Analytic Model for Quadruped Locomotion Task-Space Planning

Abstract

Despite the extensive presence of the legged locomotion in animals, it is extremely challenging to be reproduced with robots. Legged locomotion is an dynamic task which benefits from a planning that takes advantage of the gravitational pull on the system. However, the computational cost of such optimization rapidly increases with the complexity of kinematic structures, rendering impossible real-time deployment in unstructured environments. This paper proposes a simplified method that can generate desired centre of mass and feet trajectory for quadrupeds. The model describes a quadruped as two bipeds connected via their centres of mass, and it is based on the extension of an algebraic bipedal model that uses the topology of the gravitational attractor to describe bipedal locomotion strategies. The results show that the model generates trajectories that agrees with previous studies. The model will be deployed in the future as seed solution for whole-body trajectory optimization in the attempt to reduce the computational cost and obtain real-time planning of complex action in challenging environments.

The Strange Attractor of Bipedal Locomotion and Consequences on Motor Control

“…Furthermore, it identifies in the ankle strategies as the mechanism that allow to control the vertical movement of the CoM and, therefore, to regulate both the walking speed and stability. This result confirms previous results obtained with different data sets [28,29,33]. The data also indicate that humans control step length, step-frequency and mediolateral amplitudes according to an a priori optimised behaviour, which is similar to what has been observed by Collins et al [6].…”

Geometrical Postural Optimisation of 7-DoF Limb-Like Manipulators

“…They proved that the human walking strategy could be derived by analysing the principal direction of the gravitational attractor acting on the centre of mass. They also used this observation to define a close form equation for propagating the mechanical wave in the gravitational field that was used to plan locomotion trajectories in bipeds and quadrupeds [31,42,43]. These implications could explain the SP and its impact on learning and generalising motor skills.…”

Online Dynamic Trajectory Optimization and Control for a Quadruped Robot

“…There are also methods that do not utilize numerical optimization. In [16], a generalized inverted pendulum model based on the analysis of the potential energy surface in human locomotion is used to generate non-coplanar biped trajectories and was extended to quadruped trajectory planning in [17]. In [18], a stabilising foot placement planner is embedded in the whole body task space controller, where the horizontal CoM states of the biped are not controlled, but are the result of the stabilized system dynamics.…”

“…There are also methods that do not utilize numerical optimization. In [16], a generalized inverted pendulum model based on the analysis of the potential energy surface in human locomotion is used to generate non-coplanar biped trajectories and was extended to quadruped trajectory planning in [17]. However, these methods do not consider friction cone constraints that are critical to stabilise locomotion upon uneven terrain.…”