Central pivot point control of a body-attached spring-mass runner: periodic gaits, stabilization, template embedding and approximate analytic return maps
Central pivot point control of a body-attached spring-mass runner: periodic gaits, stabilization, template embedding and approximate analytic return maps
This research introduces a Central Pivot Point (CPP) control law for trunk-equipped runners, restoring central-force dynamics to enable analytic solutions. The method decouples pitch motion, stabilizes periodic gaits with bounded torque, and provides an analytic return map that predicts liftoff velocity and apex position with mean errors of 1.6% and 0.9%, respectively. A deadbeat stride controller tracks changes in speed, height, and posture, making trunk models accessible to tools developed for spring-loaded inverted pendulum (SLIP) analysis.
The paper presents a theoretical framework for restoring central-force dynamics in trunk-equipped runners via a Central Pivot Point (CPP) control law, enabling analytic solutions and stable periodic gaits previously restricted to numerical simulation.
Source: arXiv Robotics — research abstracts · Read original article ↗
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e law in virtual-leg coordinates can be embedded independently of posture. For a linear radial template, the stance radius and the constant-momentum sweep have exact closed forms. With a new gravity correction, the resulting analytic return map, to our knowledge the first for a trunk model, predicts liftoff velocity and apex position with mean errors of 1.6% and 0.9%. The natural gaits of the embedded runner are symm
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etric and need no force step at touchdown. A near-reversibility argument explains their unit multiplier, and a scalar equation predicts them within 0.8%. A deadbeat stride controller based on the analytic map tracks changes of speed, height and posture. CPP thus makes trunk models accessible to the analytic tools developed for SLIP.
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Central pivot point control of a body-attached spring-mass runner: periodic gaits, stabilization, template embedding and approximate analytic return maps
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arXiv:2611.02564v1 Announce Type: new Abstract: The spring-loaded inverted pendulum (SLIP) describes the center-of-mass (COM) motion of runners but has no trunk. In trunk models, the hip torque couples posture and COM motion and destroys the central-force structure on which SLIP analysis relies. As a result, trunk models have been studied almost only numerically. We show that this structure can be restored. The centr
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al pivot point (CPP), a hip-torque law that directs the ground reaction force through the COM, decouples pitch exactly and reduces stance to a planar central-force problem. At upright posture, time-reversal symmetry produces one-parameter families of periodic gaits. A stance-phase pitch law and a stride-level regulator stabilize all computed gaits, also with bounded hip torque and friction. Under CPP, any radial forc
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Source：arXiv Robotics — research abstracts · arxiv.org