3LP: A linear 3D-walking model including torso and swing dynamics

In this paper, we present a new mechanical model for biped locomotion, composed of three linear pendulums (one per leg and one for the whole upper body) to describe stance, swing and torso dynamics. In addition to a double support phase, this model has different actuation possibilities in the swing hip and stance ankle which produce a broad range of walking gaits. Without the need for numerical time-integration, closed form solutions help to find periodic gaits which could simply scale in certain dimensions to modulate the motion online. Thanks to linearity properties, the proposed model can potentially provide a computationally fast platform for model predictive controllers to predict the future and consider meaningful inequality constraints to ensure feasibility of the motion. Such a property comes from describing dynamics with joint torques directly and therefore, reflecting hardware limitations more precisely, even in the very abstract template space. The proposed model produces human-like torque and ground reaction force profiles, and thus, compared to point-mass models, it is more promising for the generation of dynamic walking trajectories. Despite being linear and lacking many features of human walking like center of mass excursion, knee flexion and ground clearance, we show that the proposed model can explain one of the main optimality trends in human walking, i.e. the nonlinear speed-frequency relationship. In this paper, we mainly focus on describing the model and its capabilities, comparing it with human data and calculating optimal human gait variables. Setting up control problems and advanced biomechanical analysis remains for future works.