Multi-Constrained Optimal Control of 3D Robotic Arm Manipulators

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This paper presents a generic method for optimal motion planning for three-dimensional 3-DOF multi-link robotic manipulators. We consider the operation of the manipulator systems, which involve constrained payload transportation/ capture/release, which is a subject to the minimization of the user-defined objective function, enabling for example minimization of the time of the transfer and/or actuation efforts. It should be stressed out that the task is solved in the presence of arbitrary multiple additional constraints. The solutions of the associated nonlinear differential equations of motion are obtained numerically using the direct transcription method. The direct method seeks to transform the continuous optimal control problem into a discrete mathematical programming problem, which in turn is solved using a non-linear programming algorithm. By discretizing the state and control variables at a series of nodes, the integration of the dynamical equations of motion is not required. The Chebyshev pseudospectral method, due to its high accuracy and fast computation times, was chosen as the direct optimization method to be employed to solve the problem. To illustrate the capabilities of the methodology, maneuvering of RRR 3D robot manipulators were considered in detail. Their optimal operations were simulated for the manipulators, binded to move their effectors along the specified 2D plane and 3D spherical and cylindrical surfaces (imitating for example, welding, tooling or scanning robots).

Multi-Constrained Optimal Control of 3D Robotic Arm Manipulators

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