Investigations into an optimal approach for on-line robot trajectory planning and control
The purpose of this thesis is to present a comprehensive and practical approach for the time-optimal motion planning and control of a general purpose industrial manipulator. In particular, the case of point-to-point path unconstrained motions is considered, with special emphasis towards strategies suitable for efficient on-line implementations. From a dynamic model description of the plant, and using an advanced graphical robotics simulation environment, the control algorithms are formulated. Experimental work is then conducted to verify the proposed algorithms, by interfacing the industrial manipulator to the master controller, implemented on a personal computer. The full rigid-body non-linear dynamics of the open-chain manipulator have been accommodated into the modelling, analysis and design of the control algorithms. For path unconstrained motions, this leads to a model-based regulating strategy between set points, which combines conventional trajectory planning and subsequent control tracking stages into one. Theoretical insights into these two robot motion disciplines are presented, and some are experimentally demonstrated on a CRS A251 industrial arm. A critical evaluation of current approaches which yield optimal trajectory planning and control of robot manipulators is undertaken, leading to the design of a control solution which is shown to be a combination of Pontryagin's Maximum Principle and state-space methods of design. However, in a real world setting, consideration of the relationship between optimal control and on-line viability highlights the need to approximate manipulator dynamics by a piecewise linear and decoupled function, hence rendering a near-time-optimal solution in feedback form. The on-line implementation of the proposed controller is presented together with a comparison between simulation and experimental results. Furthermore, these are compared with measurements from the industrial controller. It is shown that the model-based near-optimal-time feedback control algorithms allow faster manipulator motions, with an average speed-up of 14%, clearly outperforming current industrial controller practices in terms of increased productivity. This result was obtained by setting an acceptable absolute error limit on the target location of the joint (position and velocity) to within [2.0E-02 rad, 8.7E-03 rad/s], when the joint was regarded at rest.