Optimal coordination of robotic systems with redundancy

The research work described in this dissertation is primarily aimed at developing efficient algorithms for the rate allocation problem in redundant serial chain manipulators. While the problem of redundancy resolution in the context of robot manipulators, had been a well researched one, search for optimality in computational efficiency has caught the attention only recently. Further, the idea of modifying the already developed performance criteria to improve computational efficiency, had rarely been treated with the importance it deserves. The present work in fact, provides many alternative formulations to the existing performance criteria.; As a result of the present investigation, we developed a mathematical tool for the minimum norm solution for underdetermined systems of linear equations, using the orthogonal null space. Closed form equations were provided for cases with two or three degrees of redundancy. Detailed study of computational efficiency showed substantial reduction in the arithmetic operations necessary for such a solution. The above concept was later generalized to utilize the self motion characteristics of redundant manipulators, to provide alternate solutions. The duality concept between the Jacobian and the null space, established in this work, enabled the authors to develop a highly efficient formulation as an alternative to the commonly used pseudoinverse-based solution. In addition, by providing the example of a 7R anthropomorphic arm, the feasibility of obtaining analytical formulation of null space coefficient matrix and the transformed end effector velocity vector for any geometry has been demonstrated.; By utilizing the duality between the Jacobian and its null space, different performance criteria commonly used in the redundancy resolution problem have been modified, increasing the computational efficiency. Various simulations performed as part of the present work, utilizing the analytical null space coefficient matrix and the transformed end effector velocity vector for 3R planar case and 7R spatial anthropomorphic arm corroborates the theories. Another practical application has been demonstrated by the example of a Titan 7F arm mounted on a mobile base. The work is consolidated by reiterating the insight obtained to the physical aspects of the redundancy resolution problem and providing a direction for future work. Suggestions are given for extending the work for high d.o.r. systems, with relevant mathematical foundations. Future work in the area of dynamic modelling, is delineated which also includes an example of modified dynamic manipulability measure.