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In this paper, we develop a model predictive control (MPC) scheme for robots to follow a virtual leader. The stability of this control scheme is guaranteed by adding a terminal state penalty to the cost function and a terminal state region to the optimization constraints. The terminal state region is found by analyzing the stability. Also a terminal state controller is defined for this control scheme. The terminal state controller is a virtual controller and is never used in the control process. Two virtual leader-following formation models are studied. Simulations on different formation patterns are provided to verify the proposed control strategy.
Today mosaics are used as decorative elements both indoors and outdoors. Mosaics can be obtained by combining small pieces of stone, glass, wood and glazed tiles together to make some picture and illustration. Mosaic-making processes are carried out manually for thousand years. Complexities involved in piece selection, surface detection and mould fitting have limited the automation of this process. In this work, software that makes the mosaic patterning process automatic is developed. For this purpose, software named SMT V2 has been developed to obtain different mosaic patterning. The software also tested with experimental applications by selective compliance articulated robot arm (SCARA) robot on real environment using different shaped marble pieces and successful results are obtained.