In the present paper optimal path of the tricycle nonholonomic robot with two-link manipulator, obeying a particular equation with moving boundary conditions is obtained. These boundary conditions are a set of points that are called the moving boundaries. One of the main applications of this method is handling and transporting parts from one place to another by employing the aid of robot with cable strip. For example, for putting the tools and industrial parts in proper places in the product line, the reductions of time, cost and energy are guaranteed by a precise schematization and defining the best path. The methodology uses optimal control for finding optimum path. To do this, the dynamics and kinematic equations of robot are derived. Then by applying the optimal control method and Pontryagin’s minimum principle lead to deriving optimal conditions as a set of differential equations. Finally, will be solvable a boundary value problem. The formulation of the moving boundary for the tricycle robot using the optimal control includes state and co-state equations that replace the boundary conditions of the problem in the constant boundary state. As a result, solving the optimal path with moving boundary for minimization leads to obtaining a cost function that includes velocities and torques. Lastly, the simulation results of tricycle robot with two-link spatial mobile manipulator and moving boundary condition are presented that shows the accuracy and capability of the method.

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