title: Approximate analytical solutions to the double-stance dynamics of the lossy spring-loaded inverted pendulum.
abstract: This paper introduces approximate time-domain solutions to the otherwise non-integrable double-stance dynamics of the 'bipedal' spring-loaded inverted pendulum (B-SLIP) in the presence of non-negligible damping. We first introduce an auxiliary system whose behavior under certain conditions is approximately equivalent to the B-SLIP in double-stance. Then, we derive approximate solutions to the dynamics of the new system following two different methods: (i) updated-momentum approach that can deal with both the lossy and lossless B-SLIP models, and (ii) perturbation-based approach following which we only derive a solution to the lossless case. The prediction performance of each method is characterized via a comprehensive numerical analysis. The derived representations are computationally very efficient compared to numerical integrations, and, hence, are suitable for online planning, increasing the autonomy of walking robots. Two application examples of walking gait control are presented. The proposed solutions can serve as instrumental tools in various fields such as control in legged robotics and human motion understanding in biomechanics.
authors.affiliation: Delft Center for Systems and Control, Delft University of Technology, Mekelweg 2, 2628 CD Delft, The Netherlands. Department of Mechatronic Systems Engineering, Faculty of New Sciences and Technologies, University of Tehran, Tehran 14399-57131, Iran.
authors.forename: Mohammad
authors.initials: M
authors.lastname: Shahbazi
authors.forename: Uluç
authors.initials: U
authors.lastname: Saranlı
authors.forename: Robert
authors.initials: R
authors.lastname: Babuška
authors.forename: Gabriel A D
authors.initials: GA
authors.lastname: Lopes
mesh_terms: D000818:Animals; D001522:Behavior, Animal; D001696:Biomechanical Phenomena; D040761:Biomimetic Materials; D004867:Equipment Design / Q000379:methods*; D005684:Gait / Q000502:physiology; D006801:Humans; D006813:Humidity; D007866:Leg / Q000502:physiology; D008124:Locomotion / Q000502:physiology*; D008954:Models, Biological; D004856:Postural Balance; D012371:Robotics; D016138:Walking / Q000502:physiology