On controllable stiffness bipedal walking

Abstract

Impact at each leg transition is one of the main causes of energy dissipation in most
\nof the current bipedal walking robots. Minimizing impact can reduce the energy loss.
\nInstead of controlling the joint angle profiles to reduce the impact which requires significant
\namount of energy, installing elastic mechanisms on the robots structure is
\nproposed in this research, enabling the robot to reduce the impact, and to store part
\nof the energy in the elastic form which returns the energy to the robot. Practically,
\nthis motivates the development of the bipedal walking robots with adjustable stiffness
\nelasticity which itself creates new challenging problems. This thesis addresses some of
\nthe challenges through five consecutive stages. Firstly, an adjustable compliant series
\nelastic actuator (named ACSEA in this thesis) is developed. The velocity control mode
\nof the electric motor is used to accurately control the output force of the ACSEA. Secondly,
\nthree different conceptual designs of the adjustable stiffness artificial tendons
\n(ASAT) are proposed each of which is added at the ankle joint of a bipedal walking
\nrobot model. Simulation results of the collision phase (part of the gait between
\nthe heel-strike and the foot-touch-down in bipedal walking) demonstrate significant
\nimprovements in the energetics of the bipedal walking robot by proper stiffness adjustment
\nof ASAT. In the third stage, in order to study the effects of ASATs on reducing
\nthe energy loss during the stance phase, a simplified model of bipedal walking is introduced
\nconsisting of a foot, a leg and an ASAT which is installed parallel to the ankle
\njoint. A linear spring, with adjustable stiffness, is included in the model to simulate the generated force by the trailing leg during the double support phase. The concept
\nof impulsive constraints is used to establish the mathematical model of impacts in
\nthe collision phase which includes the heel-strike and the foot-touch-down. For the
\nfourth stage, an energy-feedback-based controller is designed to automatically adjust
\nthe stiffness of the ASAT which reduces the energy loss during the foot-touch-down.
\nIn the final stage, a speed tracking (ST) controller is developed to regulate the velocity
\nof the biped at the midstance. The ST controller is an event-based time-independent
\ncontroller, based on geometric progression with exponential decay in the kinetic energy
\nerror, which adjusts the stiffness of the trailing-leg spring to control the injected energy
\nto the biped in tracking a desired speed at the midstance. Another controller is also
\nintegrated with the ST controller to tune the stiffness of the ASAT when reduction in
\nthe speed is desired. Then, the local stability of the system (biped and the combination
\nof the above three controllers) is analyzed by calculating the eigenvalues of the linear
\napproximation of the return map. Simulation results show that the combination of the
\nthree controllers is successful in tracking a desired speed of the bipedal walking even
\nin the presence of the uncertainties in the leg’s initial angles.
\nThe outcomes of this research show the significant effects of adjustable stiffness artificial
\ntendons on reducing the energy loss during bipedal walking. It also demonstrates
\nthe advantages of adding elastic elements in the bipedal walking model which benefits
\nthe efficiency and simplicity in regulating the speed. This research paves the way
\ntoward developing the dynamic walking robots with adjustable stiffness ability which
\nminimize the shortcomings of the two major types of bipedal walking robots, i.e., passive
\ndynamic walking robots (which are energy efficient but need extensive parameters
\ntuning for gait stability) and actively controlled walking r