# Motion planning of redundant robots with obstacle avoidance

Robotic arms appear in several segments of industry, making the desired tasks easier and more accurate. Nowadays they are indispensable parts of manufacturing, and their application is growing in military or medical industry. The currently applied robotic arms move on a predefined trajectory, executing a definite motion. This has the disadvantage, that the given task specifies the motion of the whole robot body, thus robot cells are required, and it is necessary to pay special attention during programming, so the robot will not collide with any object in its area. The solution to the described problem could be the application of kinematically redundant manipulators. If the number of joints is larger than the dimension of the workspace, then we say the manipulator is kinematically redundant. A redundant robot can reach a desired position in multiple ways depending on task priorities. This property makes it able to avoid obstacles that is a great advantage in terms of security and comfort as well. The high amount of joints allows reaching locations in circumstances with limited motion possibilities due to obstacles.

The main aim of my thesis was to implement a simulation environment in MATLAB, in which I realized and tested the motion planning and obstacle avoidance of a redundant manipulator with optional number of degrees of freedom. In order to do this, I started my work with literature research about the kinematics of rigid bodies and Jacobian-based motion planning algorithms. Following this I studied the already implemented MATLAB functions, and realized the required functions.

The main task can be separated to two subproblems, i.e. forward and inverse kinematics problems of the redundant manipulator. Forward kinematics serve to visualize the robotic arm and calculate the end-effector position, with given joint variables. Solving the inverse kinematics problem by Jacobian-based algorithms give the base of tasks such as motion planning and obstacle avoidance.

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