated variant that significantly reduces end-to-end execution time while preserving the control performance of the baseline formulation. Simulation results on an agile drone racing task show that our approach achieves state-of-the-art lap times and near-limit dynamic behaviour with markedly reduced training and inference time.

Behavior cloning (BC) is a practical offline imitation learning method, but it often fails when expert demonstrations are limited. Recent works have introduced a class of architectures named predictive inverse dynamics models (PIDMs) that combine a future-state predictor with an inverse dynamics model. While PIDMs often outperform BC, the reasons behind their benefits remain unclear. In this paper, we provide a theoretical explanation: PIDMs introduce a tradeoff. Conditioning the IDM on the predicted future state can significantly reduce variance, but the prediction itself introduces additional bias and variance. We establish conditions for PIDMs to achieve higher sample efficiency and lower prediction error than BC, with the gap widening when additional data sources are available. We validate the theoretical insights empirically in 2D navigation tasks, where BC requires up to five times (three times on average) more demonstrations than PIDM to reach comparable performance. Results are also illustrated in a complex 3D environment in a modern video game with high-dimensional visual inputs and stochastic transitions, where BC requires over 66% more samples than PIDM.