Pick-to-Learn Calibration of an MPC Policy for an Origin-to-Destination Flight Problem

This paper presents a novel model predictive control (MPC) approach for autonomous pick-and-place between moving platforms with a hook-equipped aerial manipulator. First, for accurate and rapid modeling of the complex dynamics, a digital twin model of the quadcopter equipped with a hook-based gripper, implemented in MuJoCo, is constructed and used as the predictive model for the MPC. To handle uncertainties of the predictive model (e.g. due to aerodynamics and uncertain payloads), a robust adaptive MPC approach is proposed. By systematic integration of zero-order robust optimization (zoRO) based uncertainty propagation and an extended Kalman filter (EKF) for parameter estimation, the MPC algorithm ensures robust constraint satisfaction, high performance, and computational efficiency. The effectiveness of the proposed method is evaluated in complex simulated scenarios and in real-world flight experiments.

We investigate interactive trajectory planning subject to uncertainty in the decisions of surrounding agents. To control the ego-agent, we aim to first learn the decision distribution and solve a Stochastic Model Predictive Control (SMPC) problem. To account for errors in the learned distribution, we show that it is possible to utilize Probably Approximately Correct (PAC) learning in combination with Distributionally Robust (DR) optimization to obtain a solution which accounts for the errors induced by the learning model. The results indicate that our PAC learning-based DR-MPC framework provides a method to interpolate between a robust MPC and an omnipotent SMPC, based on the available number of samples.

Learning-based approaches to verifying unknown Markov decision processes (MDPs) often employ uncertain MDPs. These models use, for example, confidence intervals to capture transition uncertainty and allow synthesis of policies that are robust to this uncertainty. However, this approach typically quantifies uncertainty independently for individual transition probabilities, ignoring dependencies due to shared latent quantities. We propose to learn such models using parametric MDPs (pMDPs), where transition probabilities are expressions over a set of parameters. We project statistical uncertainty from empirical transition frequencies onto the pMDP's parameter space, yielding a probably approximately correct (PAC) uncertainty model for the underlying MDP that respects the algebraic dependencies between transitions. The resulting models are algorithmically challenging to solve, so we propose a hierarchy of sound polytopic outer approximations of the induced confidence set. We implement and evaluate our approach, demonstrating substantially tighter uncertainty estimates than classical interval-based uncertain MDP learning techniques.