ZiMPedance: Impedance-Aware ZMP Modeling and Control for Payload Carrying with Quadruped Robots

2026-06-17

AI Summary

This study addresses the challenge of oscillatory instability in quadrupedal robots carrying passively suspended loads, where dynamic coupling between the manipulator and payload threatens locomotion stability. The work proposes a novel approach that explicitly incorporates the stiffness, damping, and mass of the passive load interface into an extended Zero-Moment Point (ZMP) model, integrated within a single rigid-body dynamics framework and a model predictive control architecture to enable stable and efficient load-carrying locomotion. The method reveals critical risks associated with underdamped configurations and gait-induced harmonic resonance, while enabling accurate end-effector tracking without active actuation. Simulations demonstrate a tenfold reduction in stability violations (from 7.0% to 0.7%) and a 15% decrease in horizontal ground reaction forces. Physical experiments validate robustness under 2 kg payload conditions, successfully rejecting pull-and-release disturbances that cause baseline controllers to fail.

Abstract

Load transportation with quadruped robots is strongly affected by the dynamics of the physical interface between the robot and the load. Passive spring-based arms reduce weight and complexity compared to active manipulators, but their spring-damper dynamics can introduce oscillatory forces that degrade locomotion stability. This paper derives an extended Zero Moment Point (ZMP) formulation that includes passive payload-interface dynamics, relating stiffness, damping, and payload mass to the stability margin. The analysis shows that underdamped configurations can resonate with locomotion harmonics. Based on this insight, we augment a Single Rigid Body Dynamics model with passive subsystem dynamics and integrate it into a Model Predictive Control framework. In simulation, the proposed controller reduces stability violations by up to $10\times$, from $7.0\%$ to $0.7\%$, and increase locomotion efficiency by lowering horizontal ground reaction force effort by up to $15\%$ compared to a nominal baseline. Hardware experiments with a $2\,\mathrm{kg}$ payload show stable locomotion under pull-release disturbances where the nominal controller fails. The same model also enables end-effector tracking through passive arm dynamics without direct arm actuation.

Problem

• quadruped robots
• payload carrying
• passive interface dynamics
• locomotion stability
• oscillatory forces

Innovation

• impedance-aware control
• Zero Moment Point (ZMP)
• quadruped robot
• passive payload interface
• Model Predictive Control (MPC)