HIP: Hybrid Impedance and PD Control for Adaptive and Compliant Locomotion in Quadruped Robots

Deep reinforcement learning has enabled quadrupedal robots to traverse challenging terrains, yet energy efficiency remains a limiting factor for prolonged autonomous operation. Most existing frameworks rely on fixed or adaptively tuned proportional-derivative (PD) controllers that operate exclusively in the joint space. Such approaches typically lack an explicit mechanism for contact compliance, often applying excessive torque on benign terrains while providing insufficient absorption of reaction forces on irregular surfaces. To address these limitations, we propose HIP, a hybrid impedance and PD control framework that fuses joint-space PD control for trajectory tracking with task-space impedance control for contact compliance. The impedance term, mapped to joint torques via the Jacobian transpose, models compliant foot-tip behavior that absorbs impact energy during ground contact rather than resisting it through rigid control. To coordinate the two control modalities, we further introduce the attention for representation combiner (ARC) network. The ARC network employs a cross-attention mechanism between a gain actor and a joint actor, enabling control gains and desired joint positions to be generated in a coordinated manner. A state estimator augmented with a per-leg stumble estimator provides additional proprioceptive context to both actors for proactive gain adaptation. Simulation experiments across diverse terrains demonstrate that HIP achieves velocity tracking accuracy comparable to existing baselines while delivering improved energy efficiency. Torque decomposition analysis further confirms that the impedance component effectively reduces torque peaks during contact events.