Control Of A Compliant Humanoid Robot In Double Support Phase: A Geometric Approach September 26, 2014 Gustavo Medrano-Cerda, Houman Dallali 1 , Martin Brown Abstract Enhancing energy efficiency of bipedal walking is an important research problem that has been approached by design of recently developed compliant bipedal robots such as CoMan. While compliance leads to energy efficiency, it also complicates the walking control system due to further under-actuated degrees of freedom (DoF) associated with the compliant actuators. This problem becomes more challenging as the constrained motion of the robot in double support is considered. In this paper this problem is approached from a multi-variable geometric control aspect to systematically account for the compliant actuators dynamics and constrained motion of the robot in double support phase using a detailed electro-mechanical model of CoMan. It is shown that the formulation of constraint subspace is non- trivial in the case of non-rigid robots. A step-wise numerical algorithm is provided and the effectiveness of the proposed method is illustrated via simulation, using a ten DoF model of CoMan. 1 Introduction Research on humanoid robots is one of the most interesting topics in robotics. In par- ticular, study of bipedal walking leads to a wide range of challenging control problems. Walking involves various phases of motion such as single support, heel strike, double support and toe push-off which follow a certain discrete ordering as can be observed from human data [1, 2]. Hence walking is inherently hybrid in the sense that it consists of continuous and discrete dynamics. In addition, humanoid robots are required to enhance their walking energy efficiency. A method of enhancing the energy efficiency is to add compliant elements (springs) to the joints. The energetic benefits of springs in bipedal walking are widely studied in the literature [3, 4, 5, 6]. Compliance can be used to store and release energy and to absorb shocks from the ground impacts to protect the actua- tors. Despite the advantages of springs in walking, control of a compliant robot becomes more complex since the springs increase the under-actuated degrees of freedom. This problem becomes more interesting as the motion of a compliant robot in double support phase is considered. The motion of a humanoid in double support is subject to geometric 1 Department of Advanced Robotics, Italian Institute of Technology, Via Morego, 30 16163 Genova, Italy. houman.dallali@gmail.com, article is accepted in 2012 at International Journal of Humanoid Robotics. 1