Novel method to form adaptive internal impedance profiles in walkers Maximilano F. Escudero Morland, Kaspar Althoefer, and Thrishantha Nanayakkara Abstract— This paper proposes a novel approach to improve walking in prosthetics, orthotics and robotics without closed loop controllers. The approach requires impedance profiles to be formed in a walker and uses state feedback to update the profiles in real-time via a simple policy. This approach is open loop and inherently copes with the challenge of uncertain environment. In application it could be used either online for a walker to adjust its impedance profiles in real- time to compensate for environmental changes, or offline to learn suitable profiles for specific environments. So far we have conducted simulations and experiments to investigate the transient and steady state gaits obtained using two simple update policies to form damping profiles in a passive dynamic walker known as the rimless wheel (RW). The damping profiles are formed in the motor that moves the RW vertically along a rail, analogous to a knee joint, and the two update equations were designed to a) control the angular velocity profile and b) minimise peak collision forces. Simulation results show that the velocity update equation works within limits and can cope with varying ground conditions. Experiment results show the angular velocity average reaching the target as well as the peak force update equation reducing peak collision forces in real- time. I. INTRODUCTION There has been growing interest in the variable internal impedance of leg joints for applications in prosthetics [1] orthotics [2] and robotics [3]. Studies in passive dynamic walking show that the knee joint plays an important role in the stability and efficiency of walking [4] and separate studies have confirmed that applying variable impedance in the knee provides a wider range of stable and efficient gaits [1]. One of the biggest challenges for the control of impedance is to maintain stability in uncertain or changing environments [5]. Work on passive locomotion has exposed that in order to walk efficiently one must consider not only the kinetics of the moving body, but those of the body and the environment as a dynamic couple [6]. Systems identification studies on the human knee joint [7] report that it has internal impedance that varies non- linearly as a function of joint angle even when muscles are relaxed. This finding indicates that knee impedance comes from two separate sources: the inherent joint-angle- dependent impedance felt due to friction and elasticity of *This work was partially supported by the Engineering and Physical Sciences Research Council, UK, under grant agreements EP/I028773/1, EP/I028765/1, and EU project FourByThree grant (grant agreement no. 637095) under the Horizon 2020 European Framework funding programme for Research and Innovation Authors are with the Centre for Robotics research, Department of Informatics, King’s College London, Strand, London WC2R 2LS, UK. Email: maximiliano.escudero@kcl.ac.uk, kaspar.althoefer@kcl.ac.uk, and thrish.antha@kcl.ac.uk Fig. 1. Left: schematic diagram of setup used to derive system equations. Right: illustration of damping profile over one step with angle bins of π 24 (7.5 ◦ ). Note that this is a mere illustration and the angle bins used in experiments and simulations were π 36 and π 360 (5 ◦ and 0.5 ◦ ) respectively. tissues when the muscles are relaxed (referred to in this paper as morphological), and the active impedance imposed by antagonistic muscle contractions (referred to as neural). The impedance experienced by the human knee is then a com- bined effect of both morphological and neural impedances and we hypothesise that a better morphological impedance profile can make the gait more natural, stable and efficient while freeing up computational resources. The approach we propose in this paper is a novel em- ulation of the morphological impedance profile in the hu- man knee (hence no closed loop control to emulate neural impedance). However, instead of evolving over millions of years via natural selection it evolves in real-time via a simple policy that seeks to discreetly adjust impedance as a function of joint angle such that errors between actual and desired states are minimised. The approach is simple, overcomes the non-trivial coupling of ground and body dynamics, and should allow for real-time adaptation of impedance profiles to keep gait cycles closer to those desired. Our work in this paper aims to test and show the feasibility and potential of this approach, and to do it we focus solely on damping pro- files, keeping stiffness constant, because damping inherently stabilises systems [8] and has been studied less extensively in the past. II. METHODOLOGY A. Damping profile policy A walker in nature has knowledge of its own states and tries to use its senses to predict upcoming variations in the