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Local stability of PD controlled bipedal walking robots

Kolathaya, S (2020) Local stability of PD controlled bipedal walking robots. In: Automatica, 114 .

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Official URL: http://dx.doi.org/10.1016/j.automatica.2020.108841


We establish stability results for PD tracking control laws in bipedal walking robots. Stability of PD control laws for continuous robotic systems is an established result, and we extend this for hybrid robotic systems, an alternating sequence of continuous and discrete events. Bipedal robots have the leg-swing as the continuous event, and the foot-strike as the discrete event. In addition, bipeds largely have underactuations due to the interactions between feet and ground. For each continuous event, we establish that the convergence rate of the tracking error can be regulated via appropriate tuning of the PD gains; and for each discrete event, we establish that this convergence rate sufficiently overcomes the nonlinear impacts by assumptions on the hybrid zero dynamics. The main contributions are (1) Extension of the stability results of PD control laws for underactuated robotic systems, and (2) Exponential ultimate boundedness of hybrid periodic orbits under the assumption of exponential stability of their projections to the hybrid zero dynamics. Towards the end, we will validate these results in a 2-link bipedal walker in simulation.

Item Type: Journal Article
Publication: Automatica
Publisher: Elsevier Ltd
Additional Information: Copyright of this article belongs to Elsevier Ltd
Keywords: Biped locomotion; Control theory; Mobile robots; Robotics; Stability, Alternating sequences; Bipedal walking robot; Hybrid periodic orbits; Hybrid zero dynamics; PD controllers; Periodic motion; Ultimate boundedness; Walking, Control system stability
Department/Centre: Division of Interdisciplinary Sciences > Robert Bosch Centre for Cyber Physical Systems
Date Deposited: 14 Feb 2020 11:57
Last Modified: 14 Feb 2020 11:57
URI: http://eprints.iisc.ac.in/id/eprint/64502

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