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

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

Abstract

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.

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

Abstract

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.

Paper Structure

This paper contains 10 sections, 1 theorem, 21 equations, 8 figures, 1 table.

Table of Contents

  1. Introduction
  2. Related Work
  3. Contributions
  4. Interconnected Dynamical Model
  5. CBFs for the Interconnected System
  6. CBF-based Centralized NMPC
  7. Experiments
  8. Setup and Controller Synthesis
  9. Hardware Experiments
  10. Conclusions

Key Result

Theorem 1

Let $h : \mathcal{X}^{\textrm{global}} \rightarrow \mathbb{R}$ be a continuous HOCBF of relative degree $r$ defined on $\bigcap_{j=0}^{r-1}\mathcal{S}_{j}$. If there exists a control input $u(t) \in \mathcal{U}^{\textrm{global}}$ satisfying the HOCBF condition eq:hocbf_condition for all $x(t) \in \b

Figures (8)

  • Figure A1: Snapshot of two Unitree Go2 quadrupedal robots cooperatively transporting a shared payload using the proposed CBF-based centralized NMPC framework in a cluttered environment with cylindrical obstacles. The framework autonomously adjusts the orientations of the robots and the payload to avoid collisions while maintaining safe and stable transportation.
  • Figure A2: Overview of the proposed layered control framework. The high-level CBF-based NMPC computes optimal trajectories for the interconnected robot–payload SRB system under holonomic constraints, while low-level nonlinear whole-body controllers enforce full-order robot dynamics.
  • Figure B1: Illustration of the interconnected SRB model of the robotic agents and the shared payload, showing the rigid holonomic coupling constraints and interaction wrenches.
  • Figure B2: Illustration of the rigid mechanism between the robots and the payload, with additional masses placed in the basket. The connection enforces translational rigidity, restricts relative roll and pitch motions, and allows relative yaw motion between the robots and the payload.
  • Figure E1: Snapshots of all experiments: (a) Experiment 1 with a nominal payload of 5 kg; (b) Experiment 2 with an unmodeled payload of 11.2 kg; (c) Experiment 3 with an unmodeled payload of 11.2 kg under external push disturbances; and (d)–(e) Experiment 4 with different obstacle layouts.
  • ...and 3 more figures

Theorems & Definitions (4)

  • Remark 1
  • Definition 1: Discrete-Time CBF DT-HOCBF
  • Definition 2: Higher-Order Discrete-Time CBF DT-HOCBF
  • Theorem 1: HOCBF Condition DT-HOCBF