Model-Dependent Prosthesis Control with Real-Time Force Sensing Rachel Gehlhar, Je-han Yang, and Aaron D. Ames Abstract—Lower-limb prosthesis wearers are more prone to fall than non-amputees. Powered prostheses can reduce this instability of passive prostheses. While shown to be more stable in practice, powered prostheses generally use model- independent control methods that lack formal guarantees of stability and rely on heuristic tuning. Recent work overcame one of the limitations of model-based prosthesis control by developing a class of stable prosthesis subsystem controllers independent of the human model, except for its interaction forces with the prosthesis. Our work realizes the first model- dependent prosthesis controller that uses in-the-loop on-board real-time force sensing at the interface between the human and prosthesis and at the ground, resulting in stable human- prosthesis walking and increasing the validity of our formal guarantees of stability. Experimental results demonstrate this controller using force sensors outperforms the controller when not using force sensors with better tracking performance and more consistent tracking performance across 4 types of terrain. I. I NTRODUCTION Lower-limb prosthesis users fall more frequently than non-amputees [1]. A survey in [2] found 45% of polled amputees had fallen in the past year while wearing their prosthesis. This instability could be due to their passive prostheses, which can be less stable than powered prostheses [3]. Current powered prosthesis control methods tend to be model-independent [4], [5], requiring heuristic tuning, lacking formal guarantees of stability, and not utilizing the system’s natural dynamics. Current state of the art controllers tune impedance parameters for multiple discrete phases of a gait cycle for different subjects and behaviors [6]–[8] Model- based control methods hold potential to yield a more transfer- able method between devices, users, and behaviors since they rely on measurable model parameters and inputs instead of a large set of heuristic tuning parameters. Additionally, model- based methods can be designed to yield formal guarantees of stability since they are based on the actual system dynamics. This motivates developing model-based prosthesis control methods that lend a more transferable method between applications and guarantee stability for the user. A challenge arises in developing model-dependent pros- thesis controllers: the human dynamics are unknown. The work of [9] addressed this limitation by developing rapidly *This material is based upon work supported by the National Science Foundation Graduate Research Fellowship under Grant No. DGE-1745301. This research was approved by California Institute of Technology Institu- tional Review Board with protocol no. 16-0693 for human subject testing. R. Gehlhar and A. Ames are with the Department of Mechanical and Civil Engineering, J. Yang is with the Department of Electrical Engineering, California Institute of Technology, Pasadena, CA 91125 USA. Emails: {rgehlhar, ames, jyang5}@caltech.edu Fig. 1. (top) Gait tiles of human subject walking with model-dependent prosthesis controller using real-time force measurements on four terrains: rubber floor, outdoor track, grass, and sidewalk. (bottom) Measured socket and ground force profiles during stance for respective terrain. exponentially stabilizing control Lyapunov functions (RES- CLFs), which were shown to stabilize bipedal robotic walk- ing [10], in the context of separable systems [11], [12]. This resulted in a class of stabilizing prosthesis controllers relying only on local prosthesis information. Previously, RES-CLFs were difficult to realize on hardware due to the typical required inversion of the inertia matrix which is computationally expensive and susceptible to error. The work of [13] developed and demonstrated a RES-CLF controller on a bipedal robot without inverting the inertia matrix by constructing the RES-CLF in an inverse dynamics framework in a quadratic program (QP) [14]. The work of [13] brings the class of controllers developed in [9] closer to being implementable. Realizing RES-CLF controllers on prostheses meets an additional challenge: they require knowledge of both the ground reaction forces and moment and socket interaction forces and moment. (For simplicity we refer to these as “GRFs” and “socket forces”.) The work of [15] realized the first model-dependent prosthesis controller in stance with consideration for the forces, using holonomic constraints for the GRFs and force estimation for the socket forces. However using holonomic constraints to determine GRFs assumes a rigid contact with the ground, inaccurately representing many real-life scenarios where the terrain deforms under a load, like granular media [16]. Developing control methods accounting for non-rigid terrain is especially important for prostheses to enable amputees to walk stably on a variety of surfaces present in daily life. Additionally, this method only estimated the socket forces which may not accurately capture the varying load a user applies during stance. To more accurately account for the prosthesis system dynamics in model-dependent control, force sensors are needed. arXiv:2105.11561v2 [cs.RO] 18 Sep 2021