Mobile Multi-Robot Navigation under Runtime Uncertainty via Koopman Operator Learning and Nonlinear Model Predictive Control

This paper presents Residual Koopman MPC (RK-MPC), a Koopman-based, data-driven model predictive control framework for quadruped locomotion that improves prediction fidelity while preserving real-time tractability. RK-MPC augments a nominal template model with a compact linear residual predictor learned from data in lifted coordinates, enabling systematic correction of model mismatch induced by contact variability and terrain disturbances with provable bounds on multi-step prediction error. The learned residual model is embedded within a convex quadratic-program MPC formulation, yielding a receding-horizon controller that runs onboard at 500 Hz and retains the structure and constraint-handling advantages of optimization-based control. We evaluate RK-MPC in both Gazebo simulation and Unitree Go1 hardware experiments, demonstrating reliable blind locomotion across contact disturbances, multiple gait schedules, and challenging off-road terrains including grass, gravel, snow, and ice. We further compare against Koopman/EDMD baselines using alternative observable dictionaries, including monomial and $SE(3)$-structured bases, and show that the residual correction improves multi-step prediction and closed-loop performance while reducing sensitivity to the choice of observables. Overall, RK-MPC provides a practical, hardware-validated pathway for data-driven predictive control of quadrupeds in unstructured environments. See https://sriram-2502.github.io/rk-mpc for implementation videos.

Offline models for autonomous robots often fail under time-varying dynamics outside their training distribution. Koopman operator theory offers a linear representation of nonlinear dynamics via lifting, but its transition to real-time recursive estimation may suffer numerical vulnerabilities: covariance windup under low excitation when using exponential forgetting, and vanishing gain without forgetting. This paper introduces a Covariance-Regulated Recursive Koopman Learning (CR-RKL) framework with two complementary strategies--error dead-zone gating and constant-trace normalization--each independently capable of preventing covariance explosion and parameter freezing, with the latter additionally preserving the geometric structure of uncertainty. Validated on a non-holonomic differential-drive robot with wheel slip and Stribeck friction and on a 26-gram butterfly-inspired flapping-wing micro aerial vehicle, CR-RKL achieves numerically stable and accurate online modeling, and when embedded in model predictive control, it maintains reliable tracking performance under uncertain, time-varying dynamics.

This paper presents a safety-critical centralized nonlinear model predictive control (NMPC) framework for cooperative payload transportation by two quadrupedal robots. The interconnected robot-payload system is modeled as a discrete-time nonlinear differential-algebraic system, capturing the coupled dynamics through holonomic constraints and interaction wrenches. To ensure safety in complex environments, we develop a control barrier function (CBF)-based NMPC formulation that enforces collision avoidance constraints for both the robots and the payload. The proposed approach retains the interaction wrenches as decision variables, resulting in a structured DAE-constrained optimal control problem that enables efficient real-time implementation. The effectiveness of the algorithm is validated through extensive hardware experiments on two Unitree Go2 platforms performing cooperative payload transportation in cluttered environments under mass and inertia uncertainty and external push disturbances.