Gait-Dependent Effects on Quadruped Locomotion for Load-Carrying using Passive Mechanism

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.

LIPM is everywhere in legged-locomotion control, but almost always as a modeling choice rather than as something the controller's cost actually prefers. This note tries to make that link more explicit. Working from a small centroidal OCP that penalizes the rate of angular momentum, we look at what its optimum tends to look like. Three things come out. With full-rank stance, the optimum drifts toward a pendular force pattern at a rate determined by the SVD of the moment Jacobian; the constant is set by foot-span geometry and matches the experiments to within 16%. With N=2 stance, as in trot, the friction cone introduces a lower bound on $\|\dot{H}_G\|$ that no amount of weight tuning fixes; we also see a non-smooth feasibility kink at a critical horizontal acceleration that we can write in closed form. Adding a task term that asks for a nonzero $\dot{H}_G$ moves the optimum off the pendular set in a predictable way. None of this is far from the classical ZMP/DCM picture. We test these claims on a point-mass quadruped and on the Unitree Go1 in MuJoCo (open-loop QP and a torque-level closed-loop controller), and we note where the asymptotic story stops being a good description of what the closed loop actually does.

Locomotion in microgravity often relies on sparsely and irregularly arranged anchors, motivating grasp-based mobility with multiple limbs. In this setting, dynamic locomotion is feasible only through deliberate regulation of both anchored interactions and whole-body coordination under coupled dynamic and kinematic constraints. This paper presents design insights for grasp-based dynamic locomotion with multi-limbed robotic systems in microgravity, targeting scenarios that require 6D limb manipulation to establish contacts with candidate anchors. The investigated design parameters include gait pattern, stride length, locomotion speed, and nominal posture. A parameterizable locomotion planning framework is proposed to support variations of these parameters and to evaluate the resulting locomotion performance in terms of stability and actuation demand. Two representative quadruped morphologies are adopted for evaluation in physics-based simulation. The results demonstrate that enlarging the feasible contact wrench space and attenuating impulsive whole-body dynamics improve locomotion performance. These findings inform strategies for contact configuration selection and whole-body coordination in microgravity locomotion with multi-limbed systems.