Active AboveKnee Prosthesis Energy Regeneration Using a CrankSlider Actuator Human gait data suggests that energy regeneration is possible in an aboveknee prosthetic leg. Energy regeneration would increase the practicality of powered prosthetic legs by extending battery life. In this research, we maximize energy regeneration by designing optimal actuators for a prosthetic knee joint. Three actuator models, each with a different degree of accuracy in modeling mechanical losses, are optimized and evaluated within the framework of energy regeneration. 

Continuous Impedance Control for Prosthetic Legs Current stateoftheart prosthetic legs use impedance control settings that vary discontinuously with the gait phase of the amputee. This research involves the development of a continuous impedance controller. This approach is motivated by the continuouslyvarying impedances of natural joints, and the desire to avoid abrupt changes in torque which result from discrete changes in controller parameters. The primary goal of this new control method is to enable gait that is more natural than that provided by current prostheses. 

Control of Rigid Robots Based on Reduced Function Approximations This research develops an adaptive robot control technique that is robust to modeling errors. The controller utilizes the passivity based approach and provides an alternative to the function approximation technique. The controller eliminates the need for basis functions in the approximation of the robot dynamic equation by simplifying the estimation structure of the inertia matrix, Coriolis matrix, and gravity vector. The stability of the controller is verified with Lyapunov functions. Simulation and experimental results on a three degreeoffreedom robot demonstrate the ability to track reference trajectories using reasonable control signals when the inertia matrix, Coriolis matrix, and gravity vector are completely unknown. 

Energy Regeneration (Prosthesis) Current active aboveknee prosthetic limbs consume a large amount of power and waste excess energy as heat. To remedy this issue, a prosthesis design that includes ultracapacitors is proposed. An ultracapacitor has the ability to quickly charge and discharge a large amount of power at low voltages. To allow for proper energy conversion between the highvoltage knee motor and the lowvoltage ultracapacitor, a modulated voltage source converter is examined. Simulation results show that the ultracapacitor is able to charge while tracking proper knee angle when the modulated voltage source converter is used. 

Energy Regeneration (Rowing Machine) Impedance control and energy regeneration is currently being studied and implemented for exercise machines. The impedance control, energy regeneration, and optimization technologies used in our exercise machine research has much in common with prosthetics research. 

Ground Reaction Force Estimation Extended Kalman filters, unscented Kalman filters, and Hinfinity filters are currently being developed to estimate the ground reaction force (GRC) of a prosthesis user based only on knee and ankle angles. This technology will eliminate the need for costly and bulky load cells in the prosthetic foot, while still allowing feedback control based on GRF. Work and preparation of publications is currently in progress. 

Hybrid Function Approximation Based Control for Prosthetic Legs We developed a hybrid controller for an ndegree of freedom robot where one control algorithm is used for some joints while another control algorithm is used for the remaining joints. We combine Slotine and Li's regressor based control algorithm, and a function approximation technique (FAT) based regressorfree control algorithm, to obtain a coupled controller. We verify the closedloop stability of the hybrid controller via Lyapunov functions to show that the tracking errors converge to zero as time approaches infinity. We then apply the hybrid controller to an uncertain model of a robotic system comprised of a prosthesis which emulates the angular knee motion of a human leg, and a prosthesis test robot which emulates the vertical hip motion and the angular thigh motion of a human. Simulation results show good reference trajectory tracking in the presence of ground reaction forces while keeping the control signal magnitudes reasonably small. The tracking errors were 1.57% for the hip vertical hip motion, 0.29% for the thigh angle, and 0.34% for the knee angle (relative to their respective ranges of motion). The maximum steadystate control signal magnitudes were 840 N, 456 Nm, and 253 Nm for the vertical hip motion, thigh angle, and knee angle respectively. 

Identification of Human Control During Walking and Running This project focuses on using a combination of experimental data and modeling approaches to identify the control schemes humans use during locomotion. We are ultimately interested in mapping the identified controllers to powered prosthetic devices and exoskeletons. We start by collecting typical gait data (kinematics and kinetics) of a person walking or running while being perturbed longitudinally and laterally with pseudorandom forces in a wide frequency spectrum. We then use the collected data in various optimization techniques and plant/controller structures to identify a controller employed by the subject. This controller will ultimately be used to inform the design of a controller for a powered prosthetic device or exoskeleton which has sensors and actuators which are similar to those of the human. Work and preparation of publications is currently in progress. 

Inertial Compensation in a Moving Platform When load cells are located directly underneath a force plate, moving the platform will introduce inertial artifacts in the force measurements of the load cell. To compensate for these errors, we've developed a simple, accelerometerbased technique that assumes a linear relationship between force and acceleration. Artifacts due to inertia and gravity are estimated from accelerometer signals and subtracted from measured forces and quantified by the reduction in the rootmeansquare (RMS). The method was tested experimentally on a 2 degreeoffreedom (DOF) instrumented force treadmill capable of mediolateral translation and sagittal pitch. Mass coefficients from one trial of random movements was used to compensate for inertial errors of another trial containing different random movements. At 6 Hz bandwidth, it was found that the compensation method was capable of reducing force and moment signals by 85.34% and 69.06%, respectively. At higher bandwidths of 20 Hz, the force and moments signals were still significantly reduced by 70.07% and 36.67%, respectively. It was concluded that the compensation method is capable of reducing inertial artifacts in force and moment signals to a more reasonable level, though investigation into more appropriate instrumentation is needed for the technique to be more successful. 

Knee Moment in BelowKnee Amputees Amputees with a belowknee prosthesis show a decrease in knee moment in their prosthetic limb, even though they still have all knee muscles. This project aims to find causes for this change in gait to propose a prosthetic leg that yields an improved gait. It is hypothesized that the stiffness of the prosthetic ankle influences the knee moment. A model of the human gait is used to analyse the knee moment using different stiffness values for the prosthetic ankle. Next to this, the effect of the change on the muscle effort is studied. The advantages and disadvantages of this altered gait are studied. 

Methods for Identification of Feedback Control During Standing The mechanism of human balance control could be studied by a direct approach (DA) in which a relationship between observed joint moments and potential feedback signals was identified. However, the human balance system operates in a closed loop and this would bias the estimated controller towards the inverse of the plant, i.e. inverse multibody dynamics. The aim of this work was to validate the direct approach method for identification of feedback control in human standing and to study the effect of platform perturbation amplitude on the accuracy of the DA identification technique. Furthermore, indirect approach (IA) was used for the same system to remove the systematic error in gain estimation. Test data were obtained from a simulation in which the plant was modeled as a double inverted pendulum, perturbed with horizontal accelerations at the base to mimic a test protocol for human standing balance. 

MultiObjective Optimization of a Prosthetic Leg with Energy Regeneration This research considers control and energy regeneration for a robotic manipulator with both actively and semiactively controlled joints. The design of an impedance controller to track a desired joint trajectory and regenerate energy in a storage element (that is, an ultracapacitor) is considered here as a multiobjective optimization problem. The conflicting objectives are joint angle tracking and energy regeneration. A prosthetic leg which emulates ablebodied gait is simulated to validate the optimization and control results. Results confirm that it is possible to regenerate energy at a semiactive joint (that is, the knee joint) while still obtaining acceptable joint angle tracking. The results indicate that ultracapacitor systems, along with advanced controls and optimization, have the potential to significantly reduce external power requirements in powered prostheses. 

MultiObjective Optimization of Impedance Parameters in a Prosthesis Test Robot We design a prosthesis test robot control system that aims to mimic human walking in the sagittal plane. It has been seen in previous work that trajectory control fails to produce humanlike forces. Therefore, we utilize an impedance controller to achieve reasonable tracking of motion and force simultaneously. However, these objectives conflict. Impedance control design can therefore be viewed as a multiobjective optimization problem. We use an evolutionary multiobjective strategy called MultiObjective Invasive Weed Optimization (MOIWO) to design the impedance controller. The multiobjective optimization problem admits a set of equally valid alternative solutions known as the Pareto optimal set. We use a pseudo weight vector approach to select a single solution from the Pareto optimal set. Simulation results show that a solution that is selected for pure motion tracking performs very accurate motion tracking (RMS error of 0.06 cm) but fails to produce the desired forces (RMS error of 70% peak load). On the other hand, a solution that is selected for pure force tracking successfully tracks the desired force (RMS error of 12.7% peak load) at the expense of motion trajectory errors (RMS error of 4.5 cm). 

Muscle Mechanics and Dynamics, Virtual Muscles Powered prosthetic limbs and exoskeletons are actuated by singlejoint electric motors without the mechanical properties of muscles. Muscles themselves are actuators with nonlinear properties and internal dynamics and can actuate multiple joints simultaneously. If the torque produced by the electric motors of these powered prosthesis can be controlled with "virtual muscles," then the resultant movement would mimic the actual mechanical and dynamical properties of the human system. The goal is to simulate these virtual muscles in computer software, test on a singlejoint demonstration at the knee, and ultimately control the Parker Indego exoskeleton using muscle control at the hip and knee joints. 

NAO Project The goal of this project is to develop optimization and control algorithms for a humanoid robot. Current work in this area includes optimal path planning and visual servo control. 

Negative Reinforcement Particle Swarm Optimization (NPSO) and Fully Informed Particle Swarm Optimization (FIPSO) PSO is one of the most effective heuristic optimization algorithms. PSO is motivated by the social behavior of organisms, such as bird flocking and fish schooling. Each particle in the algorithm represents a candidate solution to an optimization problem, and is aware of its own previous best solution to the problem, and its neighbors' previous best solution. Each particle uses this information to adjust its position in the search space. Many variants of PSO have been introduced, including Fully Informed PSO (FIPSO) and Negative Reinforcement PSO (NPSO). In FIPSO, each particle updates its velocity in the search space based on information from the entire population. In NPSO, each particle updates its velocity in the search space based on its previous worst solution to the problem. Current work in this area includes developing stability conditions and applying these PSO variants to the prosthesis control optimization problem. 

Prosthesis Ground Contact Modeling and Optimization Accurate simulation environments are necessary for controller design and test. This work focuses on improving the ground contact model for a leg prosthesis simulation where the ground is comprised of a treadmill. Methods used include the creation of a detailed contact model based on the observed physical interactions of the prosthetic foot and treadmill surface, and evolutionary optimization of this model to match ablebodied gait reference data. 

Prosthesis User Intent Recognition This research involves recognizing prosthesis user activity and intent (for example, standing, walking slow, walking fast, going up stairs, going down stairs, walking up a ramp, walking down a ramp, and so on). Prosthesis control parameters are dependent on user activity, so it is important to recognize user activity, and to quickly switch control modes when the user intends to change his gait mode. User activity and intent recognition involves optimal filtering, clustering, and artificial intelligence algorithms. 

Robust Adaptive Impedance Control of Prosthetic Legs for Transfemoral Amputees This project involves the design of robust nonlinear model reference adaptive impedance controller for an active prosthesis robot for transfemoral amputees. This controller provides not only accurate parameter estimates, but also good tracking of a reference impedance model and also robustness of the controller/prosthesis combination in presence of variations of GRFs and parameters uncertainty. By the way, this project presents stability of the controller for this robotic system based on nonscalar boundary layer trajectories using Lyapunov stability theory and Barbalat’s lemma. 

Robust Function Approximation Technique Control This research develops a robust controller for rigid robots whose dynamics can be described using EulerLagrange equations of motion. The function approximation technique (FAT) represents the robot's dynamics as finite linear combinations of orthonormal basis functions. This controller provides good tracking of reference trajectories and good robustness to timevarying disturbances and random parameter perturbations. The controller developed here is most attractive in scenarios where the dynamic equation of the robot is too costly to develop or unavailable. 

Robust Tracking/Impedance Control A mixed tracking/impedance robust controller is developed based on passivity techniques. The controller is developed for general robotic manipulators and then applied to a powered knee/ankle prosthesis model attached to a robotic testing machine. Tracking control is used for the hip and thigh links of the test robot, while impedance control is used for the knee and ankle joints of the prosthesis. A Lyapunov function is used to show that the tracking errors of the motioncontrolled joints approach zero, while the impedance of the remaining joints approaches the designed target. A simulation study shows how impedance parameters can be used to trade off reference tracking of the impedancecontrolled joints and interaction forces. 

Switched Robust Tracking / Impedance Control A novel controller is developed by combining two control concepts previously applied to transfemoral prostheses. The first concept is robust tracking / impedance control. The second concept is switched impedance control. This combination is used to improve the humanlike motion and dynamics of the prosthesis. The resulting controller’s performance is optimized for a combination of angle tracking and energy regeneration with an evolutionary algorithm. 

System Identification and Control Optimization for an Active Prosthetic Knee in Swing Phase A DC motor mounted to a passive Mauch SNS prosthetic knee results in an active prosthetic knee. Evolutionary optimization methods are used to identify the motor parameters and the knee prosthesis parameters. The same methods are also used to optimize the parameters of a PID controller for knee ankle tracking during swing phase. A Kalman filter estimates knee angle velocity, which is used as an input to the DC knee motor controller. The optimization process is performed for varying shank lengths. 

Torque Optimization During Standing and Walking GPOPSII, which is generalpurpose optimal control software, has been used to optimize the torque of a oneDOF pendulum given a desired trajectory. Current work involves the optimization of the twoDOF gait problem. The optimization problem constraints include cyclic gait with a prescribed speed and cycle time, and the cost function is the integral of the squared torques. The problem is very nonlinear because of the footground contact in the gait model. 