Safety-Filtered Distributed Koopman-MPC

Shengjun Zhang; Wenhao Li; Zhenxin Lin; Zhenglong Sun

cs.ROSep 23, 2026

Safety-Filtered Distributed Koopman-MPC

Authors: Shengjun Zhang, Wenhao Li, Zhenxin Lin, Zhenglong Sun

Organizations: School of Artificial Intelligence, Hubei University, Wuhan, Hubei, 430061 China · Shenzhen Institute of Artificial Intelligence and Robotics for Society (AIRS), Shenzhen, Guangdong, China · School of Science and Engineering, The Chinese University of Hong Kong, Shenzhen (CUHK-Shenzhen), Shenzhen, Guangdong, China · Manchester Metropolitan Joint Institute, Hubei University, Wuhan, China

Abstract

Distributed model predictive control (DMPC) often constructs both predictions and collision constraints from neighbor trajectories, so packet loss can remove both. We separate these roles: received trajectories drive Koopman-MPC, while local sensing and shelf geometry define a hard-constrained quadratic program (QP) that projects the applied input. Its radial demand is the least constant acceleration that keeps a supporting-plane clearance nonnegative throughout one zero-order-hold interval. Complementary pair rows recover the coupled demand without exchanging safety decisions. We give an intersample separation theorem under bounded snapshot and directional plant errors, an exact max-min test for simultaneous local feasibility, and a sensing-radius condition for switching interaction graphs. Anticipatory high-order rows may be relaxed for performance, but the finite-hold rows contain no safety slack. Matched eight-robot warehouse simulations use a frozen Koopman model, nonlinear drift, bounded inputs and speed, shelf constraints, a 120 ms control period, and packet dropout. The full controller is collision-free in 20/20 matched trials and reaches 160/160 robot goals; predictive Koopman-MPC without the final projection is collision-free in 1/20 trials. All 38,400 full-method hard-row sets pass the online feasibility test, and every local QP solves. Five-stream fleet sweeps are collision-free and hard-row feasible through 16 robots; the 20-robot boundary fails only after the online margin turns negative, while the reconstructed per-agent critical path remains below the sampling period. Bounded-sensing and differential-drive tests provide additional deployment stress.

Figures & tables

Method	Safety decision	Online coupling and role
ORCA [ 2 ]	preferred velocity	one-shot reciprocal velocity half-planes; reactive avoidance
PSF [ 25 ]	backup horizon	model-based predictive backup and recovery
CBF-DMPC [ 14 ]	state–input horizon	iterative node–edge consensus toward a coupled solution
Ours	held acceleration	independent local QPs; hard finite-hold row and exact local feasibility test

TABLE I: Comparison of online safety mechanisms.

Fig. 1: Controller architecture. Each robot solves a Koopman-MPC from received trajectories, followed by an independent reciprocal QP from local sensing. Packet loss can change the nominal input but does not remove a finite-hold row for a sensed pair.

Fig. 2: Eight-robot warehouse benchmark. Circles and crosses are starts and goals; gray rectangles are shelves. Dashed and dotted neighborhoods illustrate trajectory communication and local safety sensing.

Parameter	Value
$N$ , $T$ , steps	8, $0.12~\mathrm{s}$ , 240
MPC horizon, $d_{\rm plan}$	8, $0.76~\mathrm{m}$
$R_{\rm comm}$ , $R_{\rm sens}$	$3.0~\mathrm{m}$ , $3.0~\mathrm{m}$
Main dropout	0.05, 0.15
$d_{\rm col}$ , $r_{\rm rob}$	$0.45~\mathrm{m}$ , $0.22~\mathrm{m}$
$k_{v}$ , $k_{p}$	5, 6

TABLE II: Main simulation parameters.

Method	Safe	Robot	Shelf	Goals	Error	$d_{\min}$	Shelf
	/20	coll.	coll.	/160	$[\mathrm{m}]$	$[\mathrm{m}]$	$[\mathrm{m}]$
ORCA	0	12.0	63.0	160	0.631	0.288	0.125
Goal + filter	20	0.0	0.0	120	2.031	0.502	0.224
Predictive MPC	1	1.3	6.2	160	0.0065	0.264	$-0.379$
Ours	20	0.0	0.0	160	0.0065	0.676	0.321

TABLE III: Fixed warehouse over dropout

\{0.05,0.15\}

and ten matched streams per level. Collision columns are mean fleet time steps per trial.

Fig. 3: Representative matched trial at 15% dropout (packet stream seed 3409652536). Lines are executed trajectories, colored dots are starts, black crosses are goals, and rectangles are shelves; Table III reports all 20 trials.

Fig. 4: Fixed-footprint fleet scaling at 15% dropout, with five packet streams per size. (a) Bars count safe and feasible trials; the line is completed robots divided by fleet size. (b) Worst online feasibility and finite-hold margins. (c) Central sequential workload and the reconstructed per-agent critical path; the dotted line is the

120~\mathrm{ms}

period.

Study	Safe	Goals	$\min\mu_{i}$	$\min L_{ij}$
Dropout 0.50	10/10	80/80	4.130	0.036
$R_{\rm sens}=3.0$ m	10/10	80/80	11.760	0.148
$\varepsilon^{p}\leq 2$ cm	15/15	120/120	7.214	0.087
Perturbed shelves	19/20	160/160	$-0.756$	$-0.030$
Scaling, $N\leq 16$	20/20	199/200	1.496	$\approx 0$
Diff. drive, $N=4$	20/20	80/80	3.388	0.028

TABLE IV: Frozen-model stress tests (

\mu_{i}

\mathrm{m/s^{2}}

L_{ij}

in m); negative

\mu_{i}

removes the theorem’s premise.

Model Predictive Control

Model Predictive Control optimizes future actions with a system model, repeatedly applying the first action as new information arrives.

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ADMM-Based Safety-Critical Distributed NMPC for Cooperative Transportation by Quadrupedal Robots

Ruturaj S. Sambhus, Kapi Ketan Mehta, Yicheng Zeng, Kaveh Akbari Hamed

Department of Mechanical Engineering, Virginia Tech, Blacksburg, VA 24061, USA

Multi-Agent Coordination Nonlinear MPC Multi-Robot Coordination

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This paper presents a safety-critical distributed nonlinear model predictive control (DNMPC) framework for cooperative payload transportation by teams of quadrupedal robots. The proposed approach models the robotic team and the shared payload as a dynamically coupled networked system with rigid holonomic coupling constraints arising from cooperative transportation. To enable distributed real-time optimization, the centralized finite-horizon optimal control problem is decomposed into parallel local NMPC subproblems coordinated through the alternating direction method of multipliers (ADMM). The resulting distributed framework enforces consensus over both payload-state and interaction-wrench trajectories while explicitly incorporating acceleration-level holonomic coupling constraints within the distributed predictive control formulation. Safety-critical obstacle avoidance constraints for both the robotic agents and payload are enforced using higher-order control barrier functions (HOCBFs). The framework is validated through numerical simulations with teams of two, three, and four quadrupedal robots transporting shared payloads in cluttered environments. Real-time experiments on two- and three-robot teams demonstrate safe and robust transportation under payload uncertainty and external disturbances. Compared with centralized NMPC, the proposed framework achieves up to 23% reduction in average NLP solve time while maintaining comparable closed-loop performance. Ablation studies further demonstrate robustness to communication delays and show that explicit payload-state consensus and holonomic constraints substantially improve payload tracking and distributed coordination over existing wrench-only consensus formulations.

Abstract

Model Predictive Control

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