Bayesian Optimization for Learning Nonlinear MPC in Autonomous Agent Navigation

This paper explores the benefits of computing arborescent trajectories (trajectory-trees) instead of commonly used sequential trajectories for partially observable robotic planning problems. In such environments, a robot infers knowledge from observations, and the optimal course of action depends on these observations. \revise{Trajectory-trees, optimized in belief space, naturally capture this dependency by branching where the belief state is expected to evolve into multiple distinct scenarios, such as upon receiving an observation. Unlike sequential trajectories, which model a single forward evolution of the system, trajectory-trees capture multiple possible contingencies.} First, we focus on Model Predictive Control (MPC) and demonstrate the benefits of planning tree-like trajectories. We formulate the control problem as the optimization of a tree with a single branching (PO-MPC). This improves performance by reducing control costs through more informed planning. To satisfy the real-time constraints of MPC, we develop an optimization algorithm called Distributed Augmented Lagrangian (D-AuLa), which leverages the decomposability of the PO-MPC formulation to parallelize and accelerate the optimization. We apply the method to both linear and non-linear MPC problems using autonomous driving examples. Second, we address Task And Motion Planning (TAMP), and introduce a planner (PO-LGP) reasoning on decision trees at task level, and trajectory-trees at motion-planning level. This approach builds upon the Logic-Geometric-Programming Framework (LGP) and extends it to partially observable problems. The experiments show the method's applicability to problems with a small belief state size, and scales to larger problems by optimizing explorative policies, which are used as macro-actions in an overarching task plan.

Model Predictive Control (MPC) is widely used for autonomous-vehicle (AV) motion planning, but its real-time applicability is often limited by the need for accurate models and online solution of nonlinear, nonconvex optimization problems in dynamic road environments. Actor-critic reinforcement learning offers a promising alternative for online policy generation, yet its policy-learning process often lacks explicit control-theoretic structure. This article proposes a learning predictive control (LPC) framework with deep Koopman operators for efficient real-time motion planning under nonconvex constraints. To address nonlinear and uncertain vehicle dynamics, a deep-Koopman-based predictor is used to lift the system into an interpretable linear observable space in a data-driven manner. Unlike traditional MPC, which computes open-loop control sequences, the proposed LPC framework yields a closed-loop state-feedback policy within each prediction interval through receding-horizon actor-critic learning. To ensure safety under nonconvex environmental constraints, LPC constructs convex local surrogate representations of obstacles and defines corresponding potential-field functions. These functions and their gradients are directly embedded into the actor-critic structure, enabling efficient, safety-aware policy learning. Extensive simulations and real-world experiments on the HongQi-EHS3 platform demonstrate favorable performance in diverse obstacle-avoidance scenarios in terms of safety, computational efficiency, and driving comfort, compared with benchmark methods such as CBF-MPC and LMPCC.

This paper investigates the optimization mechanisms of non-convex Model Predictive Control (MPC) using the Maximum Entropy Differential Dynamic Programming (ME-DDP) framework. Navigating non-convex cost landscapes induced by nonlinear dynamics, multiple obstacles, etc. remains a fundamental challenge in robotics, where gradient-based methods frequently converge to suboptimal local minima. We demonstrate a dual-step optimization mechanism designed to overcome these traps. (1) an initial phase of using DDP to exploit the gradient of the cost landscape, followed by (2) disruption of the optimization via sampling from policies characterized by the inverse Hessian of the action-value function. We provide a rigorous analysis of this sampling mechanism of three ME-DDP variants: Unimodal Gaussian ME-DDP, Multimodal Gaussian ME-DDP, and Stein Variational DDP. Furthermore, with navigation tasks of four robotic systems under cluttered environments, we conduct extensive benchmarking of three variants of the ME-DDP, against deterministic DDP, and one of the most successful sampling-based schemes, Model Predictive Path Integral (MPPI) control with three policy parameterizations and update laws that correspond to those of ME-DDPs. The results show that in low-dimensional systems where the cost landscapes are relatively simple and local information is sufficiently representative, our framework consistently outperforms MPPIs. In high-dimensional systems, MPPI can occasionally discover aggressive maneuvers that enable it to steer the systems faster than DDP-based methods, whereas our method maintains a higher, more stable success rate. Finally, we validate the practical efficacy of the framework through hardware experiments with a quadrotor navigating a dense, non-convex obstacle field, confirming the robustness of the proposed framework for real-world deployment.