Design of Optimal Control Processes for Closed-Loop Chain SCARA-Like Robots

Doktorsavhandling, 2004

The design of optimal control processes for closed-loop chain SCARA-like robots is the subject of this thesis. In comparison with the well-known SCARA robot, the proposed new structure is characterized by the incorporation of an additional powered actuator, several unpowered actuators and an additional link that gives a closed-loop chain robot. The performance of the SCARA-like robot with various arrangements of powered and unpowered actuators is addressed by formulating and solving energy-optimal and time-optimal control problems for periodic pick-and-place operations in the horizontal plane. Two computational methods suitable for solving optimal control problems for two-degree-of-freedom closed-loop chain SCARA-like robots are developed. With the direct parameter optimization approach, the relevant optimal control problems are converted into nonlinear programming problems using an inverse dynamics based method with polynomial-Fourier series approximation of the generalized coordinates and the redundant torques. The resulting constrained nonlinear optimization problems are solved using sequential quadratic programming (SQP). An indirect computational method based on Pontryagin’s maximum principle is also developed. The necessary conditions of optimality are derived for the problems considered, and the resulting multi-point boundary-value problems are solved with a smoothing-continuation approach and an adaptive collocation method. In closed-loop chain robots with more actuators than degrees-of-freedom (overactuation), the dynamic redundancy enables optimization of the force distribution. Unpowered spring-like drives can assist the powered actuators or control some of the degrees-of-freedom of a manipulator robot (semi-passive control). Here, the advantages of overactuation and semi-passive control for the SCARA-like robots are demonstrated analytically and numerically for both given motion and periodic pick-and-place operations. The numerical results for the solutions to the energy-optimal control problems show that the energy consumption and maximum torque required of the active actuators for typical pick-and-place operations can be reduced by using overactuation or adding unpowered drives to the structure of the robot. Using semi-passive control of the SCARA-like robot also allows simplification of the control system by reducing the number of powered actuators (underactuation). The results from the time-optimal control problems confirm the advantages of overactuation and semi-passive control. The results obtained in this thesis suggest that other mechanical systems and machines with periodic motion, such as various robots, automatic cyclic machines and bipedal robots, can benefit from overactuation and semi-passive control.