Task-space Control for Robotic Prostheses
Overview
For individuals with lower-limb amputation (LLA), daily activities like walking become more challenging due to loss of joint functionality. The typical standard of care following LLA includes the prescription of a passive prosthesis to replace the missing limb. While passive prostheses can help individuals move through their surroundings, joint movements that require net positive work, such as high-power ankle push-off at the end of stance, are not achievable. By incorporating actuators into the joints, powered prostheses can generate positive work, and, with appropriate control, offer the promise of avoiding these downsides of passive devices.
In the ROAM lab, we are investigating how to build those appropriate controllers. This thrust of work is interested in designing a control framework that treats the individual and their device as a system, rather than two separate components. This shift in perspective away from solely focusing on the joint is achieved by expanding the available sensing information beyond the lower half of the individual's body, and incorporating system-level information like center of mass (CoM) progression into the control framework. This concept, termed task-space control (TSC), draws motivation from research in the literature that has studied the role of the CoM in maintaining balance and stability, where the underlying joint-level actions taken are dictated by this overarching goal, or task-level decision.
Technical Approach
The TSC framework that we have designed is composed of three core components, two of which are visualized in the figure above. The lefthand side of the figure depicts the first component, which focuses on generating task-space reference trajectories for the controller. In this work, the system-level characteristics we are interested in are CoM kinematics, due to their role in balance/stability, and the ground reaction forces (GRFs), since they are the direct result of our interactions with the environment. We generate reference trajectories for these characteristics by taking able-bodied human CoM information that has been normalized by factors such as height and walking speed, and rescaling those out based on the individual's own values for those same factors. From there, a custom-built optimization framework is used to fit a template model, such as the bipedal spring-loaded inverted pendulum (B-SLIP), to the scaled out CoM kinematics as accurately as possible. Template models are used because they are low-dimensional formulations of highly complex systems that can still retain the desired characteristics of said system, while removing a lot of the complexity and redundancy. From the optimization, we obtain not only accurate and smooth reference information for the CoM kinematics, but also GRF reference profiles based on the simplified dynamics of the template models. While these references can be generated for multiple tasks such as ramp and stair navigation, the initial focus has been geared towards steady-state level-ground walking.
The righthand side of the figure depicts the second component, which details the online implementation of the TSC framework. The reference trajectories generated offline are used in a feedforward/feedback fashion to calculate and command the desired joint torques. The GRF profiles are converted into feedforward torque commands for the joints by calculating the Jacobian of the lower-leg for the individual, and applying it as a transformation to the desired GRF information. The CoM kinematics are used for feedback control, by finding the residual between the reference CoM information and real-time estimations of the individual's CoM kinematics, which are obtained using a motion capture suit. The discrepancy between real-time and reference CoM information is converted into a force correction term before transforming into a torque command using the same Jacobian from the feedforward term. The feedforward and feedback components are used additively as the overall actuator commands to the joints of the prosthesis. Since GRFs are required for the feedforward term, this methodology is only active while the prosthesis is in contact with the ground. During the swing phase, a standard impedance control law commonly used in the literature prevents foot scuffing and prepares the prosthesis for the next instance of ground contact.
The third component not depicted in the figure above manages how a user's progression through their gait cycle is monitored, which is critical for mapping to the appropriate reference values and transitioning between stance and swing. An individual's progression through the gait cycle is estimated using a phase variable, which can be defined as a metric that changes monotonically throughout a gait cycle, such that the value of the phase variable can be mapped uniquely to a specific instance in the gait cycle. For ankle-only prosthetic control, the phase portrait generated by the global tibia kinematics is used, while a thigh-based piecewise mapping is used for knee-ankle control.
Outcomes
For further details regarding individual components of the framework, the publications listed below go more in depth behind the underlying mathematics and performance metrics. To date, the work regarding the custom-built trajectory optimization framework can be found in a conference publication (Kelly et al., ICORR, 2022), as well as a journal publication (Kelly et al., PLoSOne, 2024). The use of the framework to generate reference trajectories is detailed in a conference publication (Kelly et al., ICRA, 2024), with a journal publication in the works.
The work regarding the use of the TSC framework has initially focused on ankle-only control for level-ground walking. An initial test-case with an individual without amputation can be found in a conference publication (Kelly et al., ICRA, 2024). A complete human subject test was conducted that featured 10 individuals (7 w/o amputation, 3 w/ amputation), who all tested the TSC framework across multiple speeds. The results from this subject test are currently being prepared for consideration as a journal submission. Extension to knee-ankle control is currently being tested in the lab, along with extensions to stair navigation as well.
The work regarding the monitoring of gait cycle progression can be found in multiple conference publications (Kelly et al., ICRA, 2024), (Posh et al., ICRA, 2024) for the tibia-based phase variable. Tests are currently being conducted for the thigh-based phase variable, and its impact on the performance of the TSC framework.
Recent Work
Publications
Kelly, David J., and Patrick M. Wensing. "Optimizing Template Models to Quantifiably Assess Center of Mass Kinematic Reconstruction." 2022 International Conference on Rehabilitation Robotics (ICORR). IEEE, 2022.
Kelly, David J., Ryan R. Posh, and Patrick M. Wensing. "Task-space control of a powered ankle prosthesis." 2024 IEEE International Conference on Robotics and Automation (ICRA). IEEE, 2024.
Posh, Ryan R., Jonathan A. Tittle , David J. Kelly, James P. Schmiedeler, and Patrick M. Wensing. "Hybrid volitional control of a robotic transtibial prosthesis using a phase variable impedance controller." 2024 IEEE International Conference on Robotics and Automation (ICRA). IEEE, 2024.
Kelly, David J., and Patrick M. Wensing. "Center of mass kinematic reconstruction during steady-state walking using optimized template models." PloS one 19.11 (2024): e0313156.