Annals of Biomedical Engineering, Vol. 23, pp. 691-696, 1995 0090-6964/95 $10.50 + .00 Printed in the USA. All rights reserved. Copyright 9 1995 Biomedical Engineering Society Parameter Estimation for a Prosthetic Ankle ELHANAN SINGER,* GIDEON ISHAI,* and EITAN KIMMELt Departments of *Biomedical Engineering and tAgricultural Engineering, Technion, Haifa, Israel Abstract--The mechanical parameters of a model of an energy storage and return ankle prosthesis are estimated for normal level walking by means of an optimization procedure. The walking cycle is divided into six fields, such that the power does not change sign within each field; the transition between successive fields occurs at zero power. The optimal spring stiffness as a function of time, is found by optimizing a quadratic cost function to minimize the difference between the estimated ankle moments and the moments in normal walking. The optimization is sub- jected to four continuous constraints within each field and to two continuity constraints for the transitions between successive fields. The time-varying spring stiffness and the implications of additional external energy are discussed and are presented as recommendations for the designer. KeywordsmAnkle prosthesis, Optimization, Normal walking. INTRODUCTION Lower limb prostheses usually employ a relatively rigid ankle mechanism, the primary objective being to secure stability in standing. The functioning of such a relatively rigid ankle prosthesis is quite limited in other locomotor activities such as level and slope walking, and running. Furthermore, it narrows the range of dorsi and plantar flexion during walking and disturbs the smoothness of movement of the center of pressure in the foot-ground interface. These negative effects can be reduced by prop- erly designing the mechanical parameters of the ankle. In the last decade, energy-storing ankle prostheses, such as the Flex-Foot or Quantum prostheses, which are designed to improve walking and running by improving the energy storage and recovery capabilities, have become available. Several investigations have been conducted in order to evaluate the performance (subjective evaluation, meta- bolic cost, and kinetic parameters) of the new energy stor- age and return prostheses during walking, and to compare them with conventional prostheses (2-7). The energy stor- ing prostheses were found to have some advantages in metabolic energy consumption (5), in temporal parameters (3), in interlimb symmetry of ground vertical impulse (6), Address correspondence to E. Kimmel, Departmentof Agricultural Engineering, Technion IIT, Haifa 32000, Israel. (Received 8July94, Revised 18Apr95, Revised, Accepted 10May95) in selected walking velocity (5), and especially in medium and fast walking (7). Interlimb asymmetries were less pro- nounced in the flexible knee prosthesis. The advantages of energy storing prostheses over conventional prostheses di- minish at low walking velocity. It is expected that future designs will incorporate some adaptive features that will apply different stiffness characteristics to different activi- ties (standing, slow and fast level walking, etc.) of the amputee. Moreover, the stiffness for a given walking ve- locity is expected to vary with time over a walking cycle. The lower limb prosthesis differs from the physiologi- cal limb mainly in the mass distribution, foot stump- socket interface, and the mechanical characteristics of the foot and the ankle joint. The muscles in the physiological ankle joint are an active source of mechanical energy, generating 25 to 30 Nm per walking cycle in a normal gait (calculated from Winter's kinetic data [8]). In conven- tional lower limb prostheses, there is no such source of energy; and therefore, even if the only difference between the prosthesis and the normal limb were the function of the ankle joint, it would be impossible to replicate normal walking. The complexity of the above parameters make it diffi- cult to design a lower limb prosthesis. One of the major issues of designing such a prosthesis is determining the required mechanical impedance (stiffness and damping) at the ankle joint. The question is should the stiffness remain constant during the walking cycle or should it vary? And if it varies, in what way? The answer to these questions would be complete if we knew the required moments and kinematics that were regarded as optimal by the amputee. Since these requirements are not known, it was decided to assume, as a first guess, that the characteristics of the mechanical impedance calculated from data measured in normal walking, would indicate the required impedance in the prosthetic ankle. We believe that such a prosthesis may have a good chance of arriving at the so-called indi- vidual optimal impedance if it is tuned further during the fitting process. In the present study, a method is suggested for deter- mining the mechanical parameters of optimal simulated ankle-foot prosthesis from known moments and angles at the ankle joint. 691