Trajectory control of robotic systems under constraints and uncertainties

In this section we consider the research of mobile robot motion control for complex composite piecewise smooth path which is  the task to be resoleved in robot movement in the workspace with predefined trajectory of a given piecewise smooth functions.

 The problem of robot movement in the workspace on the prescribed trajectory with respect to a given unsteady external environment has also been solved.

This type of roblems arise in developent of robotic systems operating under the presence of moving obstacles, i.e during the movement of the robot in the transient external environment , in the planning of movements in multichannel dynamical systems, when building systems of coordinated control group of mobile objects, as well as the development of systems for  moving objects tracking.

To illustrate the efficiency of the synthesized algorithms trajectory a control model has been  selected for a wheeled mobile robot . As a plant a mobile robot is a multiple nonlinear dynamical system.The  problem resolved by the control system of the mobile robot is to establish control actions providing predefined displacement of the center of mass in the workspace.

The solution of these problems is based on the useage of differential geometric methods of nonlinear control theory. The technique of multi-channel systems analysis and synthesis procedure of control algorithms provides a solution trajectory problem as a problem of stabilization relatively smooth segment of predefined  trajectory model, such as lines and circles that build the desired path of movement with fixes waypoints.

Management approach that is used in the research , provides a nonlinear transformation model of the robot system to the task specific coordinates. This approach alows to reduce the complexity of  task to  control multi-channel to a number of more simple tasks to compensate  linear and angular deviations ,followed by  usage standard techniques to find adequate stabilization of nonlinear control laws .