Design and Validation of a Powered Knee-Ankle Prosthesis with High-Torque, Low-Impedance Actuators.

We present the design of a powered knee-ankle prosthetic leg, which implements high-torque actuators with low-reduction transmissions. The transmission coupled with a high-torque and low-speed motor creates an actuator with low mechanical impedance and high backdrivability. This style of actuation presents several possible benefits over modern actuation styles in emerging robotic prosthetic legs, which include free-swinging knee motion, compliance with the ground, negligible unmodeled actuator dynamics, less acoustic noise, and power regeneration. Benchtop tests establish that both joints can be backdriven by small torques (~1-3 Nm) and confirm the small reflected inertia. Impedance control tests prove that the intrinsic impedance and unmodeled dynamics of the actuator are sufficiently small to control joint impedance without torque feedback or lengthy tuning trials. Walking experiments validate performance under the designed loading conditions with minimal tuning. Lastly, the regenerative abilities, low friction, and small reflected inertia of the presented actuators reduced power consumption and acoustic noise compared to state-of-art powered legs.

Effects of a Powered Knee-Ankle Prosthesis on Amputee Hip Compensations: A Case Series.

Transfemoral amputee gait often exhibits compensations due to the lack of ankle push-off power and control over swing foot position using passive prostheses. Powered prostheses can restore this functionality, but their effects on compensatory behaviors, specifically at the residual hip, are not well understood. This paper investigates residual hip compensations through walking experiments with three transfemoral amputees using a low-impedance powered knee-ankle prosthesis compared to their day-to-day passive prosthesis. The powered prosthesis used impedance control during stance for compliant interaction with the ground, a time-based push-off controller to deliver high torque and power, and phase-based trajectory tracking during swing to provide user control over foot placement. Experiments show that when subjects utilized the powered ankle push-off, less mechanical pull-off power was required from the residual hip to progress the limb forward. Overall positive work at the residual hip was reduced for 2 of 3 subjects, and negative work was reduced for all subjects. Moreover, all subjects displayed increased step length, increased propulsive impulses on the prosthetic side, and improved impulse symmetries. Hip circumduction improved for subjects who had previously exhibited this compensation on their passive prosthesis. These improvements in gait, especially reduced residual hip power and work, have the potential to reduce fatigue and overuse injuries in persons with transfemoral amputation.

Extremum Seeking Control for Model-Free Auto-Tuning of Powered Prosthetic Legs.

This paper proposes an extremum seeking controller (ESC) for simultaneously tuning the feedback control gains of a knee-ankle powered prosthetic leg using continuous-phase controllers. Previously, the proportional gains of the continuous-phase controller for each joint were tuned manually by trial-and-error, which required several iterations to achieve a balance between the prosthetic leg tracking error performance and the user's comfort. In this paper, a convex objective function is developed, which incorporates these two goals. We present a theoretical analysis demonstrating that the quasi-steady-state value of the objective function is independent of the controller damping gains. Furthermore, we prove the stability of error dynamics of continuous-phase controlled powered prosthetic leg along with ESC dynamics using averaging and singular perturbation tools. The developed cost function is then minimized by ESC in real-time to simultaneously tune the proportional gains of the knee and ankle joints. The optimum of the objective function shifts at different walking speeds, and our algorithm is suitably fast to track these changes, providing real-time adaptation for different walking conditions. Benchtop and walking experiments verify the effectiveness of the proposed ESC across various walking speeds.

Minimizing Energy Consumption and Peak Power of Series Elastic Actuators: A Convex Optimization Framework for Elastic Element Design.

Compared to rigid actuators, series elastic actuators (SEAs) offer a potential reduction of motor energy consumption and peak power, though these benefits are highly dependent on the design of the torque-elongation profile of the elastic element. In the case of linear springs, natural dynamics is a traditional method for this design, but it has two major limitations-arbitrary load trajectories are difficult or impossible to analyze and it does not consider actuator constraints. Parametric optimization is also a popular design method that addresses these limitations, but solutions are only optimal within the space of the parameters. To overcome these limitations, we propose a nonparametric convex optimization program for the design of the nonlinear elastic element that minimizes energy consumption and peak power for an arbitrary periodic reference trajectory. To obtain convexity, we introduce a convex approximation to the expression of peak power; energy consumption is shown to be convex without approximation. The combination of peak power and energy consumption in the cost function leads to a multiobjective convex optimization framework that comprises the main contribution of this paper. As a case study, we recover the elongation-torque profile of a cubic spring, given its natural oscillation as the reference load. We then design nonlinear SEAs for an ankle prosthesis that minimize energy consumption and peak power for different trajectories and extend the range of achievable tasks when subject to actuator constraints.

A Phase Variable Approach for Improved Rhythmic and Non-Rhythmic Control of a Powered Knee-Ankle Prosthesis.

Although there has been recent progress in control of multi-joint prosthetic legs for rhythmic tasks such as walking, control of these systems for non-rhythmic motions and general real-world maneuvers is still an open problem. In this article, we develop a new controller that is capable of both rhythmic (constant-speed) walking, transitions between speeds and/or tasks, and some common volitional leg motions. We introduce a new piecewise holonomic phase variable, which, through a finite state machine, forms the basis of our controller. The phase variable is constructed by measuring the thigh angle, and the transitions in the finite state machine are formulated through sensing foot contact along with attributes of a nominal reference gait trajectory. The controller was implemented on a powered knee-ankle prosthesis and tested with a transfemoral amputee subject, who successfully performed a wide range of rhythmic and non-rhythmic tasks, including slow and fast walking, quick start and stop, backward walking, walking over obstacles, and kicking a soccer ball. Use of the powered leg resulted in clinically significant reductions in amputee compensations for rhythmic tasks (including vaulting and hip circumduction) when compared to use of the take-home passive leg. In addition, considerable improvements were also observed in the performance for non-rhythmic tasks. The proposed approach is expected to provide a better understanding of rhythmic and non-rhythmic motions in a unified framework, which in turn can lead to more reliable control of multi-joint prostheses for a wider range of real-world tasks.

Robust Optimal Design of Energy Efficient Series Elastic Actuators: Application to a Powered Prosthetic Ankle.

Design of rehabilitation and physical assistance robots that work safely and efficiently despite uncertain operational conditions remains an important challenge. Current methods for the design of energy efficient series elastic actuators use an optimization formulation that typically assumes known operational requirements. This approach could lead to actuators that cannot satisfy elongation, speed, or torque requirements when the operation deviates from nominal conditions. Addressing this gap, we propose a convex optimization formulation to design the stiffness of series elastic actuators to minimize energy consumption and satisfy actuator constraints despite uncertainty due to manufacturing of the spring, unmodeled dynamics, efficiency of the transmission, and the kinematics and kinetics of the load. To achieve convexity, we write energy consumption as a scalar convex-quadratic function of compliance. As actuator constraints, we consider peak motor torque, peak motor velocity, limitations due to the speed-torque relationship of DC motors, and peak elongation of the spring. We apply our formulation to the robust design of a series elastic actuator for a powered prosthetic ankle. Our simulation results indicate that a small trade-off between energy efficiency and robustness is justified to design actuators that can operate with uncertainty.

Intuitive Clinician Control Interface for a Powered Knee-Ankle Prosthesis: A Case Study.

This paper presents a potential solution to the challenge of configuring powered knee-ankle prostheses in a clinical setting. Typically, powered prostheses use impedance-based control schemes that contain several independent controllers which correspond to consecutive periods along the gait cycle. This control strategy has numerous control parameters and switching rules that are generally tuned by researchers or technicians and not by a certified prosthetist. We propose an intuitive clinician control interface (CCI) in which clinicians tune a powered knee-ankle prosthesis based on a virtual constraint control scheme, which tracks desired periodic joint trajectories based on a continuous measurement of the phase (or progression) of gait. The interface derives virtual constraints from clinician-designed joint kinematic trajectories. An experiment was conducted in which a certified prosthetist used the control interface to configure a powered knee-ankle prosthesis for a transfemoral amputee subject during level-ground walking trials. While it usually takes engineers hours of tuning individual parameters by trial and error, the CCI allowed the clinician to tune the powered prosthesis controller in under 10 min. This allowed the clinician to improve several amputee gait outcome metrics, such as gait symmetry. These results suggest that the CCI can improve the clinical viability of emerging powered knee-ankle prostheses.

Design and Benchtop Validation of a Powered Knee-Ankle Prosthesis with High-Torque, Low-Impedance Actuators.

This paper describes the design of a powered knee- and-ankle transfemoral prosthetic leg, which implements high torque density actuators with low-reduction transmissions. The low reduction of the transmission coupled with a high-torque and low-speed motor creates an actuator with low mechanical impedance and high backdrivability. This style of actuation presents several possible benefits over modern actuation styles implemented in emerging robotic prosthetic legs. Such benefits include free-swinging knee motion, compliance with the ground, negligible unmodeled actuator dynamics, and greater potential for power regeneration. Benchtop validation experiments were conducted to verify some of these benefits. Backdrive and free-swinging knee tests confirm that both joints can be backdriven by small torques (~3 Nm). Bandwidth tests reveal that the actuator is capable of achieving frequencies required for walking and running. Lastly, open-loop impedance control tests prove that the intrinsic impedance and unmodeled dynamics of the actuator are sufficiently small to control joint impedance without torque feedback.

A Phase Variable Approach to Volitional Control of Powered Knee-Ankle Prostheses.

Although there has been recent progress in control of multi-joint prosthetic legs for periodic tasks such as walking, volitional control of these systems for non-periodic maneuvers is still an open problem. In this paper, we develop a new controller that is capable of both periodic walking and common volitional leg motions based on a piecewise holonomic phase variable through a finite state machine. The phase variable is constructed by measuring the thigh angle, and the transitions in the finite state machine are formulated through sensing foot contact together with attributes of a nominal reference gait trajectory. The controller was implemented on a powered knee-ankle prosthesis and tested with a transfemoral amputee subject, who successfully performed a wide range of periodic and non-periodic tasks, including low- and high-speed walking, quick start and stop, backward walking, walking over obstacles, and kicking a soccer ball. The proposed approach is expected to provide better understanding of volitional motions and lead to more reliable control of multi-joint prostheses for a wider range of tasks.

A GENERAL FRAMEWORK FOR MINIMIZING ENERGY CONSUMPTION OF SERIES ELASTIC ACTUATORS WITH REGENERATION.

The use of actuators with inherent compliance, such as series elastic actuators (SEAs), has become traditional for robotic systems working in close contact with humans. SEAs can reduce the energy consumption for a given task compared to rigid actuators, but this reduction is highly dependent on the design of the SEA's elastic element. This design is often based on natural dynamics or a parameterized optimization, but both approaches have limitations. The natural dynamics approach cannot consider actuator constraints or arbitrary reference trajectories, and a parameterized elastic element can only be optimized within the given parameter space. In this work, we propose a solution to these limitations by formulating the design of the SEA's elastic element as a non-parametric convex optimization problem, which yields a globally optimal conservative elastic element while respecting actuator constraints. Convexity is proven for the case of an arbitrary periodic reference trajectory with a SEA capable of energy regeneration. We discuss the optimization results for the tasks defined by the human ankle motion during level-ground walking and the natural motion of a single mass-spring system with a nonlinear spring. For all these tasks, the designed SEA reduces energy consumption and satisfies the actuator's constraints.

A Control Framework for Anthropomorphic Biped Walking Based on Stabilizing Feedforward Trajectories.

Although dynamic walking methods have had notable successes in control of bipedal robots in the recent years, still most of the humanoid robots rely on quasi-static Zero Moment Point controllers. This work is an attempt to design a highly stable controller for dynamic walking of a human-like model which can be used both for control of humanoid robots and prosthetic legs. The method is based on using time-based trajectories that can induce a highly stable limit cycle to the bipedal robot. The time-based nature of the controller motivates its use to entrain a model of an amputee walking, which can potentially lead to a better coordination of the interaction between the prosthesis and the human. The simulations demonstrate the stability of the controller and its robustness against external perturbations.