  In this paper, we present a new model of biped locomotion which is 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 double support, this
model has different actuation possibilities in the swing hip and stance ankle
which could be widely used to produce different walking gaits. Without the need
for numerical time-integration, closed-form solutions help finding periodic
gaits which could be simply scaled in certain dimensions to modulate the motion
online. Thanks to linearity properties, the proposed model can 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 property is coming from describing dynamics with joint torques
directly and therefore, reflecting hardware limitations more precisely, even in
the very abstract high level 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 precise control of humanoid robots.
Despite being linear and lacking many other features of human walking like CoM
excursion, knee flexion and ground clearance, we show that the proposed model
can predict one of the main optimality trends in human walking, i.e. 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 still remain for future works.
