Impedance and Admittance Controller for a Multi-axis Powered Ankle-foot Prosthesis

This paper introduces a finite state machine to select between impedance and admittance control for a powered anklefoot prosthesis controllable in both Dorsiflexion-Plantarflexion (DP) and Inversion-Eversion (IE). Strain gauges are installed on the prosthesis’ foot to measure the strain caused by ground reaction forces, which are correlated to the external torques in DP and IE. The external torques are used for the admittance and impedance controllers. Additionally, the finite state machine uses the strain gauges feedback to detect the heel-strike and switch to admittance control. The admittance control accepts torque feedback to generate motion, this way larger feedback torques effectively reduces the stiffness of the ankle. During push off, the finite state machine switches to impedance control, accepting motion feedback to generate the appropriated torques. The quasi-static stiffness of the prosthesis with impedance control was tested, showing a near linear relationship between the torque feedback gain and the stiffness of the ankle. The finite state machine and controllers were also evaluated using a custom-made circular treadmill and the results were compared to the results of position and passive controllers; showing that the impedance/admittance controller was capable of tracking the desired input trajectory while decreasing the required torque at the ankle joint. INTRODUCTION Walking in a straight line requires a complex modulation of muscle contractions to control the ankle’s stiffness and generate forward propulsion. Similar muscle contractions are required to generate the appropriate ground reaction forces to steer the body while turning [1]. Below knee amputees with passive prosthesis expend 20-30% more energy than non-amputees to walk at the same speed, resulting in a preferred walking speed which is 3040% slower than non amputees [2, 3]. As a possible solution, powered prostheses have been developed and it is shown that they reduce the metabolic cost during straight walking by providing energy to the gait at push-off [4, 5]. While the focus on developing powered prostheses has been on increased mobility in forward locomotion; it has been shown that daily activities contain an average of 25% turning steps [6]. Turning requires modulation of the ankles impedance in both DP and IE directions to control the lateral and forward reaction forces to maintain the body’s center of mass along the desired trajectory; resulting in increased lateral and forward forces when compared to the straight walking [7]. Due to the lack of appropriate propulsion from their passive prostheses, amputees rely on different gait strategies than non amputees [1]; suggesting that amputees can benefit from powered prostheses capable of providing power in both DP and IE with impedance modulation similar to the human ankle. While physical systems interact with each other, they are behaving either as an impedance (e.g. accepts external motion inputs and generates force outputs) or an admittance (e.g. accepts external force inputs and generates motion outputs) [8]. The coupled mechanical systems must physically complement each other, meaning that in any degree of freedom, if one system is an impedance, the other system has to be an admittance [8]. During gait, at the moment the heel interacts with the ground (heel-strike) the ankle is being manipulated by the environment since the ankle accepts the external force and generates the appropriate motion, so it may be considered as a system in admittance. At push off, the ankle manipulates the environment, generating the necessary torques to produce the required motion, and so it may be considered as impedance. This suggests that ankle-foot prostheses should use an admittance controller at heel -strike and an impedance controller at push off. In general, an impedance controller uses position encoders mounted in the actuators to determine the position of the robot end effector. The controller uses the desired and feedback positions to generate the actuators’ desired torques. Torque sensors are used to provide the means for estimation of the external torque feedback that, along 1 Copyright © 2014 by ASME Proceedings of the ASME 2014 Dynamic Systems and Control Conference DSCC2014 October 22-24, 2014, San Antonio, TX, USA