Non-invasive Determination of Ankle Rotation Axes Using a Robotic Gyroscopic Mechanism

Among four joints of human foot in the ankle area, the tibiotalar and subtalar joints play the most important role in making it possible for the foot to perform rotational movements such that kinematic behavior of foot is almost completely affected by orientation of their rotation axes. Deviation of the axis of rotation from the normal position can impair the function of the ankle and even the lower extremity. In this study, a new non-invasive method has been proposed, through which, using a gyroscopic mechanism, the orientation of the rotation axes of the tibiotalar and subtalar joints can be determined. This method is based on indirect data acquisition from the kinematic behavior of the foot. Using the calculated matrices and through the optimization method, the orientation and position of the rotation axes were respectively calculated at relatively high precision. These results were also assessed in practice by building an ankle mechanical model and a robotic gyroscopic mechanism which is used as a robotic rehabilitation device for ankle rehabilitation. Obtained results show that the maximum error in determining the orientation of the rotation axes is about 2 degrees

TRAJECTORY OPTIMIZATION OF A MOBILE ROBOT WITH FLEXIBLE LINKS USING PONTRYAGIN’S METHOD

In this study, the open-loop optimal control method is used to optimize the trajectory of a mobile robot with flexible links. Equations of motion for the mobile robot are initially obtained via the Lagrangian method. The assumed modes method is then used to obtain a model with limited degrees of freedom. The relevant kinematic model is established based on the standard frame transformation matrices including rigid rotations and elastic displacements assuming that the values for these parameters are small. The Book modified method is also used to obtain the kinematic elastic links. Elastic manipulator links are modeled as Euler-Bernoulli beams with Clamped-Mass (CM) boundary conditions. Nonholonomic constraints and additional kinematic constraints are considered in order to specify the base motion. A performance criterion is defined that involves the square of the angular velocity and joint torque. The torque and velocity are determined such that the performance criterion is minimized. The optimal control problem is converted into a two-point boundary value problem using the calculus of variations, the Hamiltonian function, and the Pontryagin’s minimum principle. By considering the different weight coefficients for angular velocity joints and the torques on the joints of the robot in the performance criterion, the effects of weight coefficients are investigated on the solution. In another stage of the study, a flexible arm with a mobile base is simulated to illustrate the capability of the proposed method and the relevant equations are solved by MATLAB. Finally, the results are compared with those reported in previous studies to evaluate the dynamic model