Duty Factor Predicts Robust Constrained Quadrupedal Locomotion Across Gait Types
Authors: James Zhu, David Ologan, George Ortiz, Thomas Chun Fai Lee, Selvin Garcia Gonzalez, Ardalan Tajbakhsh, Pinhas Ben-Tzvi, Aaron M. Johnson
Organizations: Department of Electrical and Computer Engineering, University of Miami, Coral Gables, FL, USA · Department of Mechanical Engineering, 3 Robotics Institute, Carnegie Mellon University, Pittsburgh, PA, USA
Quadrupedal robots are increasingly deployed in environments where locomotion must remain robust to disturbances and constrained terrain. Gait type, such as walking or trotting, is commonly used to characterize quadrupedal locomotion. However, gait type does not uniquely define locomotion, as parameters such as duty factor, speed, and stance width can vary within a single gait type. In this work, we investigate the relationship between these gait parameters using three distinct quadrupedal locomotion control approaches. First, using whole body trajectory optimization with LQR feedback, we show that duty factor is a stronger predictor of local error convergence than nominal gait type. Second, we investigate duty factor selection with a learned locomotion controller, suggesting how duty factor may serve as a low-dimensional parameter for adapting locomotion robustness in narrow-terrain environments. Finally, we show that these trends persist under a centroidal model predictive control framework and validate them through narrow-terrain experiments on a physical quadruped. These results show that duty factor provides a simple and effective basis for understanding and selecting robust quadrupedal locomotion across gait types and control architectures.
Figures & tables
Fig. 1 : In this work, we demonstrate that the robustness of quadruped locomotion improves with an increase in duty factor. This finding is validated with the first demonstration of a quadruped robot walking across a narrow beam without the aid of external mechanisms like a reaction wheel.
Investigation
Planning/Control Architecture
Robot Model
Evaluation Environment
1
Whole-Body Optimization w/ LQR Feedback
Ghost Spirit 40
Pinocchio
2
Gait-Conditioned RL
Unitree Go2
NVIDIA Isaac Sim
3
Centroidal MPC
Unitree Go2
Hardware
TABLE I : Across three control architectures, two quadruped robot models, and three different evaluation environments in both simulation and hardware, we find consistent evidence that duty factor, as opposed to gait type, is a primary parameter that determines robustness of quadrupedal locomotion.
Predictor
Estimate β
Standard Error
p -value
Gait (Walk)
0.3867
0.221
8.82 ⋅ 10 -2
Speed
0.646
0.111
1.21 ⋅ 10 -6
Stance Width
-0.312
0.112
8.42 ⋅ 10 -3
TABLE II : Linear regression predicting convergence for walking and trotting gaits at matched DF=0.75.
Fig. 2 : Convergence across walking and trotting gaits over a range of speeds and duty factors. Walking and trotting exhibit a continuous transition at the matched duty factor of 0.75 . Overall, convergence is strongly associated with duty factor.
Predictor
Estimate β
Standard Error
p -value
Duty Factor
-0.677
0.0863
1.42 ⋅ 10 -10
Speed
0.262
0.0853
3.29 ⋅ 10 -3
Stance Width
-0.0621
0.0791
4.35 ⋅ 10 -1
TABLE III : Linear regression predicting convergence for walking and trotting gaits over a range of duty factors, speeds, and stance widths.
Fig. 3 : Across both trot and walk gaits, success rate of simulated trials increases with duty factor.
Fig. 4 : The duty factor selector network shows a trend of selecting higher duty factors as stance width narrows. Plot shows mean values and shaded regions represent minimum and maximum chosen values at each stance width.
Gait Type
Duty Factor
Speed (m/s)
Success Rate
Trot
0.5
0.3
4/5
0.4
4/5
0.5
4/5
Trot
0.75
0.3
5/5
0.4
5/5
0.5
5/5
TABLE IV : At the duty factor of 0.75, the trot and walk both achieved 100% success on the hardware experiment. The lower duty factor trot experienced several failures.
School of Engineering and Applied Science, University of Pennsylvania, Philadelphia, PA 19104, USA · Department of Aeronautics & Astronautics, Stanford University, Stanford, CA 94305, USA