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Gait-Dependent Effects on Quadruped Locomotion for Load-Carrying using Passive Mechanism
Giovanni B. Dessy, Claudio Semini, Victor Barasuol
TL;DR
Quadruped payload carrying needs lightweight interfaces without losing locomotion stability, but passive-arm impedance couples payload dynamics to gait. This paper simulates damped and underdamped configurations across gaits and payloads, finding increased oscillations and possible ZMP-margin reduction for underdamped crawl locomotion, while treating trot only as a dynamic excitation case.
Problem
Passive interfaces could reduce the complexity and cost of actuated manipulators, but their impedance couples payload dynamics with locomotion and requires analysis across gait and payload conditions.
Method
The paper uses a fixed MPC controller to simulate damped and underdamped passive-arm configurations during flat-ground quadruped locomotion across gait and payload conditions.
Results
Underdamped impedance increases passive-joint oscillations and can reduce ZMP margin during crawl gaits, with effects depending on gait and payload; trot is evaluated only through passive-arm excitation.
Takeaways & Limitations
Passive-interface configuration and gait selection should be considered jointly when assessing payload-carrying locomotion.
Takeaways & Limitations
Trot is excluded from direct ZMP-margin comparison because diagonal support produces a degenerate two-point support region.
Abstract
from arXiv · showhide
Passive mechanical interfaces offer a lightweight alternative to actuated manipulators for quadruped payload carrying, but their impedance directly couples the payload dynamics with the locomotion pattern. This paper analyzes how passive-arm stiffness-damping selection affects payload-carrying locomotion under different gait and payload conditions. We compare damped and underdamped passive-arm impedance configurations in simulation during flat-ground locomotion. For crawl gaits, where the support polygon remains well defined, the results show that underdamped impedance increases passive-joint oscillations and can reduce the ZMP margin with respect to the support polygon. Trot is retained as a dynamic excitation case for the passive arm, but it is not used for direct ZMP-margin stability comparison. The results are summarized in gait-payload-stiffness-damping maps, where ZMP-margin reduction is evaluated for crawl gaits and trot is retained only as a passive-arm excitation case.
1 Introduction and Related Work
Quadruped payload carrying needs locomotion stability during physical interaction, while passive interfaces trade active-manipulation versatility for lower mechanical and control complexity. The paper analyzes how such interfaces couple payload motion to locomotion and summarizes the study’s contributions.
- Payload carrying requires quadrupeds to maintain locomotion stability while exchanging forces with carried loads or collaborating partners.
- Active manipulators enable versatile force regulation but increase mechanical complexity, mass, power consumption, control requirements, and cost.
- Non-dexterous interfaces reduce reliance on fully actuated arms but couple robot motion with payload motion, so the load is not always a static attached mass.
- The paper analyzes passive-arm stiffness-damping effects and quantifies passive-joint oscillations and crawl-gait ZMP-margin metrics across gait, payload, and configuration.
- The results are summarized in gait-payload-stiffness-damping maps that identify configurations with small ZMP-margin changes and larger underdamped losses.
2 Passive Payload Coupling Model
The paper models a lightweight passive arm as a compliant interface between a quadruped base and carried payload, linking gait-induced relative motion to interaction forces and ZMP-margin behavior. It evaluates this coupling with a fixed MPC controller and support-polygon stability metric.
- 2.1 Passive arm mechanism: The passive arm is a 3-DoF yaw-pitch-pitch mechanism whose unactuated motion arises from rigid-body coupling, elastic elements, and damping.
- 2.1 Passive arm mechanism: The passive arm permits payload-base relative motion, with stiffness governing restoring behavior and damping attenuating gait-induced oscillations.
- 2.2 Equivalent horizontal coupling model: The passive arm-payload subsystem is approximated as a two-dimensional Cartesian spring-damper interface in the horizontal plane.
- 2.2 Equivalent horizontal coupling model: Horizontal payload-base displacement is transformed through equivalent stiffness and damping into interaction forces whose variation can affect locomotion stability margins.
- 2.3 Interaction and ZMP-margin metrics: The unchanged MPC uses an SRBD model accounting for the passive-arm interaction wrench, while ZMP margin measures signed distance from the ZMP to the support-polygon boundary.
- 2.3 Interaction and ZMP-margin metrics: The evaluated chain is gait → ∆xxy → fxy → mzmp, connecting gait-induced relative motion to interface forces and ZMP-margin behavior.
3 Simulation Protocol
The simulation varies gait, payload mass, and passive-arm impedance while keeping the platform, controller, and locomotion command fixed. Crawl gaits support consistent ZMP-margin evaluation, whereas trot serves as a dynamic reference case because its support degenerates to a two-point line.
- Platform and controller: The simulations use a 23 kg Aliengo with a 1.5 kg passive arm in MuJoCo, under fixed flat-ground commands of 0.1 m/s forward velocity and zero yaw rate.Each run lasts 60 s, and the controller and nominal carrying configuration remain fixed across conditions.
- Gaits: Crawl gaits are the main ZMP-margin comparison because their contact sequences maintain at least three feet on the ground and provide a finite support polygon.Trot is retained as an additional dynamic reference, but its diagonal support phase forms a two-point line that limits direct ZMP-margin comparison.
- Passive-arm configurations: The damped and underdamped configurations differ primarily through reduced q1 and q3 stiffness and damping in the underdamped case, while q2 damping remains unchanged.The q2 stiffness is selected according to payload mass, and Table 1 summarizes the joint parameters.
- Assessment matrix: The protocol evaluates four gaits, four payload conditions, and two passive-arm configurations, with each test repeated three times.The gait set comprises three crawl patterns and trot; payloads are no-load, 1 kg, 2 kg, and 5 kg.
- Metrics: The analysis logs base, payload, passive-joint, force, and ZMP-margin signals after discarding the initial transient.Joint oscillation RMS is computed for q1, q2, and q3 after subtracting each joint’s post-settling reference value.
- Metrics: ZMP evaluation uses mean and minimum margin, time below 0.04 m, and time below zero, with 0.04 m treated as a diagnostic threshold rather than a hard stability limit.The horizontal-arm index A13 summarizes motion associated with horizontal payload-base coupling and excludes q2.
4 Results
Underdamped passive-arm impedance increases arm oscillations and can reduce crawl-gait ZMP margins, with effects varying by gait and payload. Trot is treated as an excitation case rather than compared through ZMP-margin stability.
- 4.1 ZMP-margin degradation: CC shows the largest increase in near-threshold ZMP-margin time at 5 kg, whereas CDC remains least sensitive among crawl gaits.The near-threshold condition is mzmp < 0.04 m.
- 4.1 ZMP-margin degradation: Trot is excluded from direct ZMP-margin comparison because its diagonal support phase produces a degenerate support region, so it is evaluated only through passive-arm oscillation metrics.Crawl gaits retain finite support polygons for the ZMP-margin analysis.
- 4.1 ZMP-margin degradation: Negative ZMP-margin events remain close to zero at low payloads and become relevant mainly in underdamped, high-payload crawl cases.The negative-margin metric is defined by mzmp < 0.
- 4.2 Passive-arm motion: At 2 kg, underdamping increases the combined q1 and q3 oscillation index by approximately 0.155 rad for BDC, 0.196 rad for CDC, 0.214 rad for CC, and 0.133 rad for trot.CC has the largest arm-oscillation increase among crawl gaits, while CDC has much smaller ZMP-margin degradation despite comparable oscillation.
- 4.3 Gait-payload-stiffness-damping design map: Underdamped impedance increases passive-arm oscillations, while its ZMP-margin impact varies across gait and payload conditions.The design maps compare underdamped with damped behavior across gait-payload-stiffness-damping combinations.
5 Conclusion
The analysis shows that passive-arm impedance, gait, and payload jointly shape oscillations and ZMP-margin behavior. Crawl gaits support direct stability comparison, while trot is retained as a dynamic excitation case rather than a ZMP-margin comparison.
- Reducing passive-arm stiffness and damping increases arm oscillations and can reduce the available ZMP margin, with effects dependent on gait and payload.The study compares damped and underdamped configurations in flat-ground simulation.
- Crawl-gait results: Among crawl gaits, CDC has the smallest increase near the support-polygon boundary, CC the largest near-threshold ZMP-margin increase, and BDC the largest increase in negative-margin events at high payload.
- Trot: Trot is retained for passive-arm dynamic excitation but excluded from direct ZMP-margin stability comparison because diagonal support creates a two-point support region.
- The gait-payload-stiffness-damping map indicates that passive-interface configuration and gait selection should be considered jointly.The authors propose broader impedance studies, analytical modeling, impedance-aware predictive control, and hardware validation as future work.