This paper deals with the online path planning of mobile robots. We first suggest a systematic method to incrementally construct the Medial Axis of the workspace. This is done by using sensor information for land-marking the nodes of medial axis, which will guide the robot to explore the unknown environment thoroughly. Next, this approach is implemented in an online motion planning algorithm. This method can be generalized to higher spaces, and uses only the line of sight information of sonar sensors. It is much simpler than HGVG method, and is complete. The simulations showed good results for different environments.

In this paper, a mathematical model capable of handling a three-dimensional (3D) flexible n-degree of freedom manipulator having both revolute and prismatic joints is considered. This model is used to study the longitudinal, transversal, and torsional vibration characteristics of the robot manipulator and obtain kinematic and dynamic equations of motion. The presence of prismatic joints makes the mathematical derivation complex. In this paper, for the first time, prismatic joints as well as revolute joints have been considered in the structure of a 3D flexible n-degree of freedom manipulator. The kinematic and dynamic equations of motion representing longitudinal, transversal, and torsional vibration characteristics have been solved in parametric form with no discretization. In this investigation, in order to obtain an analytical solution of the vibrational equations, a novel approach is presented using the perturbation method. By solving the equations of motion, it is shown that mode shapes of the link with prismatic joints can be modeled as the equivalent clamped beam at each time instant. As an example, this method is applied to a three degrees of freedom robot with revolute and prismatic joints. The obtained equations are solved using the perturbation method and the results are used to simulate vibrational behavior of the manipulator.

A nonlinear system with complicated mathematical model is partitioned into two slow and fast subsystems, using singular perturbation theory. A fuzzy controller is designed by specialized learning for the slow subsystem to control the nonlinear system. Simulation results show good performance for the closed-loop system.