The Gough Stewart Robotic manipulator is a parallel manipulator with six-degree of freedom, which has six equations of Kinematics (Inverse and forward), with six variables (Lengths, Position, and Orientation). In this work derived the inverse equations, which used to compute the lengths of the linkages and its changes depended on the position and orientation of the platform's center, then derived the forward equations to calculate the position and orientation of the moving platform in terms of the lengths. This theoretical model of the kinematics analysis of the Gough Stewart has been built into the Simulink package in Matlab to obtain the lengths, position, and orientation for the manipulator at any time of motion. The input parameters (Position and Orientation) in inverse blocks compared with the output parameters (Position and Orientation) in the forward blocks, which show good results.

The wheeled mobile robot has been considered a planner mechanism with linear and angular movement over a horizontal plane. In particular, the wheeled mobile robot’s movement is assumed to result from pure rolling of wheels without slipping. The kinematics model is one of the most fundamental steps in studying any mobile robot. This research presents the kinematic equations of movement of a mobile robot with mecanum wheels. The resulting mathematical model of a wheeled mobile robot was produced using the MATLAB R2014a program. The kinematic modeling technique was investigated by simulating a robot’s walk on a square path.

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Obstacle avoidance is an important concept to be considered when a robotic system is installed in an environment. Obstacles within the working space of a robotic system can prevent the robot from performing the tasks assigned to it properly; hence, the designer of the robotic system must program the robot to follow an emergency strategy that enables it to avoid any contact with a probable obstacle anywhere anytime within the working space of the robot. For mobile robots this task is relatively easier to accomplish since this type of robots have the flexibility to change their routes and take alternatives that are free of obstacles. For fixed robotic arm manipulators the situation is much more complex. In this paper we are only concerned with obstacle avoidance techniques and present a real-time obstacle avoidance method for fixed robotic arms that combines the benefits of both global and local techniques in that it can be used for both static and dynamic environments with a reduced computational effort.