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Towards Bipedal Behavior on a Quadrupedal Platform Using Optimal Control

SPIE 2016

T.T. Topping, Vasileios Vasilopoulos, Avik De, and D. E. Koditschek
Electrical and Systems Engineering, University of Pennsylvania
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Abstract
This paper explores the applicability of a Linear Quadratic Regulator (LQR) controller design to the problem of bipedal stance on the Minitaur [1] quadrupedal robot. Balancing the body on only the rear legs affords the possibility of using the front legs for other tasks such as manipulation or bracing. Restricted to the sagittal plane, this behavior exposes a 3DOF (degree of freedom) double inverted pendulum with extensible length actuated at the prismatic (“shank”) and second revolute (“knee/hip”) joints per Figure 1 and section 2.1. Locking the prismatic (shank) DOF reduces the Lagrangian model of the pinned toe mechanism to that of the familiar singularly-actuated 2 DOF (revolute-revolute) acrobot per section 2.2 and lemma 2.1 . Since the linearized 3DOF dynamics at any vertically erect stance exposes a decoupled linearized acrobot, we focus on stabilizing this subsystem in isolation per section 2.3.
This work was supported by the ARL/GDRS RCTA project, Coop. Agreement #W911NF-10–2−0016.

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