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

Xiaobin Zhang; Konstantinos Karydis

cs.ROSep 12, 2026

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

Authors: Xiaobin Zhang, Konstantinos Karydis

Organizations: University of California, Riverside, Riverside CA 92551, USA

Abstract

In this work, we developed a nonlinear model predictive control (NMPC) framework that employs learned dynamics via the Koopman Operator theory for mobile multi-robot navigation. We formulated and solved NMPC problems using a lifted bilinear Koopman-based model that accurately predicts affine input systems affected by perturbations and uncertainties. Two exemplary multi-robot navigation problems are considered: target reaching and formation control. The output of our method enables closed-loop multi-robot navigation and formation control in environments populated with obstacles, whereby the Koopman operator-based model used in the NMPC formulation addresses runtime uncertainties, namely, various degrees of random wheel slipping. We validated the effectiveness of our method for both problems via extensive numerical simulations in different environments with wheeled robots affected by different amounts of slip and without knowledge of their true dynamic models.

Figures & tables

Panel of Figure 1 — Figure 1: Comparison of the Koopman-bilinear approximation with the exact differential-drive robot model without (left) and with (right) slip.

Panel of Figure 2 — Figure 2: Qualitative results on target reaching in Map 1 for (left) nominal, (center) low-slip, and (right) high-slip settings. (Best viewed in color.)

Panel of Figure 3 — Figure 3: Sample target-reaching trajectories in Map 2 for (left) low-slip and (right) high-slip cases. The nominal case is not depicted for brevity but resembles the low-slip case, as in Map 1 (cf. Fig. 2 ). (Best viewed in color.)

Map	Slip	SR	mean $\pm$ SD final distance [ $\times 10^{-2}m$ ]
Map	Slip	SR	Robot 1	Robot 2	Robot 3
Map 1	Nominal	10/10	$0.9$	$1.9$	$1.9$
	Low	9/10	$3.1\pm 0.7$	$2.7\pm 0.1$	$6.6\pm 4.1$
	High	8/10	$1.9\pm 1.5$	$2.7\pm 0.2$	$6.6\pm 1.9$
Map 2	Nominal	10/10	$2.8$	$1.8$	$2.3$
	Low	9/10	$5.0\pm 0.4$	$2.4\pm 0.4$	$6.4\pm 2.4$

Table 1: Koopman-NMPC Statistics for Target Reaching.

Map	Slip	SR	mean $\pm$ SD final distance [ $\times 10^{-2}m$ ]
Map	Slip	SR	Robot 1	Robot 2	Robot 3
Map 1	Nominal	10/10	$1.8$	$1.5$	$15.6$
	Low	8/10	$1.3\pm 0.4$	$1.8\pm 0.2$	$3.5\pm 2.7$
	High	3/10	$1.1\pm 0.4$	$2.4\pm 0.2$	$4.0\pm 2.5$
Map 2	Nominal	0/10	NaN	NaN	NaN
	Low	1/10	$2.4$	$0.5$	$3.4$

Table 2: Nominal NMPC Statistics for Target Reaching.

Panel of Figure 4 — Figure 4: Qualitative results on formation control in Map 3 for (left) nominal, (center) low-slip, and (right) high-slip settings. (Best viewed in color.)

Map	Slip	SR	mean $\pm$ SD final distance [ $\times 10^{-2}m$ ]
Map	Slip	SR	Robot 1	Robot 2	Robot 3
Map 3	Nominal	10/10	$0.9$	$1.9$	$1.9$
	Low	9/10	$1.7\pm 0.1$	$4.5\pm 0.1$	$3.9\pm 0.8$
	High	8/10	$1.7\pm 0.2$	$2.4\pm 1.1$	$1.1\pm 0.7$
Map 4	Nominal	10/10	$2.5$	$7.0$	$7.5$
	Low	8/10	$2.6\pm 0.0$	$8.4\pm 0.0$	$9.6\pm 4.0$

Table 3: Koopman-NMPC Statistics for Formation Control.

Panel of Figure 5 — Figure 5: Sample formation control trajectories in Map 4 for (left) low-slip and (right) high-slip cases. The nominal case is not depicted for brevity but resembles the low-slip case, as in Map 3 (cf. Fig. 4 ). (Best viewed in color.)

Map	Slip	SR	mean $\pm$ SD final distance [ $\times 10^{-2}m$ ]
Map	Slip	SR	Robot 1	Robot 2	Robot 3
Map 3	Nominal	10/10	$0.5$	$1.0$	$1.1$
	Low	0/10	NaN	NaN	NaN
	High	0/10	NaN	NaN	NaN
Map 4	Nominal	10/10	$1.7$	$4.1$	$3.8$
	Low	4/10	$2.0\pm 0.1$	$3.7\pm 0.5$	$8.6\pm 1.6$

Table 4: Nominal NMPC Statistics for Formation Control.

Map	Slip	SR	mean $\pm$ SD final distance [ $\times 10^{-2}m$ ]
			Robot 1	Robot 2	Robot 3
Map 3	Nominal	10/10	$4.1$	$76.3$	$45.1$
	Low	9/10	4.1	$148.3\pm 63.0$	$50.3\pm 4.5$
	High	9/10	4.1	$158.3\pm 54.9$	$51.0\pm 12.1$
Map 4	Nominal	10/10	$7.4$	$71.4$	$82.6$
	Low	10/10	$7.4$	$69.5\pm 0.8$	$113.2\pm 66.2$

Table 5: Consensus-based Statistics for Formation Control.

Panel of Figure 6 — Figure 6: Sample formation control trajectories in Map 3 for the consensus-control method. (left) Ignoring collisions, consensus control provides well-matching trajectories. (right) When collision avoidance is enforced, the followers fail to reach their targets within the allotted time, even in the nominal (no slip) case. (Best viewed in color.)

Robot Navigation

Robot navigation studies how robots perceive, localize, plan, and move safely toward goals in static or changing environments.

See all 554 papers

RK-MPC: Residual Koopman Model Predictive Control for Quadruped Locomotion in Offroad Environments
Apr 5, 2026Sriram S. K. S. Narayanan, Umesh VaidyaModel Predictive Control Quadruped Locomotion
Department of Mechanical Engineering, Clemson University, Clemson, SC 29630, USA
Covariance-Regulated Recursive Koopman Learning for Nonlinear Systems with Uncertain Time-Varying Dynamics
Jun 13, 2026Weibin Gu, Chen Yang, Lu Shi +1Online System Identification Recursive Least Squares
1Tsinghua University, PR China · 2China University of Petroleum-Beijing at Karamay, PR China · 3Xinchen Qihang Inc., PR China
Safety-Critical Centralized Nonlinear MPC for Cooperative Payload Transportation by Two Quadrupedal Robots
Apr 3, 2026Ruturaj S. Sambhus, Yicheng Zeng, Kapi Ketan Mehta +2Multi-Robot Cargo Transportation Nonlinear MPC
R.S. Sambhus, Y. Zeng, K. K. Mehta, and K. Akbari Hamed are with the Department of Mechanical Engineering, Virginia Tech, Blacksburg, VA 24061, USA · J. Kim is with The University of Texas at El Paso, El Paso, TX 79968, USA

Apr 5, 2026J/K move · Enter open · S save

RK-MPC: Residual Koopman Model Predictive Control for Quadruped Locomotion in Offroad Environments

Sriram S. K. S. Narayanan, Umesh Vaidya

Department of Mechanical Engineering, Clemson University, Clemson, SC 29630, USA

Model Predictive Control Quadruped Locomotion Residual Dynamics Learning Koopman Operator Learning Terrain-Aware Robot Locomotion

Open paper AskPDF arXiv

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.

Abstract

Robot Navigation

Explore similar work

RK-MPC: Residual Koopman Model Predictive Control for Quadruped Locomotion in Offroad Environments

Covariance-Regulated Recursive Koopman Learning for Nonlinear Systems with Uncertain Time-Varying Dynamics

Safety-Critical Centralized Nonlinear MPC for Cooperative Payload Transportation by Two Quadrupedal Robots