The Transverse Function (TF) control approach is applied to the control of a generic motorboat endowed with a surge force along the stern-bow direction and a torque actuation to modify the boat's orientation. With respect to more conventional methods this approach allows for uniform practical stabilization of any smooth reference pose (i.e. position+orientation) trajectory. This includes fixed-poses in the absence of a sea-current, whose asymptotic stabilization cannot be achieved by classical feedback controllers, and non-feasible pose trajectories, i.e. trajectories that are not solutions to the system's motion equations and thus cannot be stabilized asymptotically.
A mechanical system consisting of a hoop and a pole is considered, for which the corresponding dynamic model represents an underactuated system subject to second-order nonholonomic constraints. The pursued goal is to simultaneously track a trajectory in the unactuated coordinates and to stabilize the actuated ones. For the model under consideration, the well-known noncollocated partial feedback linearization algorithm fails since the corresponding zero dynamics is unstable. In this work, we show that the actuated coordinates, i.e., the pole can be stabilized by exploiting the null space of the coupling inertia matrix without affecting the performance in the underactuated coordinates tracking. We present a formal mathematical analysis, which guarantees ultimate boundedness of all coordinates. Performed simulations bolster the proposed approach.
In order to identify the group of muscles related to deterioration of balance function in the elderly, an exploratory experiment was conducted to analyze and study the influence of lower limb muscular fatigue on balance disturbance in the stable upright position. A stabilometer and a multipurpose muscle function testing and training system were used to assess 12 normal healthy subjects. Evaluations were made using the total trajectory length and the trajectory length per unit area with the eyes-open for 30 seconds. All statistical analyses were performed using SPSS Ver. 13.0 with analysis of variance (repeated measures) at a significance level of below 5%. In the gluteus maximus muscles, the total trajectory length showed a significant downward trend while the trajectory length per unit area showed a significant upward trend.