CoVO-MPC: Theoretical Analysis of Sampling-based MPC and Optimal Covariance Design

Sampling-based Model Predictive Control (MPC) has been a practical and effective approach in many domains, notably model-based reinforcement learning, thanks to its flexibility and parallelizability. Despite its appealing empirical performance, the theoretical understanding, particularly in terms of convergence analysis and hyperparameter tuning, remains absent. In this paper, we characterize the convergence property of a widely used sampling-based MPC method, Model Predictive Path Integral Control (MPPI). We show that MPPI enjoys at least linear convergence rates when the optimization is quadratic, which covers time-varying LQR systems. We then extend to more general nonlinear systems. Our theoretical analysis directly leads to a novel sampling-based MPC algorithm, CoVariance-Optimal MPC (CoVo-MPC) that optimally schedules the sampling covariance to optimize the convergence rate. Empirically, CoVo-MPC significantly outperforms standard MPPI by 43-54% in both simulations and real-world quadrotor agile control tasks. Videos and Appendices are available at \url{https://lecar-lab.github.io/CoVO-MPC/}.

Task-Driven In-Hand Manipulation of Unknown Objects with Tactile Sensing

Manipulation of objects in-hand without an object model is a foundational skill for many tasks in unstructured environments. In many cases, vision-only approaches may not be feasible; for example, due to occlusion in cluttered spaces. In this paper, we introduce a method to reorient unknown objects by incrementally building a probabilistic estimate of the object shape and pose during task-driven manipulation. Our method leverages Bayesian optimization to strategically trade-off exploration of the global object shape with efficient task completion. We demonstrate our approach on a Tactile-Enabled Roller Grasper, a gripper that rolls objects in hand while continuously collecting tactile data. We evaluate our method in simulation on a set of randomly generated objects and find that our method reliably reorients objects while significantly reducing the exploration time needed to do so. On the Roller Grasper hardware, we show successful qualitative reconstruction of the object model. In summary, this work (1) presents a system capable of simultaneously learning unknown 3D object shape and pose using tactile sensing; and (2) demonstrates that task-driven exploration results in more efficient object manipulation than the common paradigm of complete object exploration before task-completion.