A Koopman Operator-based NMPC Framework for Mobile Robot Navigation under Uncertainty

TL;DR

The paper tackles robust mobile robot navigation under uncertainty by integrating a data-driven Koopman operator into nonlinear model predictive control. A bilinear Koopman model is learned offline via a Kronecker-product formulation, yielding a compact linear-in-observables representation that is used inside an NMPC framework operating in the original state space. The approach improves resilience to stochastic velocity perturbations and obstacle-rich environments, outperforming standard NMPC in both simulated and real-world-like settings, including Gazebo digital twins and physical hardware experiments. This work demonstrates practical real-time applicability on resource-constrained platforms and opens avenues for extending Koopman-based learning to broader dynamics and online adaptation.

Abstract

Mobile robot navigation can be challenged by system uncertainty. For example, ground friction may vary abruptly causing slipping, and noisy sensor data can lead to inaccurate feedback control. Traditional model-based methods may be limited when considering such variations, making them fragile to varying types of uncertainty. One way to address this is by leveraging learned prediction models by means of the Koopman operator into nonlinear model predictive control (NMPC). This paper describes the formulation of, and provides the solution to, an NMPC problem using a lifted bilinear model that can accurately predict affine input systems with stochastic perturbations. System constraints are defined in the Koopman space, while the optimization problem is solved in the state space to reduce computational complexity. Training data to estimate the Koopman operator for the system are given via randomized control inputs. The output of the developed method enables closed-loop navigation control over environments populated with obstacles. The effectiveness of the proposed method has been tested through numerical simulations using a wheeled robot with additive stochastic velocity perturbations, Gazebo simulations with a realistic digital twin robot, and physical hardware experiments without knowledge of the true dynamics.

Figures (8)

• Figure 1: Comparison of the learned Koopman-bilinear approximation with the exact differential-drive robot model to predict a structured (circular) path. Recall that model learning occurs via randomly-generated control input.
• Figure 2: Resulting trajectory (left) and commanded control velocities (right) for the nominal robot while using the learned Koopman-based model for prediction and control in our Koopman-NMPC method.
• Figure 3: Resulting trajectories of the robot subject to stochastic velocity perturbations when using (a) nominal NMPC (for $\lambda=0.01$) and (b) our Koopman-NMPC (for $\lambda=0.1$). It can be readily observed that the nominal NMPC is fragile even with very small perturbations (note the collision with the topmost obstacle). In contrast, our method can successfully drive the robot to its goal while avoiding collisions even under larger perturbations.
• Figure 4: Resulting trajectories of the robot subject to stochastic velocity perturbations when using our developed Koopman-NMPC framework for (left) $\lambda=0.15$ and (right) $\lambda=0.2$. We highlight here that the Koopman-based model used in the depicted cases was trained from data produced with a different rate ($\lambda=0.1$).
• Figure 5: Snapshot from one simulated testing case with ROSbot in Gazebo. The goal is depicted with a small circular disk (in red), while obstacles are shown as larger cylinders (in black). Sample trials can be accessed at https://youtu.be/zWRlT7ntFnA.