Data-Driven Variable Impedance Control of a Powered Knee-Ankle Prosthesis for Adaptive Speed and Incline Walking.

Most impedance-based walking controllers for powered knee-ankle prostheses use a finite state machine with dozens of user-specific parameters that require manual tuning by technical experts. These parameters are only appropriate near the task (e.g., walking speed and incline) at which they were tuned, necessitating many different parameter sets for variable-task walking. In contrast, this paper presents a data-driven, phase-based controller for variable-task walking that uses continuously-variable impedance control during stance and kinematic control during swing to enable biomimetic locomotion. After generating a data-driven model of variable joint impedance with convex optimization, we implement a novel task-invariant phase variable and real-time estimates of speed and incline to enable autonomous task adaptation. Experiments with above-knee amputee participants (N=2) show that our data-driven controller 1) features highly-linear phase estimates and accurate task estimates, 2) produces biomimetic kinematic and kinetic trends as task varies, leading to low errors relative to able-bodied references, and 3) produces biomimetic joint work and cadence trends as task varies. We show that the presented controller meets and often exceeds the performance of a benchmark finite state machine controller for our two participants, without requiring manual impedance tuning.

Real-Time Gait Phase and Task Estimation for Controlling a Powered Ankle Exoskeleton on Extremely Uneven Terrain.

Positive biomechanical outcomes have been reported with lower-limb exoskeletons in laboratory settings, but these devices have difficulty delivering appropriate assistance in synchrony with human gait as the task or rate of phase progression change in real-world environments. This paper presents a controller for an ankle exoskeleton that uses a data-driven kinematic model to continuously estimate the phase, phase rate, stride length, and ground incline states during locomotion, which enables the real-time adaptation of torque assistance to match human torques observed in a multi-activity database of 10 able-bodied subjects. We demonstrate in live experiments with a new cohort of 10 able-bodied participants that the controller yields phase estimates comparable to the state of the art, while also estimating task variables with similar accuracy to recent machine learning approaches. The implemented controller successfully adapts its assistance in response to changing phase and task variables, both during controlled treadmill trials (N=10, phase RMSE: 4.8 ± 2.4%) and a real-world stress test with extremely uneven terrain (N=1, phase RMSE: 4.8 ± 2.7%).

Nonholonomic Virtual Constraints for Control of Powered Prostheses Across Walking Speeds.

This paper presents a method to design a nonholonomic virtual constraint (NHVC) controller that produces multiple distinct stance-phase trajectories for corresponding walking speeds. NHVCs encode velocity-dependent joint trajectories via momenta conjugate to the unactuated degree(s)-of-freedom of the system. We recently introduced a method for designing NHVCs that allow for stable bipedal robotic walking across variable terrain slopes. This work extends the notion of NHVCs for application to variable-cadence powered prostheses. Using the segmental conjugate momentum for the prosthesis, an optimization problem is used to design a single stance-phase NHVC for three distinct walking speed trajectories (slow, normal, and fast). This stance-phase controller is implemented with a holonomic swing phase controller on a powered knee-ankle prosthesis, and experiments are conducted with an able-bodied user walking in steady and non-steady velocity conditions. The control scheme is capable of representing 1) multiple, task-dependent reference trajectories, and 2) walking gait variance due to both temporal and kinematic changes in user motion.

Design Principles for Compact, Backdrivable Actuation in Partial-Assist Powered Knee Orthoses.

This paper presents the design and validation of a backdrivable powered knee orthosis for partial assistance of lower-limb musculature, which aims to facilitate daily activities in individuals with musculoskeletal disorders. The actuator design is guided by design principles that prioritize backdrivability, output torque, and compactness. First, we show that increasing the motor diameter while reducing the gear ratio for a fixed output torque ultimately reduces the reflected inertia (and thus backdrive torque). We also identify a tradeoff with actuator torque density that can be addressed by improving the motor's thermal environment, motivating our design of a custom Brushless DC motor with encapsulated windings. Finally, by designing a 7:1 planetary gearset directly into the stator, the actuator has a high package factor that reduces size and weight. Benchtop tests verify that the custom actuator can produce at least 23.9 Nm peak torque and 12.78 Nm continuous torque, yet has less than 2.68 Nm backdrive torque during walking conditions. Able-bodied human subjects experiments (N=3) demonstrate reduced quadriceps activation with bilateral orthosis assistance during lifting-lowering, sit-to-stand, and stair climbing. The minimal transmission also produces negligible acoustic noise.

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.

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.

Decentralized Passivity-Based Control With a Generalized Energy Storage Function for Robust Biped Locomotion.

This paper details a decentralized passivity-based control (PBC) to improve the robustness of biped locomotion in the presence of gait-generating external torques and parametric errors in the biped model. Previous work demonstrated a passive output for biped systems based on a generalized energy that, when directly used for feedback control, increases the basin of attraction and convergence rate of the biped to a stable limit cycle. This paper extends the concept with a theoretical framework to address both uncertainty in the biped model and a lack of sensing hardware, by allowing the designer to neglect arbitrary states and parameters in the system. This framework also allows the control to be implemented on wearable devices, such as a lower limb exoskeleton or powered prosthesis, without needing a model of the user's dynamics. Simulations on a six-link biped model demonstrate that the proposed control scheme increases the convergence rate of the biped to a walking gait and improves the robustness to perturbations and to changes in ground slope.

Continuous-Phase Control of a Powered Knee-Ankle Prosthesis: Amputee Experiments Across Speeds and Inclines.

Control systems for powered prosthetic legs typically divide the gait cycle into several periods with distinct controllers, resulting in dozens of control parameters that must be tuned across users and activities. To address this challenge, this paper presents a control approach that unifies the gait cycle of a powered knee-ankle prosthesis using a continuous, user-synchronized sense of phase. Virtual constraints characterize the desired periodic joint trajectories as functions of a phase variable across the entire stride. The phase variable is computed from residual thigh motion, giving the amputee control over the timing of the prosthetic joint patterns. This continuous sense of phase enabled three transfemoral amputee subjects to walk at speeds from 0.67 to 1.21 m/s and slopes from -2.5 to +9.0 deg. Virtual constraints based on task-specific kinematics facilitated normative adjustments in joint work across walking speeds. A fixed set of control gains generalized across these activities and users, which minimized the configuration time of the prosthesis.

Underactuated Potential Energy Shaping with Contact Constraints: Application to a Powered Knee-Ankle Orthosis.

Body-weight support (i.e., gravity compensation) is an effective clinical tool for gait rehabilitation after neurological impairment. Body-weight supported training systems have been developed to help patients regain mobility and confidence during walking, but conventional systems constrain the patient's treatment in clinical environments. We propose that this challenge could be addressed by virtually providing patients with bodyweight support through the actuators of a powered orthosis (or exoskeleton) utilizing potential energy shaping control. However, the changing contact conditions and degrees of underactuation encountered during human walking present significant challenges to consistently matching a desired potential energy for the human in closed loop. We therefore derive a generalized matching condition for shaping Lagrangian systems with holonomic contact constraints. By satisfying this matching condition for four phases of gait, we derive passivity-based control laws to achieve virtual body-weight support through a powered knee-ankle orthosis. We demonstrate beneficial effects of virtual body-weight support in simulations of a human-like biped model, indicating the potential clinical value of this proposed control approach.

Toward Unified Control of a Powered Prosthetic Leg: A Simulation Study.

This brief presents a novel control strategy for a powered knee-ankle prosthesis that unifies the entire gait cycle, eliminating the need to switch between controllers during different periods of gait. A reduced-order Discrete Fourier Transformation (DFT) is used to define virtual constraints that continuously parameterize periodic joint patterns as functions of a mechanical phasing variable. In order to leverage the provable stability properties of Hybrid Zero Dynamics (HZD), hybrid-invariant Bézier polynomials are converted into unified DFT virtual constraints for various walking speeds. Simulations of an amputee biped model show that the unified prosthesis controller approximates the behavior of the original HZD design under ideal scenarios and has advantages over the HZD design when hybrid invariance is violated by mismatches with the human controller. Two implementations of the unified virtual constraints, a feedback linearizing controller and a more practical joint impedance controller, produce similar results in simulation.

Stable, Robust Hybrid Zero Dynamics Control of Powered Lower-Limb Prostheses.

To improve the quality of life for lower-limb amputees, powered prostheses are being developed. Advanced control schemes from the field of bipedal robots, such as hybrid zero dynamics (HZD), may provide great performance. HZD-based control specifies the motion of the actuated joints using output functions to be zeroed, and the required torques are calculated using input-output linearization. For one-step periodic gaits, there is an analytic metric of stability. To apply HZD-based control on a powered prosthesis, several modifications must be made. Because the prosthesis and amputee are only connected via the socket, the prosthesis controller does not have access to the full state of the biped, which decentralizes the form of the input-output linearization. The differences between the amputated and contralateral sides result in a two-step periodic gait, which requires the orbital stability metric to be extended. In addition, because human gait is variable, the prosthesis controller must be robust to continuous moderate perturbations. This robustness is proved using local input-to-state stability and demonstrated with simulations of an above-knee amputee model.

Decentralized Feedback Controllers for Robust Stabilization of Periodic Orbits of Hybrid Systems: Application to Bipedal Walking.

This paper presents a systematic algorithm to design time-invariant decentralized feedback controllers to exponentially and robustly stabilize periodic orbits for hybrid dynamical systems against possible uncertainties in discrete-time phases. The algorithm assumes a family of parameterized and decentralized nonlinear controllers to coordinate interconnected hybrid subsystems based on a common phasing variable. The exponential and [Formula: see text] robust stabilization problems of periodic orbits are translated into an iterative sequence of optimization problems involving bilinear and linear matrix inequalities. By investigating the properties of the Poincaré map, some sufficient conditions for the convergence of the iterative algorithm are presented. The power of the algorithm is finally demonstrated through designing a set of robust stabilizing local nonlinear controllers for walking of an underactuated 3D autonomous bipedal robot with 9 degrees of freedom, impact model uncertainties, and a decentralization scheme motivated by amputee locomotion with a transpelvic prosthetic leg.

Incorporating Human-like Walking Variability in an HZD-Based Bipedal Model.

Predictive simulations of human walking could be used to investigate a wide range of questions. Promising moderately complex models have been developed using the robotics control technique hybrid zero dynamics (HZD). Existing simulations of human walking only consider the mean motion, so they cannot be used to investigate fall risk, which is correlated with variability. This work determines how to incorporate human-like variability into an HZD-based healthy human model to generate a more realistic gait. The key challenge is determining how to combine the existing mathematical description of variability with the dynamic model so that the biped is still able to walk without falling. To do so, the commanded motion is augmented with a sinusoidal variability function and a polynomial correction function. The variability function captures the variation in joint angles while the correction function prevents the variability function from growing uncontrollably. The necessity of the correction function and the improvements with a reduction of stance ankle variability are demonstrated via simulations. The variability in temporal measures is shown to be similar to experimental values.

Virtual Constraint Control of a Powered Prosthetic Leg: From Simulation to Experiments with Transfemoral Amputees.

Recent powered (or robotic) prosthetic legs independently control different joints and time periods of the gait cycle, resulting in control parameters and switching rules that can be difficult to tune by clinicians. This challenge might be addressed by a unifying control model used by recent bipedal robots, in which virtual constraints define joint patterns as functions of a monotonic variable that continuously represents the gait cycle phase. In the first application of virtual constraints to amputee locomotion, this paper derives exact and approximate control laws for a partial feedback linearization to enforce virtual constraints on a prosthetic leg. We then encode a human-inspired invariance property called effective shape into virtual constraints for the stance period. After simulating the robustness of the partial feedback linearization to clinically meaningful conditions, we experimentally implement this control strategy on a powered transfemoral leg. We report the results of three amputee subjects walking overground and at variable cadences on a treadmill, demonstrating the clinical viability of this novel control approach.

Towards Biomimetic Virtual Constraint Control of a Powered Prosthetic Leg.

This brief presents a novel control strategy for a powered prosthetic ankle based on a biomimetic virtual constraint. We first derive a kinematic constraint for the "effective shape" of the human ankle-foot complex during locomotion. This shape characterizes ankle motion as a function of the Center of Pressure (COP)-the point on the foot sole where the resultant ground reaction force is imparted. Since the COP moves monotonically from heel to toe during steady walking, we adopt the COP as a mechanical representation of the gait cycle phase in an autonomous feedback controller. We show that our kinematic constraint can be enforced as a virtual constraint by an output linearizing controller that uses only feedback available to sensors onboard a prosthetic leg. Using simulations of a passive walking model with feet, we show that this novel controller exactly enforces the desired effective shape whereas a standard impedance (i.e., proportional-derivative) controller cannot. This work provides a single, biomimetic control law for the entire single-support period during robot-assisted locomotion.

Transfer Learning for Efficient Intent Prediction in Lower-Limb Prosthetics: A Strategy for Limited Datasets.

This paper presents a transfer learning method to enhance locomotion intent prediction in novel transfemoral amputee subjects, particularly in data-sparse scenarios. Transfer learning is done with three pre-trained models trained on separate datasets: transfemoral amputees, able-bodied individuals, and a mixed dataset of both groups. Each model is subsequently fine-tuned using data from a new transfemoral amputee subject. While subject-dependent models, trained and tested using individual user data, can achieve the least error rate, they require extensive training datasets. In contrast, our transfer learning approach yields comparable error rates while requiring significantly less data. This highlights the benefit of using preexisting, pre-trained features when data is scarce. As anticipated, the performance of transfer learning improves as more data from the subject is made available. We also explore the performance of the intent prediction system under various sensor configurations. We identify that a combination of a thigh inertial measurement unit and load cell offers a practical and efficient choice for sensor setup. These findings underscore the potential of transfer learning as a powerful tool for enhancing intent prediction accuracy for new transfemoral amputee subjects, even under data-limited conditions.

Robustification of Bayesian-Inference-Based Gait Estimation for Lower-limb Wearable Robots.

Lower-limb wearable robots designed to assist people in everyday activities must reliably recover from any momentary confusion about what the user is doing. Such confusion might arise from momentary sensor failure, collision with an obstacle, losing track of gait due to an out-of-distribution stride, etc. Systems that infer a user's walking condition from angle measurements using Bayesian filters (e.g., extended Kalman filters) have been shown to accurately track gait across a range of activities. However, due to the fundamental problem structure and assumptions of Bayesian filter implementations, such estimators risk becoming 'lost' with little hope of a quick recovery. In this paper, we 1) introduce a Monte Carlo-based metric to quantify the robustness of pattern-tracking gait estimators, 2) propose strategies for improving tracking robustness, and 3) systematically evaluate them against this new metric using a publicly available gait biomechanics dataset. Our results, aggregating 2,700 trials of simulated walking of 10 able-bodied subjects under random perturbations, suggest that drastic improvements in robustness (from 8.9% to 99%) are possible using relatively simple modifications to the estimation process without noticeably degrading estimator accuracy.

Data-Driven Phase-Based Control of a Powered Knee-Ankle Prosthesis for Variable-Incline Stair Ascent and Descent.

Powered knee-ankle prostheses can offer benefits over conventional passive devices during stair locomotion by providing biomimetic net-positive work and active control of joint angles. However, many modern control approaches for stair ascent and descent are often limited by time-consuming hand-tuning of user/task-specific parameters, predefined trajectories that remove user volition, or heuristic approaches that cannot be applied to both stair ascent and descent. This work presents a phase-based hybrid kinematic and impedance controller (HKIC) that allows for semi-volitional, biomimetic stair ascent and descent at a variety of step heights. We define a unified phase variable for both stair ascent and descent that utilizes lower-limb geometry to adjust to different users and step heights. We extend our prior data-driven impedance model for variable-incline walking, modifying the cost function and constraints to create a continuously-varying impedance parameter model for stair ascent and descent over a continuum of step heights. Experiments with above-knee amputee participants (N=2) validate that our HKIC controller produces biomimetic ascent and descent joint kinematics, kinetics, and work across four step height configurations. We also show improved kinematic performance with our HKIC controller in comparison to a passive microprocessor-controlled device during stair locomotion.

Controlled Reduction with Unactuated Cyclic Variables: Application to 3D Bipedal Walking with Passive Yaw Rotation.

This paper shows that viscous damping can shape momentum conservation laws in a manner that stabilizes yaw rotation and enables steering for underactuated 3D walking. We first show that unactuated cyclic variables can be controlled by passively shaped conservation laws given a stabilizing controller in the actuated coordinates. We then exploit this result to realize controlled geometric reduction with multiple unactuated cyclic variables. We apply this underactuated control strategy to a five-link 3D biped to produce exponentially stable straight-ahead walking and steering in the presence of passive yawing.