This paper proposes a novel variable impedance controller for a redundantly actuated parallel robot to allow execution of passive ankle rehabilitation exercises while taking into consideration of human biomechanics online. By using a biomechanical model of the human ankle which describes the kinematics and dynamics of the ankle foot structure, the kinematic parameters of the ankle can be estimated online to allow identification of the constrained direction of motion. Impedance adjustment heuristics were also formed by investigating the ankle stiffness over a range of joint displacements through the use of the ankle model developed. The variable impedance controller can prevent application of excessive actuator forces which could threaten the safety of the patient.

This article deals with forward kinematics (FK) mapping of a parallel robot, especially designed for ankle joint rehabilitation treatments. Parallel robots exhibit highly coupled non-linear motions hence conventionally a unique closed form solution of their FK cannot be obtained. However, since FK is a key module in closed loop position and force control, its accurate and fast solution is indispensable. To solve the FK problem, a modified fuzzy inference system (FIS) is proposed in this paper for the first time which is time efficient and becomes very accurate when its parameters are optimized. In the proposed work, FIS has been optimized using three approaches namely: gradient descent (GD), genetic algorithm (GA) and modified genetic algorithm (MGA). The FIS, optimized by MGA has been found to be more accurate than the GD and GA optimized FIS. Performance of the MGA based fuzzy system has been found better both in terms of accuracy and computation time, when compared with Newton–Raphson iterative method and other fuzzy and neural approaches.

The kinematics of the human ankle is commonly modeled as a biaxial hinge joint model. However, significant variations in axis orientations have been found between different individuals and also between different foot configurations. For ankle rehabilitation robots, information regarding the ankle kinematic parameters can be used to estimate the ankle and subtalar joint displacements. This can in turn be used as auxiliary variables in adaptive control schemes to allow modification of the robot stiffness and damping parameters to reduce the forces applied at stiffer foot configurations. Due to the large variations observed in the ankle kinematic parameters, an online identification algorithm is required to provide estimates of the model parameters. An online parameter estimation routine based on the recursive least-squares (RLS) algorithm was therefore developed in this research. An extension of the conventional biaxial ankle kinematic model, which allows variation in axis orientations with different foot configurations had also been developed and utilized in the estimation algorithm. Simulation results showed that use of the extended model in the online algorithm is effective in capturing the foot orientation of a biaxial ankle model with variable joint axis orientations. Experimental results had also shown that a modified RLS algorithm that penalizes a deviation of model parameters from their nominal values can be used to obtain more realistic parameter estimates while maintaining a level of estimation accuracy comparable to that of the conventional RLS routine.

Biomechanical information can be used in the design and control of rehabilitation robots to enhance the safety and performance of these devices. In this work, a trajectory generation routine has been developed whereby the rehabilitation trajectory is produced from constrained optimization of a cost function which is computed from the outputs of a biomechanical model. Specifically, a rigid body based biomechanical model for the human ankle has been constructed and used to estimate the tensions along ligaments and tendons, as well as the joint reaction moments at a given foot configuration. These quantities can then be used to define an objective function to be minimised. Simulations have shown that a 20% reduction in cost function can be achieved using this method. Inspection of the optimized trajectory shows that the shortest path between two foot configurations is not necessarily the most optimal, thus highlighting the applicability of the proposed method in rehabilitation robots.

Interaction control is an important aspect in rehabilitation robots to ensure system safety and allow effective rehabilitation. Due to the significant variability of human limb and joint characteristics, adaptability in the interaction controller is vital for enabling the adjustment of robot behavior to better suit the patient's requirements. A parallel manipulator has been developed for ankle rehabilitation. Computer models for both the robot and human ankle have also been constructed for evaluation of controller performance. Using these models, computer simulations were carried out to investigate the potential advantage of using a variable impedance controller to perform ankle rehabilitation exercises. The impedance parameters of this controller are selected by referring to the ankle compliance as determined by the ankle model at corresponding foot configurations. Simulation results have shown that selecting the manipulator impedance in proportion to the environmental compliance has the effect of limiting force application in stiff directions such as those encountered when approaching limits of joint motion.

Impedance control is a common interaction control strategy used in rehabilitation robots. A joint force controller has been developed for a redundantly actuated parallel robot to facilitate force based impedance control. The proposed controller utilizes only position/orientation dependent information and therefore does not require accurate dynamic modeling and measurement of velocity quantities. The proposed controller uses a disturbance observer based approach and is designed for situations where the external forces applied on the robot are dominant compared to the inertial terms in the robot dynamics. Since the robot used is redundantly actuated, control of forces along the null space of the manipulator Jacobian transpose was also considered. Rationale behind the structure of the controller is developed throughout the paper and experimental results are also presented.

The use of robots in rehabilitation, particularly for physical therapy has the potential to bring about various benefits including reduction of physical workload of physiotherapists and improved repeatability. A three degree of freedom parallel robot is proposed in this paper to accommodate range of motion and muscle strengthening exercises for ankle rehabilitation. Singularity analysis of the design revealed that a redundantly actuated robot is required to avoid singularity in the workspace. Kinematic parameters of the robot were selected so that the available workspace could closely match the available ankle range of motion. An impedance control scheme has been utilized to allow control of both force and motion to ensure safety of the patient. The redundant actuation degree of freedom is exploited to regulate the vertical reaction force at the ankle.