Robust Adaptive Koopman MPC Under Structured and Stochastic Uncertainty for Soft Continuum Robots

Koopman-based model predictive control for nonlinear systems with bounded model uncertainty

Dynamic Modeling and Real-Time Control of Continuum Soft Robots

Continuum soft robots have attracted significant attention due to their high flexibility, compliance, and ability to perform complex tasks in unstructured environments. However, their inherent nonlinear, distributed-parameter dynamics pose major challenges for accurate modeling and real-time control. Existing approaches typically face a trade-off between computational efficiency and model fidelity, where simplified models lack accuracy, while high-fidelity formulations are computationally prohibitive for real-time implementation. This study addresses these limitations by proposing a hybrid framework for dynamic modeling and real-time control of continuum soft robots.The proposed approach integrates a reduced-order dynamic model derived from continuum mechanics with a data-driven compensation module to enhance modeling accuracy while maintaining computational efficiency. The reduced-order formulation captures the dominant deformation behavior of the robot, while a learning-based component compensates for unmodeled dynamics and uncertainties. Based on this hybrid model, a real-time control strategy is developed to achieve accurate trajectory tracking under nonlinear and uncertain operating conditions.Comprehensive evaluations are conducted through simulation-based studies and comparative analysis with state-of-the-art modeling and control methods. The results demonstrate that the proposed framework achieves improved accuracy, reduced tracking error, and significantly enhanced computational efficiency compared to conventional approaches such as constant curvature, Cosserat rod, and FEM-based models. This improvement is achieved because the reduced-order dynamic model preserves the dominant deformation characteristics while lowering computational complexity, and the data-driven compensation module corrects unmodeled dynamics and nonlinear effects that are not captured by conventional formulations. Consequently, the framework enables faster computation, more accurate state prediction, and more reliable real-time control performance. Furthermore, the proposed method maintains real-time feasibility while ensuring robustness against disturbances and noise.

Trajectory Tracking Control of Autonomous Mobile Robots via Linearized Model Predictive Control: Theory and Simulation Validation

Accurate trajectory tracking is a fundamental requirement for autonomous mobile robots (AMRs) operating in complex environments. This paper addresses the tracking control problem for AMRs subject to kinematic constraints. A linearized model predictive control (LMPC) framework is proposed to effectively reduce trajectory tracking errors while ensuring smooth control inputs and high computational efficiency. First, the nonlinear kinematic model of the robot is derived and linearized around the reference trajectory using Taylor series expansion to obtain a discrete-time linear error dynamic model. Second, the tracking problem is formulated as a constrained finite-horizon optimization problem, which is transformed into a standard quadratic programming (QP) form to guarantee computational efficiency. Extensive simulations are conducted using a complex butterfly-shaped trajectory characterized by continuous curvature variations. The results demonstrate that the proposed controller achieves high tracking accuracy with centimeter-level position errors and generates feasible control inputs that strictly satisfy constraints, thereby demonstrating the robustness and effectiveness of the proposed controller.

Physics-Based Online Adaptive Koopman Model Predictive Attitude Control for Combined Spacecraft With Dynamic Uncertainties

This paper proposes a physics-based adaptive Koopman Model Predictive Control (MPC) strategy for combined spacecraft attitude stabilization under inertia uncertainties and active target maneuverability. A novel, quaternion-based Koopman model is constructed from a set of analytical lifting functions derived from the quaternion kinematics, which provides a more compact and physically interpretable linear representation of the nonlinear dynamics compared with the conventional black-box EDMD and higher-dimensional DCM-based model. Leveraging the linear structure of this nominal model, a gradient descent-based update law is employed to efficiently identify time-varying inertial uncertainties from real-time input/output data. By integrating this adaptive linear model into the MPC framework, the optimal control problem reduces to a computationally efficient Quadratic Program (QP), thereby significantly lowering the online computational burden compared to nonlinear adaptive MPC. Recursive feasibility and regional input-to-state stability are formally established through the design of terminal ingredients for the MPC. The effectiveness and superiority of the proposed strategy are validated through comparative simulations of an attitude stabilization task for combined spacecraft in a high-fidelity 3D simulator. Note to Practitioners—On-orbit servicing missions such as refueling and debris removal face a critical challenge: once a spacecraft docks with another target, its inertial properties change abruptly and unpredictably. Furthermore, if the target is non-cooperative, it may also apply competitive torques that actively destabilize the combined system. Such unknown physical variations can endanger the entire mission. Conventional control schemes typically depend on complex nonlinear models of the spacecraft, which impose a heavy computational burden and fail to achieve rapid on-orbit adjustments. To overcome these limitations, this work introduces a unified, online adaptive strategy built upon Koopman operator theory and Model Predictive Control (MPC). The proposed strategy delivers a significantly faster and more precise control response under inertial uncertainty and competitive torques, as validated in high-fidelity simulations. Beyond spacecraft applications, the strategy is potentially applicable to a broader class of nonlinear dynamic systems, especially those with structured kinematics and significant parametric uncertainties. In particular, the proposed physics-enhanced Koopman-based modeling approach can be directly extended to engineering fields such as uncrewed aerial vehicle attitude control and robotic manipulator operations.

Hierarchical PIwFF–Koopman-Based Offset-Free MPC for AUV Trajectory Tracking: Simulation and Pool Experiments

Accurate trajectory tracking of autonomous underwater vehicles (AUVs) is challenging because nonlinear hydrodynamics, actuator constraints, and persistent plant–model mismatch degrade controller performance. This paper proposes a hierarchical proportional-integral with feedforward (PIwFF)–Koopman-based offset-free model predictive control (MPC) for trajectory tracking of the Xplorer-mini AUV. The outer PIwFF loop converts pose-tracking errors and reference pose rates into body-fixed velocity commands using a proportional-integral structure augmented with a velocity feedforward term to anticipate reference motion, while the inner Koopman-based MPC tracks the velocity/lifted-state commands with actuator and velocity constraints enforced by construction. A cascade stability analysis establishes uniform ultimate boundedness (UUB) of the tracking errors under standard MPC assumptions. To reduce persistent velocity-output bias caused by finite-dimensional Koopman approximation errors, unmodeled dynamics, and unknown persistent disturbances, the inner MPC is augmented with an output-error integrator. DMDc and eDMDc are compared as prediction models; although eDMDc improves open-loop prediction accuracy, DMDc is selected for closed-loop control because it provides comparable tracking performance at a lower computational cost. Furthermore, a preview command is introduced for time-varying references. Simulation and pool experiments demonstrate that the proposed controller reduces steady-state bias and improves trajectory tracking relative to the PIwFF–Koopman-based nominal MPC and PID–PID baselines under the tested conditions.

A Reinforcement Learning-Based Robust Path Tracking Controller for Nonlinear Mobile Robot Dynamics under Uncertainty