Central pivot point control simplifies analysis and control of spring-mass runners
Central pivot point control of a body-attached spring-mass runner: periodic gaits, stabilization, template embedding and approximate analytic return maps
Robotics
Summary
Running robots with bodies and legs are hard to analyze because their trunk and leg movements affect each other. The authors found a way to control hip torque that makes the leg forces pass through the runner's center of mass, simplifying the math and allowing them to predict running patterns and stabilize the runner. They created exact formulas to describe these running motions and showed their predictions are very close to actual simulated results. This approach makes it easier to study and control robots that run with a trunk, similar to how simpler leg models have been analyzed before.
What this means in practice
- •For robotics engineers: Design control systems for legged robots with trunks that achieve stable, energy-efficient running gaits using exact mathematical models.
- •For biomechanics modelers: Use simplified analytical tools to study human or animal running dynamics incorporating trunk and leg interactions.
Authors
İzel Sever, O. Kaan Karagöz, M. Mert Ankaralı
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 central 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 force 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 symmetric 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.