SPARC: Spine with Prismatic and Revolute Compliance for Quadruped Robot

Abstract: We present SPARC, a compact, open-source 3-DoF sagittal-plane spine module that combines revolute (pitch) and prismatic (axial) motion with programmable task-space impedance for quadruped robots. The system integrates three torque-controlled actuators, a custom 1 kHz control board, and a protected power unit in a 1.26 kg package, enabling closed-loop stiffness and damping shaping along x, z, and theta. We develop an RNEA-based computed-acceleration controller with smooth Stribeck friction compensation to render spring-damper behavior without explicit inertia shaping. Bench experiments validate the approach. Quasi-static push-pull tests show linear force-displacement characteristics with commanded horizontal stiffness spanning 300-700 N/m and <= 1.5% relative error (R^2 >= 0.992, narrow 95% CIs). Dynamic displace-and-release trials confirm mass-spring-damper responses over multiple damping settings, with small, interpretable phase deviations due to configuration-dependent inertia and low-speed friction effects. A task-space PD controller produces roughly linear stiffness but with greater variability and coupling sensitivity. SPARC provides a portable platform for systematic studies of spine compliance in legged locomotion and will be released with complete hardware and firmware resources.