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The mechanical impedance of the human lower-limb joints during locomotion encodes our understanding of how the neuromotor system regulates the behavior of these tasks. Impedance is also a key component of several strategies for translating this behavior to robots, powered prosthetic limbs, and people empowered by exoskeletons. However, due to difficulty in making accurate measurements, there is little empirical evidence for the impedance behaviors of joints other than the ankle during active walking tasks. In this letter we propose a measurement system based on a highly backdrivable quasi-direct-drive actuator and a carefully calibrated actuator torque model. Bench-top validation with known mechanical impedance human-substitutes, confirms the viability of this system as an impedance measurement tool. A pilot study with two subjects utilizing a custom knee-exoskeleton apparatus confirms the feasibility of this system for human walking experiments. 

Emerging wearable, assistive, and mobile robots seek to interact with the environment and/or humans in a compliant, dynamic, and adaptable way. Springs are critical to achieving this objective, but the associated increase in volume, mass, and complexity is limiting their application and impact in this rapidly developing field. This article presents a novel rotary spring architecture that is both lightweight and compact. Our two-part spring consists of radially-spaced cantilever beams that interface with an internal, gear-like camshaft. We present the concept and equations governing their mechanics and design. To facilitate broad adoption, we introduce an open-source design tool, which enables the design of custom springs in minutes instead of hours or days. We also empirically demonstrate our design with four test springs and validate the achievement of target spring rates and deflections. Finally, we present several redesigns of existing springs in the robotics literature to demonstrate the wide applicability of our spring architecture. 

Accurate impedance control is key for biomimetic mechanical behavior in lower-limb robotic prostheses. However, due to compliance, friction, and inertia in the drivetrain, the commonly used open-loop impedance control strategy can often produce inaccurate results without appropriate compensation. This article presents a controller that accounts for these dynamics to improve the impedance rendering accuracy of a robotic prosthesis research platform, the Open-Source Leg (OSL v2). We first develop a dynamic model of the OSL v2’s drivetrain and show that it accurately predicts the system's joint torque with 97% mean explained variance across a diverse array of experiments. We then present a controller that compensates for the OSL v2’s inherent dynamics using a combination of feedback linearization and actuator-state feedback control. We experimentally validate this controller on the OSL v2 with a rotary dynamometer and in treadmill walking experiments. We show that it can render various constant impedance behaviors with higher stiffness and damping accuracy than a baseline controller. We also show our controller's ability to replicate the variable impedance trajectories of the human ankle joint, suggesting that this control approach could enable robotic prostheses that are biomimetic in their mechanical impedance in addition to their kinematics and kinetics. 

Natural dynamics, nonlinear optimization, and, more recently, convex optimization are available methods for stiffness design of energy-efficient series elastic actuators. Natural dynamics and general nonlinear optimization only work for a limited set of load kinetics and kinematics, cannot guarantee convergence to a global optimum, or depend on initial conditions to the numerical solver. Convex programs alleviate these limitations and allow a global solution in polynomial time, which is useful when the space of optimization variables grows (e.g., when designing optimal nonlinear springs or co-designing spring, controller, and reference trajectories). Our previous work introduced the stiffness design of series elastic actuators via convex optimization when the transmission dynamics are negligible, which is an assumption that applies mostly in theory or when the actuator uses a direct or quasi-direct drive. In this work, we extend our analysis to include friction at the transmission. Coulomb friction at the transmission results in a non-convex expression for the energy dissipated as heat, but we illustrate a convex approximation for stiffness design. We experimentally validated our framework using a series elastic actuator with specifications similar to the knee joint of the Open Source Leg, an open-source robotic knee-ankle prosthesis. 

In this work, we introduce a novel approach to assistive exoskeleton (or powered orthosis) control which avoids needing task and gait phase information. Our approach is based on directly designing the Hamiltonian dynamics of the target closed-loop behavior, shaping the energy of the human and the robot. Relative to previous energy shaping controllers for assistive exoskeletons, we introduce ground reaction force and torque information into the target behavior definition, reformulate the kinematics so as to avoid explicit matching conditions due to under-actuation, and avoid the need to switch between swing and stance energy shapes. Our controller introduces new states into the target Hamiltonian energy that represent a virtual second leg that is connected to the physical leg using virtual springs. The impulse the human imparts to the physical leg is amplified and applied to the virtual leg, but the ground reaction force acts only on the physical leg. A state transformation allows the proposed control to be available using only encoders, an IMU, and ground reaction force sensors. We prove that this controller is stable and passive when acted on by the ground reaction force and demonstrate the controller's strength amplifying behavior in a simulation. A linear analysis based on small signal assumptions allows us to explain the relationship between our tuning parameters and the frequency domain amplification bandwidth.