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SAC-Loco: Safe and Adjustable Compliant Quadrupedal Locomotion
Aoqian Zhang, Zixuan Zhuang, Chunzheng Wang, Shuzhi Sam Ge, Fan Shi, Cheng Xiang
TL;DR
Quadruped controllers often lack diverse adjustable compliance while maintaining stability under external forces. SAC-Loco combines adjustable compliant locomotion with recovery and safety monitoring. In hardware pulls, SAC-Loco had 0 failures, while HAC-Loco and FACET experienced failures at average peak forces of 120.4 N and 193.8 N, respectively.
Problem
Existing quadruped controllers often lack diverse responses to external forces while maintaining stability, and robust adaptive responses remain challenging.
Source: §I · p. 1Method
SAC-Loco combines a teacher-student force-compliant policy, a capture-point-based recovery policy, and a learned safety critic, without requiring explicit force sensing for compliant-policy deployment.
Source: §I · p. 1Results
In hardware pulls, SAC-Loco had 0 failures; HAC-Loco and FACET averaged peak forces of 120.4 N and 193.8 N among their five collected failures each.
Source: §V · p. 8Takeaways & Limitations
The authors report that SAC-Loco broadens quadruped compliance and safety across a wider range of external forces, supported by simulation and hardware experiments.
Source: §VI · p. 8
Abstract
from arXiv · showhide
Quadruped robots are designed to achieve agile and robust locomotion by drawing inspiration from legged animals. However, most existing control methods for quadruped robots lack a key capacity observed in animals: the ability to exhibit diverse compliance behaviors while ensuring stability when experiencing external forces. In particular, achieving adjustable compliance while maintaining robust safety under force disturbances remains a significant challenge. In this work, we propose a safety aware compliant locomotion framework that integrates adjustable disturbance compliance with robust failure prevention. We first train a force compliant policy with adjustable compliance levels using a teacher student reinforcement learning framework, allowing deployment without explicit force sensing. To handle disturbances beyond the limits of compliant control, we develop a safety oriented policy for rapid recovery and stabilization. Finally, we introduce a learned safety critic that monitors the robot's safety in real time and coordinates between compliant locomotion and recovery behaviors. Together, this framework enables quadruped robots to achieve smooth force compliance and robust safety under a wide range of external force disturbances.
I. INTRODUCTION
The paper addresses the challenge of giving quadruped robots adjustable responses to external forces without sacrificing stability. SAC-Loco combines compliant locomotion with recovery and safety monitoring.
I. INTRODUCTION
- Existing controllers often prioritize strict task execution, while diverse responses to large or prolonged disturbances remain challenging.The paper identifies adjustable resistance or yielding while maintaining stability as a needed capability.Source: §I · p. 1
- SAC-Loco integrates a force-compliant policy, a recovery policy for large disturbances, and a learned critic that monitors safety.The critic supports smooth compliance in safe interactions and timely recovery when destabilized.Source: §I · p. 1
- The teacher-student framework trains adjustable force compliance for deployment without explicit force sensing.The safe policy uses capture-point dynamics for recovery and stabilization.Source: §I · p. 1
- Extensive simulation and hardware experiments validate the proposed method's effectiveness.Source: §I · p. 1
II. RELATED WORKS
The related-work discussion describes limits in force tolerance, gait flexibility, and adjustable compliance. SAC-Loco uses separate compliant and recovery policies, with a problem formulation that shifts from velocity tracking to stabilization when disturbances become unsafe.
II. RELATED WORKS
- Model-based approaches are described as limited to perturbations below 50N and pre-defined, low-speed gaits; one adjustable-compliance approach loses success above 500N.The related-work discussion also notes limitations in fixed compliance and the need to retrain some high-level policies to change compliance.Source: §II · p. 2
III. METHODS
- The framework comprises an adjustable-compliance policy, a safe recovery policy, and a critic that activates recovery when needed.Source: §III · p. 2
A. Problem Formulation
- The controller tracks commanded velocities while tuning compliance, then shifts to balance restoration when a disturbance may drive the robot into an unsafe state.Commands include linear and angular velocity and a tunable compliance parameter; failure is defined as base contact with the ground or falling over.Source: A. Problem Formulation · p. 2
B. Compliant Policy Training
The compliant-policy training uses a desired velocity to express adjustable responses to external forces. A privileged-observation teacher is distilled into a student policy for deployment using observable robot state.
B. Compliant Policy Training
- The teacher force-compliant policy is trained with privileged simulation observations to track the desired velocity produced for compliance.Velocity-tracking rewards support following that target, with regularization for stable posture and smooth joint actions.Source: B. Compliant Policy Training · p. 3
- The student policy uses observable states and a 20-step observation history to compensate for missing privileged information.Source: B. Compliant Policy Training · p. 3
- PPO distillation matches student actions to teacher actions, while additional rewards guide early exploration toward teacher-like actions.Source: B. Compliant Policy Training · p. 3
- Asymmetric PPO gives the critic privileged observations during training.Source: B. Compliant Policy Training · p. 3
C. Safe Policy Training
The safe policy is trained to restore balance under large disturbances by repositioning the support polygon centroid toward a Corrected Capture Point. It also learns to orient the robot toward the disturbance, using its stronger longitudinal force capacity to manage lateral forces.
C. Safe Policy Training
- The safe policy aims to prevent failure under large force disturbances by actively restoring the robot’s balance.The Corrected Capture Point specifies the required planar displacement of the support polygon centroid to neutralize external forces.Source: C. Safe Policy Training · p. 3
- The robot’s structural anisotropy lets it sustain larger longitudinal than lateral forces, motivating alignment of its x-axis with the disturbance.For forces toward the front the robot faces the force; for rearward forces it aligns its tail, converting lateral disturbances into longitudinal ones.Source: C. Safe Policy Training · p. 4
- Training proceeds from randomized pose tracking to disturbance recovery, where the policy tracks offsets computed from the force and target pose.Stage I samples target position offsets from −3 m to 3 m and yaw offsets from −π to π radians; Stage II applies external forces.Source: C. Safe Policy Training · p. 4
- The trained teacher safe policy is distilled into a student safe policy using the same method as the compliant policy.Source: C. Safe Policy Training · p. 4
D. Safety Critic Training
The safety critic uses compliant-policy failures to build an unsafe-state dataset and assess whether the safe policy can recover from those states. The dataset also supplies dangerous-state initializations during safe-policy training.
D. Safety Critic Training
- The critic evaluates observations in real time to support switching from compliant locomotion to the safe policy before failure.It uses information from both policies during training, unlike approaches based on fixed switching rules or a single policy.Source: D. Safety Critic Training · p. 4
- The unsafe dataset contains the 150 privileged observations preceding each compliant-policy failure in simulation.Source: D. Safety Critic Training · p. 4
- Unsafe observations initialize safe-policy training and later test whether the trained policy can recover the robot.Source: D. Safety Critic Training · p. 4
E. Training details
Policies are trained in Isaac Gym with parallel environments and PPO, while curriculum learning increases command and disturbance magnitudes. Dynamics uncertainty and sensor noise are included to reduce the simulation-to-real gap.
E. Training details
- All policies use PPO in Isaac Gym with 4,096 environments running in parallel.Source: E. Training details · p. 4
- Policy networks are MLPs with hidden layers of 512, 256, and 128 units; the safety critic uses a two-layer GRU with 256 hidden units and an MLP head.The critic head has layers of 128 and 64 units.Source: E. Training details · pp. 4–5
- Curriculum learning gradually increases command velocity and external force and torque magnitudes.Source: E. Training details · p. 5
- Each episode applies four disturbances at random timesteps, with randomized impact durations, dynamics uncertainties, and sensor noise.The randomization details are listed in Table III.Source: E. Training details · p. 5
IV. SIMULATION EXPERIMENTS
The simulation experiments assess adjustable compliance, recovery, success, and power, and compare SAC-Loco with HAC-Loco and FACET. The stated evaluation questions also cover the safety threshold and teacher-student training framework.
IV. SIMULATION EXPERIMENTS
- The experiments ask whether the switched-policy method provides adjustable compliance and safety across disturbances, and examine threshold, distillation, and baseline-comparison effects.Source: §IV · p. 5
A. Metrics and Baselines
- The effective compliance range ΔC is the difference between the highest- and lowest-setting directional compliance; larger ΔC means a wider achievable range.Directional effective compliance quantifies velocity response along the applied force.Source: A. Metrics and Baselines · p. 5
- Command velocity tracking error is averaged over force-free timesteps; lower error indicates faster recovery to the commanded velocity.Source: A. Metrics and Baselines · p. 5
- Success rate measures the percentage of disturbance occurrences after which the robot maintains locomotion without failure.Source: A. Metrics and Baselines · p. 5
- The comparison uses HAC-Loco and FACET, with both baselines re-implemented under the same disturbance settings as SAC-Loco.HAC-Loco uses β = 10 and β = 1000 as its highest and lowest compliance settings; FACET uses Kp = 0, Kd = 4 and Kp = 48, Kd = 13.85.Source: A. Metrics and Baselines · p. 5
B. Evaluation on compliance and safety
SAC-Loco increases compliance with its adjustable parameter and outperforms the baselines on safety across tested force disturbances. Its safety gains come with faster restoration of velocity tracking and generally lower power use.
B. Evaluation on compliance and safety
- Average effective compliance C increases monotonically with compliance parameter k across the three tested force ranges.The increase becomes less pronounced at higher compliance because of the robot’s maximum velocity limits.Source: B. Evaluation on compliance and safety · p. 5, Figure 4 · p. 6
- SAC-Loco consistently achieves higher success rates than the baselines across tested force disturbances.It also uses less power except when force exceeds 400 N and achieves lower velocity-tracking error, indicating faster restoration from compliance to tracking.Source: Table IV · p. 6, B. Evaluation on compliance and safety · p. 6, Figure 4 · p. 6
- SAC-Loco achieves a larger compliance range ΔC than HAC-Loco and FACET.This indicates a wider range of achievable compliance behaviors.Source: Figure 4 · p. 6
- SAC-Loco maintains more uniform success rates across force directions and higher rates under larger forces and longer impacts than HAC-Loco and FACET.HAC-Loco drops under lateral forces and larger magnitudes, while FACET also declines under lateral forces and longer impacts.Source: B. Evaluation on compliance and safety · p. 6, Figure 4 · p. 6
C. Effect of different ϵ for policy switching ϵ
The safety-critic threshold has little effect under moderate disturbances, but raising it improves safety under stronger forces with only marginal increases in tracking error and motor power. A sinusoidal-force test also compares teacher and student velocity responses at different compliance settings.
C. Effect of different ϵ for policy switching ϵ
- The threshold-sensitivity evaluation varies ϵ from 0 to 0.9 and measures success rate, motor power, and velocity-tracking error.Each threshold is tested over 40,000 episodes.Source: C. Effect of different ϵ for policy… · p. 6
- For |F| > 200 N, increasing threshold ϵ improves success rate, while causing only marginal increases in velocity-tracking error and motor power.At |F| < 200 N, performance is insensitive to ϵ, suggesting the safe policy is rarely activated under moderate disturbance.Source: C. Effect of different ϵ for policy… · p. 6
- The velocity test plots robot response to Fx = Fy = 100sin(0.5t) at different compliance parameters, with teacher shown dashed and student solid.Source: Figure 6 · p. 7
D. Policy distillation performance
Policy distillation preserves compliance and recovery capabilities while removing reliance on privileged force information. Ablations identify distinct roles for teacher guidance, capture-point recovery, and safety-critic switching.
D. Policy distillation performance
- The student policy performs slightly below the teacher but tracks desired velocity under sinusoidal force with small errors at different compliance levels.The results support distillation for deployment without privileged force information while preserving compliance and recovery capabilities.Source: D. Policy distillation performance · p. 7
E. Ablation studies on SAC-Loco
- Without teacher guidance, the compliance policy cannot track desired velocity and the recovery policy cannot recover because force and desired velocity are unobservable, increasing failures, tracking error, and power use.Source: E. Ablation studies on SAC-Loco · p. 7
- Removing corrected capture-point dynamics from safe-policy training drastically decreases success rate.Source: E. Ablation studies on SAC-Loco · p. 7
- Replacing the safety critic with a rule-based switch based on angular velocity also increases failures.The example cases show the critic switching to recovery below ϵ = 0.9 and returning to compliance after safety output rises above 0.9.Source: E. Ablation studies on SAC-Loco · p. 7, Figure 7 · p. 7
V. HARDWARE DEPLOYMENT
Hardware tests demonstrate adjustable pulling behavior, recovery during force-induced balance loss, and stable locomotion against substantial pulls. The conclusion presents SAC-Loco as a controller for adjustable compliant tracking and robustness to large impulses.
V. HARDWARE DEPLOYMENT
- Adjusting compliance parameter k varies the pulling speed when the robot pulls an approximately 70 kg chair and seated person at a 0.6 m/s command.The robot pulls the chair at lower speed as k increases.Source: §V · pp. 7–8, Figure 8 · p. 8
- Under deliberate rope-pull disturbances measured by a digital force gauge, HAC-Loco averaged 120.4 N and FACET 193.8 N across five failures each, while SAC-Loco had zero failures in the experiment.In two examples, the robot promptly switches from πcomply to πsafe to restore balance; it turns its head or tail to align with force toward that end.Source: §V · p. 8
- At a maximum velocity command of 2.5 m/s with k = 0, SAC-Loco sustained forward and backward pulls of 10.54 kg and 10.45 kg, versus FACET’s 7.5 kg and 10 kg.Source: §V · p. 8
VI. CONCLUSION
- The conclusion characterizes SAC-Loco as providing adjustable compliant velocity tracking under external disturbances and robustness against large impulses.It identifies adaptive compliance across environments and safety integration into highly dynamic maneuvers as future research directions.Source: §VI · p. 8