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

Evaluation of controllers for augmentative hip exoskeletons and their effects on metabolic cost of walking: explicit versus implicit synchronization

Background: Efficient gait assistance by augmentative exoskeletons depends on reliable control strategies. While numerous control methods and their effects on the metabolic cost of walking have been explored in the literature, the use of different exoskeletons and dissimilar protocols limit direct comparisons. In this article, we present and compare two controllers for hip exoskeletons with different synchronization paradigms. Methods: The implicit-synchronization-based approach, termed the Simple Reflex Controller (SRC), determines the assistance as a function of the relative loading of the feet, resulting in an emerging torque profile continuously assisting extension during stance and flexion during swing. On the other hand, the Hip-Phase-based Torque profile controller (HPT) uses explicit synchronization and estimates the gait cycle percentage based on the hip angle, applying a predefined torque profile consisting of two shorter bursts of assistance during stance and swing. We tested the controllers with 23 naïve healthy participants walking on a treadmill at 4 km ⋅ h-1, without any substantial familiarization. Results: Both controllers significantly reduced the metabolic rate compared to walking with the exoskeleton in passive mode, by 18.0% (SRC, p < 0.001) and 11.6% (HPT, p < 0.001). However, only the SRC led to a significant reduction compared to walking without the exoskeleton (8.8%, p = 0.004). The SRC also provided more mechanical power and led to bigger changes in the hip joint kinematics and walking cadence. Our analysis of mechanical powers based on a whole-body analysis suggested a reduce in ankle push-off under this controller. There was a strong correlation (Pearson's r = 0.778, p < 0.001) between the metabolic savings achieved by each participant with the two controllers. Conclusion: The extended assistance duration provided by the implicitly synchronized SRC enabled greater metabolic reductions compared to the more targeted assistance of the explicitly synchronized HPT. Despite the different assistance profiles and metabolic outcomes, the correlation between the metabolic reductions with the two controllers suggests a difference in individual responsiveness to assistance, prompting more investigations to explore the person-specific factors affecting assistance receptivity.

Optimal Energy Shaping Control for a Backdrivable Hip Exoskeleton

Task-dependent controllers widely used in exoskeletons track predefined trajectories, which overly constrain the volitional motion of individuals with remnant voluntary mobility. Energy shaping, on the other hand, provides task-invariant assistance by altering the human body's dynamic characteristics in the closed loop. While human-exoskeleton systems are often modeled using Euler-Lagrange equations, in our previous work we modeled the system as a port-controlled-Hamiltonian system, and a task-invariant controller was designed for a knee-ankle exoskeleton using interconnection-damping assignment passivity-based control. In this paper, we extend this framework to design a controller for a backdrivable hip exoskeleton to assist multiple tasks. A set of basis functions that contains information of kinematics is selected and corresponding coefficients are optimized, which allows the controller to provide torque that fits normative human torque for different activities of daily life. Human-subject experiments with two able-bodied subjects demonstrated the controller's capability to reduce muscle effort across different tasks.

Lower limb exoskeleton robot and its cooperative control: A review, trends, and challenges for future research

Effective control of an exoskeleton robot (ER) using a human-robot interface is crucial for assessing the robot's movements and the force they produce to generate efficient control signals. Interestingly, certain surveys were done to show off cutting-edge exoskeleton robots. The review papers that were previously published have not thoroughly examined the control strategy, which is a crucial component of automating exoskeleton systems. As a result, this review focuses on examining the most recent developments and problems associated with exoskeleton control systems, particularly during the last few years (2017-2022). In addition, the trends and challenges of cooperative control, particularly multi-information fusion, are discussed.

Bio-inspired design of a self-aligning, lightweight, and highly-compliant cable-driven knee exoskeleton

Powered knee exoskeletons have shown potential for mobility restoration and power augmentation. However, the benefits of exoskeletons are partially offset by some design challenges that still limit their positive effects on people. Among them, joint misalignment is a critical aspect mostly because the human knee joint movement is not a fixed-axis rotation. In addition, remarkable mass and stiffness are also limitations. Aiming to minimize joint misalignment, this paper proposes a bio-inspired knee exoskeleton with a joint design that mimics the human knee joint. Moreover, to accomplish a lightweight and high compliance design, a high stiffness cable-tension amplification mechanism is leveraged. Simulation results indicate our design can reduce 49.3 and 71.9% maximum total misalignment for walking and deep squatting activities, respectively. Experiments indicate that the exoskeleton has high compliance (0.4 and 0.1 Nm backdrive torque under unpowered and zero-torque modes, respectively), high control bandwidth (44 Hz), and high control accuracy (1.1 Nm root mean square tracking error, corresponding to 7.3% of the peak torque). This work demonstrates performance improvement compared with state-of-the-art exoskeletons.

Optimally Biomimetic Passivity-Based Control of a Lower-Limb Exoskeleton Over the Primary Activities of Daily Life

Task-specific, trajectory-based control methods commonly used in exoskeletons may be appropriate for individuals with paraplegia, but they overly constrain the volitional motion of individuals with remnant voluntary ability (representing a far larger population). Human-exoskeleton systems can be represented in the form of the Euler-Lagrange equations or, equivalently, the port-controlled Hamiltonian equations to design control laws that provide task-invariant assistance across a continuum of activities/environments by altering energetic properties of the human body. We previously introduced a port-controlled Hamiltonian framework that parameterizes the control law through basis functions related to gravitational and gyroscopic terms, which are optimized to fit normalized able-bodied joint torques across multiple walking gaits on different ground inclines. However, this approach did not have the flexibility to reproduce joint torques for a broader set of activities, including stair climbing and stand-to-sit, due to strict assumptions related to input-output passivity, which ensures the human remains in control of energy growth in the closed-loop dynamics. To provide biomimetic assistance across all primary activities of daily life, this paper generalizes this energy shaping framework by incorporating vertical ground reaction forces and global planar orientation into the basis set, while preserving passivity between the human joint torques and human joint velocities. We present an experimental implementation on a powered knee-ankle exoskeleton used by three able-bodied human subjects during walking on various inclines, ramp ascent/descent, and stand-to-sit, demonstrating the versatility of this control approach and its effect on muscular effort.

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.

A Complex Stiffness Human Impedance Model With Customizable Exoskeleton Control

The natural impedance, or dynamic relationship between force and motion, of a human operator can determine the stability of exoskeletons that use interaction-torque feedback to amplify human strength. While human impedance is typically modelled as a linear system, our experiments on a single-joint exoskeleton testbed involving 10 human subjects show evidence of nonlinear behavior: a low-frequency asymptotic phase for the dynamic stiffness of the human that is different than the expected zero, and an unexpectedly consistent damping ratio as the stiffness and inertia vary. To explain these observations, this article considers a new frequency-domain model of the human joint dynamics featuring complex value stiffness comprising a real stiffness term and a hysteretic damping term. Using a statistical F-test we show that the hysteretic damping term is not only significant but is even more significant than the linear damping term. Further analysis reveals a linear trend linking hysteretic damping and the real part of the stiffness, which allows us to simplify the complex stiffness model down to a 1-parameter system. Then, we introduce and demonstrate a customizable fractional-order controller that exploits this hysteretic damping behavior to improve strength amplification bandwidth while maintaining stability, and explore a tuning approach which ensures that this stability property is robust to muscle co-contraction for each individual.

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.

Design and Validation of a Partial-Assist Knee Orthosis with Compact, Backdrivable Actuation

This paper presents the mechatronic design and initial validation of a partial-assist knee orthosis for individuals with musculoskeletal disorders, e.g., knee osteoarthritis and lower back pain. This orthosis utilizes a quasi-direct drive actuator with a low-ratio transmission (7:1) to greatly reduce the reflected inertia for high backdrivability. To provide meaningful assistance, a custom Brushless DC (BLDC) motor is designed with encapsulated windings to improve the motor's thermal environment and thus its continuous torque output. The 2.69 kg orthosis is constructed from all custom-made components with a high package factor for lighter weight and a more compact size. The combination of compactness, backdrivability, and torque output enables the orthosis to provide partial assistance without obstructing the natural movement of the user. Several benchtop tests verify the actuator's capabilities, and a human subject experiment demonstrates reduced quadriceps muscle activation when assisted during a repetitive lifting and lowering task.

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.

Towards Total Energy Shaping Control of Lower-Limb Exoskeletons

Current robotic exoskeletons enforce fixed reference joint patterns during gait rehabilitation. These control methods aim to replicate normative joint kinematics but do not facilitate learning patient-specific kinematics. Trajectory-free control methods for exoskeletons are required to promote user control over joint kinematics. Our prior work on potential energy shaping provides virtual body-weight support through a trajectory-free control law, but altering only the gravitational forces does not assist the subject in accelerating/decelerating the body forward. Kinetic energy is velocity dependent and thus shaping the kinetic energy in addition to potential energy can yield greater dynamical changes in closed loop. In this paper, we generalize our previous work to achieve underactuated total energy shaping of the human body through a lower-limb exoskeleton. By shaping the fully-actuated part of the body's mass matrix, we satisfy the matching condition for different contact phases and obtain trajectory-free control laws. Simulations of a human-like biped demonstrate speed regulation in addition to body-weight support, indicating the potential clinical value of this control approach.

Design and Validation of a Torque Dense, Highly Backdrivable Powered Knee-Ankle Orthosis

This paper presents the mechatronic design and experimental validation of a novel powered knee-ankle orthosis for testing torque-driven rehabilitation control strategies. The modular actuator of the orthosis is designed with a torque dense motor and a custom low-ratio transmission (24:1) to provide mechanical transparency to the user, allowing them to actively contribute to their joint kinematics during gait training. The 4.88 kg orthosis utilizes frameless components and light materials, such as aluminum alloy and carbon fiber, to reduce its mass. A human subject experiment demonstrates accurate torque control with high output torque during stance and low backdrive torque during swing at fast walking speeds. This work shows that backdrivability, precise torque control, high torque output, and light weight can be achieved in a powered orthosis without the high cost and complexity of variable transmissions, clutches, and/or series elastic components.

Experimental Implementation of Underactuated Potential Energy Shaping on a Powered Ankle-Foot Orthosis

Traditional control methodologies of rehabilitation orthoses/exoskeletons aim at replicating normal kinematics and thus fall into the category of kinematic control. This control paradigm depends on pre-defined reference trajectories, which can be difficult to adjust between different locomotor tasks and human subjects. An alternative control category, kinetic control, enforces kinetic goals (e.g., torques or energy) instead of kinematic trajectories, which could provide a flexible learning environment for the user while freeing up therapists to make corrections. We propose that the theory of underactuated potential energy shaping, which falls into the category of kinetic control, could be used to generate virtual body-weight support for stroke gait rehabilitation. After deriving the nonlinear control law and simulating it on a human-like biped model, we implemented this controller on a powered ankle-foot orthosis that was designed specifically for testing torque control strategies. Experimental results with an able-bodied human subject demonstrate the feasibility of the control approach for both positive and negative virtual body-weight augmentation.