Quantifying the effect of sagittal plane joint angle variability on bipedal fall risk

Falls are a major issue for bipeds. For elderly adults, falls can have a negative impact on their quality of life and lead to increased medical costs. Fortunately, interventional methods are effective at reducing falls assuming they are prescribed. For biped robots, falls prevent them from completing required tasks. Thus, it is important to understand what aspects of gait increase fall risk. Gait variability may be associated with increased fall risk; however, previous studies have not investigated the variation in the movement of the legs. The purpose of this study was to determine the effect of joint angle variability on falling to determine which component(s) of variability were statistically significant. In order to investigate joint angle variability, a physics-based simulation model that captured joint angle variability as a function of time through Fourier series was used. This allowed the magnitude, the frequency mean, and the frequency standard deviation of the variability to be altered. For the values tested, results indicated that the magnitude of the variability had the most significant impact on falling, and specifically that the stance knee flexion variability magnitude was the most significant factor. This suggests that increasing the joint variability magnitude may increase fall risk, particularly if the controller is not able to actively compensate. Altering the variability frequency had little to no effect on falling.

Singular Configurations and Underactuated Balance Control for Biped Robot with Point Contact

This paper presents a hierarchical controller and extracts the singular configurations based on underactuated system and optimal distribution of forces. Unlike multi-legged and large-sole robots, biped robot with point contact cannot maintain a stable standing state, much less to adjust attitude and resist external impact. The support domain of point-foot bipedal robot degenerates into a line segment consisting of two footholds, introducing the underdactuated characteristic that challenges traditional algorithms based on polygonal domains and full variable optimization. To fully exploit the dynamic connection between support line and balance control, the accurate model is established as feedforward terms using virtual leg and floating reference system. The dynamics model is decomposed into an underactuated module and a force distribution module for hierarchical control, in which the former determines the control forces of base and the singularity corresponding to robot configuration, and the latter distributes forces on each leg according to its capability by solving a quadratic programming with constraints. The results verify the advanced stability of attitude adjustment and impact from external force of biped robot with point contact comparing to model predictive control, which is improved based on robot’s singular configuration.

Multiphase and Multivariable Linear Controllers That Account for the Joint Torques in Normal Human Walking

OBJECTIVE

The objective of this paper is to investigate whether a small number of sequentially composed multivariable linear controllers can be used to recover a defining relation between the joint torques, angles, and velocities hidden in the walking data of multiple human subjects.

METHODS

We solve a mixed integer programming problem that defines the optimal multivariable and multiphase relation between the torques, angles, and velocities for the hip, knee, and ankle joints.

RESULTS

Using the data of seven healthy subjects, we show that the aforementioned relation can be remarkably well represented by four sequentially composed and independently activated multivariable linear controllers; the controllers account for [Formula: see text] (mean ± sem) of the variance in the joint torques across subjects, and [Formula: see text] of the variance for a new subject. We further show that each controller is associated with one of the four phases of the gait cycle, separated by toe-off and heel-strike.

CONCLUSION

The proposed controller generalizes previously developed multiphase single variable, and single phase multivariable controllers, to a multiphase multivariable controller that better explains the walking data of multiple subjects, and better generalizes to new subjects.

SIGNIFICANCE

Our result provides strong support to extend previously developed decoupled single joint controllers to coupled multijoint multivariable controllers for the control of human assistive and augmentation devices.

A Phase-Invariant Linear Torque-Angle-Velocity Relation Hidden in Human Walking Data

Human walking is a sequential composition of gait cycles. Each gait cycle can be divided into four motion phases separated by heel strike and toe off. A classical conjecture in the control of lower limb assistive devices, state-of-the-art prostheses, and exoskeletons, is that each motion phase requires a different controller, such that adequate control of locomotion requires at least four distinct controllers. In this paper, we show that the joint torque versus joint angle and velocity relation hidden in the normal human walking data can be remarkably well represented with a single linear controller. In particular, based on the analysis of seven healthy subjects, we show that a one phase 20±5% sparse linear relation between the joint torques, angles and velocities explains 96.1±0.4% (mean±sem) of the normal human walking data (sparsity defines the percentage of zero control parameters). This result is comparable to what can be achieved using a significantly more complex four-phase non-sparse linear controller which explains 98.7±0.2% of the walking data, and is significantly better than a one-phase fully sparsified linear controller that could only explain 11.9±0.2% of the same data. Based on these results, we posit that the proposed phase-invariant sparse linear controller provides one of the simplest representations that can adequately explain the joint torque, angle and velocity relation present in the human walking data. The resulting control structure may be useful in developing simple yet competent phase-invariant controllers for next-generation prostheses and exoskeleton devices used for human assistance and augmentation.

Simulation Analysis of Linear Quadratic Regulator Control of Sagittal-Plane Human Walking-Implications for Exoskeletons

The linear quadratic regulator (LQR) is a classical optimal control approach that can regulate gait dynamics about target kinematic trajectories. Exoskeletons to restore gait function have conventionally utilized time-varying proportional-derivative (PD) control of leg joints. But, these PD parameters are not uniquely optimized for whole-body (full-state) performance. The objective of this study was to investigate the effectiveness of LQR full-state feedback compared to PD control to maintain bipedal walking of a sagittal-plane computational model against force disturbances. Several LQR controllers were uniquely solved with feedback gains optimized for different levels of tracking capability versus control effort. The main implications to future exoskeleton control systems include (1) which LQR controllers out-perform PD controllers in walking maintenance and effort, (2) verifying that LQR desirably produces joint torques that oppose rapidly growing joint state errors, and (3) potentially equipping accurate sensing systems for nonjoint states such as hip-position and torso orientation. The LQR controllers capable of longer walk times than respective PD controllers also required less control effort. During sudden leg collapse, LQR desirably behaved like PD by generating feedback torques that opposed the direction of leg-joint errors. Feedback from nonjoint states contributed to over 50% of the LQR joint torques and appear critical for whole-body LQR control. While LQR control poses implementation challenges, such as more sensors for full-state feedback and operation near the desired trajectories, it offers significant performance advantages over PD control.

Passivity-Based Control with a Generalized Energy Storage Function for Robust Walking of Biped Robots

This paper offers a novel generalization of a passivity-based, energy tracking controller for robust bipedal walking. Past work has shown that a biped limit cycle with a known, constant mechanical energy can be made robust to uneven terrains and disturbances by actively driving energy to that reference. However, the assumption of a known, constant mechanical energy has limited application of this passivity-based method to simple toy models (often passive walkers). The method presented in this paper allows the passivity-based controller to be used in combination with an arbitrary inner-loop control that creates a limit cycle with a constant generalized system energy. We also show that the proposed control method accommodates arbitrary degrees of underactuation. Simulations on a 7-link biped model demonstrate that the proposed control scheme enlarges the basin of attraction, increases the convergence rate to the limit cycle, and improves robustness to ground slopes.

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.

Unified Phase Variables of Relative Degree Two for Human Locomotion

A starting point to achieve stable locomotion is synchronizing the leg joint kinematics during the gait cycle. Some biped robots parameterize a nonlinear controller (e.g., input-output feedback linearization) whose main objective is to track specific kinematic trajectories as a function of a single mechanical variable (i.e., a phase variable) in order to allow the robot to walk. A phase variable capable of parameterizing the entire gait cycle, the hip phase angle, has been used to control wearable robots and was recently shown to provide a robust representation of the phase of human gait. However, this unified phase variable relies on hip velocity, which is difficult to measure in real-time and prevents the use of derivative corrections in phase-based controllers for wearable robots. One derivative of this phase variable yields accelerations (i.e., the equations of motion), so the system is said to be relative degree-one. This means that there are states of the system that cannot be controlled. The goal of this paper is to offer relative degree-two alternatives to the hip phase angle and examine their robustness for parameterizing human gait.

Orthotic Body-Weight Support Through Underactuated Potential Energy Shaping with Contact Constraints

Body-weight support 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 body-weight 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 introduce a generalized matching condition for shaping Lagrangian systems with holonomic contact constraints. By satisfying this matching condition for four phases of gait, we derive 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.

Optimal periodic gain scheduling for bipedal walking with hybrid dynamics

We present an optimal gain scheduling control design for bipedal walking with minimum tracking error. We obtained a linear approximation by linearizing the nonlinear hybrid dynamic model about a nominal periodic trajectory. This linearization allows us to identify the linear model as a linear periodic system. An optimal feedback was designed using Bellman's dynamic programming. The linear periodic system allows us to determine a linear quadratic regulator (LQR) for a single period and to set the Hamilton-Jacobi-Bellman (HJB) function in a linear quadratic form. In this way, the dynamic programming yielded an admissible continuous gain scheduling that was designed with regard to the hybrid dynamics of the system. We tuned the optimization parameters such that the tracking error and the average energy consumption are minimized. Due to linearization, we were able to examine the stability of the approximated periodic system achieved by the periodic gain according to Floquet's theory, by calculating the monodromy matrix of the closed-loop hybrid system. In addition to determining stability, the eigenvalues of this approximated monodromy matrix allowed us to evaluate the settling time of the system. This approach presents a direct method for optimal solution of locomotion control according to a given reference trajectory.

Energy-efficient SVM learning control system for biped walking robots

An energy-efficient support vector machine (EE-SVM) learning control system considering the energy cost of each training sample of biped dynamic is proposed to realize energy-efficient biped walking. Energy costs of the biped walking samples are calculated. Then the samples are weighed with the inverses of the energy costs. An EE-SVM objective function with energy-related slack variables is proposed, which follows the principle that the sample with the lowest energy consumption is treated as the most important one in the training. That means the samples with lower energy consumption contribute more to the EE-SVM regression function learning, which highly increases the energy efficiency of the biped walking. Simulation results demonstrate the effectiveness of the proposed method.

Passive and dynamic gait measures for biped mechanism: formulation and simulation analysis

Understanding and mimicking human gait is essential for design and control of biped walking robots. The unique characteristics of normal human gait are described as passive dynamic walking, whereas general human gait is neither completely passive nor always dynamic. To study various walking motions, it is important to quantify the different levels of passivity and dynamicity, which have not been addressed in the current literature. In this paper, we introduce the initial formulations of Passive Gait Measure (PGM) and Dynamic Gait Measure (DGM) that quantify passivity and dynamicity, respectively, of a given biped walking motion, and the proposed formulations will be demonstrated for proof-of-concepts using gait simulation and analysis. The PGM is associated with the optimality of natural human walking, where the passivity weight functions are proposed and incorporated in the minimization of physiologically inspired weighted actuator torques. The PGM then measures the relative contribution of the stance ankle actuation. The DGM is associated with the gait stability, and quantifies the effects of inertia in terms of the Zero-Moment Point and the ground projection of center of mass. In addition, the DGM takes into account the stance foot dimension and the relative threshold between static and dynamic walking. As examples, both human-like and robotic walking motions during single support phase are generated for a planar biped system using the passivity weights and proper gait parameters. The calculated PGM values show more passive nature of human-like walking as compared with the robotic walking. The DGM results verify the dynamic nature of normal human walking with anthropomorphic foot dimension. In general, the DGMs for human-like walking are greater than those for robotic walking. The resulting DGMs also demonstrate their dependence on the stance foot dimension as well as the walking motion; for a given walking motion, smaller foot dimension results in increased dynamicity. Future work on experimental validation and demonstration will involve actual walking robots and human subjects. The proposed results will benefit the human gait studies and the development of walking robots.

Variable stiffness actuated prosthetic knee to restore knee buckling during stance: a modeling study

Most modern intelligent knee prosthesis use dampers to modulate dynamic behavior and prevent excessive knee flexion, but they dissipate energy and do not assist in knee extension. Energy efficient variable stiffness control (VSA) can reduce the energy consumption yet effectively modulate the dynamic behavior and use stored energy during flexion to assist in subsequent extension. A principle design of energy efficient VSA in a prosthetic knee is proposed and analyzed for the specific case of rejection of a disturbed stance phase. The concept is based on the principle that the output stiffness of a spring can be changed without changing the energy stored in the elastic elements of the spring. The usability of this concept to control a prosthetic knee is evaluated using a model. Part of the stance phase of the human leg was modeled by a double pendulum. Specifically the rejection of a common disturbance of transfemoral prosthetic gait, an unlocked knee at heel strike, was evaluated. The ranges of spring stiffnesses were determined such that the angular characteristics of a normal stance phase were preserved, but disturbances could also be rejected. The simulations predicted that energy efficient VSA can be useful for the control of prosthetic knees.