ZiMPedance: Impedance-Aware ZMP Modeling and Control for Payload Carrying with Quadruped Robots
For quadruped robot locomotion with passive payload interfaces, this work provides a method to mitigate stability issues caused by underdamped dynamics, enabling more reliable load transportation.
This paper addresses the challenge of payload carrying with quadruped robots using passive spring-based arms, which introduce oscillatory forces that degrade stability. The authors derive an extended ZMP formulation incorporating passive dynamics and integrate it into a Model Predictive Control framework, achieving up to 10x reduction in stability violations and 15% lower horizontal ground reaction force effort in simulation, with successful hardware experiments under disturbances.
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.