Coordinated set stabilization : application to robotic manipulators

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Consider the problem of designing algorithms that make a collection of robotic manipulators work together to paint the fuselage of an aircraft. The paintbrush attached to the end-effector of each robot is charged with staying on the surface that describes the shape of the fuselage. Each robot's end-effector is restricted, through feedback control, to move along the surface describing the fuselage. On the surface, the team of robots must communicate and co-operate to coordinate their motions so that they do not unnecessarily paint over the same region too often and efficiently complete the task.**Partially motivated by the above example, the proposed research project studies the coordination of nonlinear control systems on pre-specified sets in their output spaces. Given a heterogeneous collection of nonlinear control systems, the objective is to design a feedback control laws, one for each system, that drive the closed-loop output of each system to its pre-defined target set. The target sets must be invariant, in other words, if each system is initialized on its target set, it remains on the target set. Once on the target set, the systems should cooperatively complete application specific tasks in an optimal manner. This proposal focuses on (a) set stabilization of nonlinear systems while ensuring desired dynamics on the target set (b) coordinated set stabilization for nonlinear control systems with emphasis on Euler-Lagrange systems (c) experimental verification of coordinated set stabilization algorithms. The expected outcomes of this proposal are distributed nonlinear control algorithms whose effectiveness are mathematically proven and demonstrated experimentally on laboratory equipment.**This research is partly motivated by the emergence of self-organizing factories in industrialized nations as a way to increase productivity and compete with low-cost manufacturing in developing nations. North America and Europe are moving to significantly increase industrial value creation. The next stage of industrial manufacturing, a move towards `smart factories', has been described as a fourth stage of the industrial revolution. This notion of `industry 4.0', or `the internet of things', is modernizing manufacturing processes and increasing productivity in industrial manufacturing in North America. The 'internet of things' has been identified as a disruptive technology that will transform life, business, and the global economy. For example, Boeing is using a team of robots, working together, to paint the wings of the Boeing 777. These robots have boosted output and dramatically reduced the time required to paint the wings from 4.5 hours to 24 minutes.**This research aims to generate systematic methods to design control algorithms for coordinated set stabilization of systems with nonlinear dynamics. We seek to mathematically prove the correctness of the algorithms while also experimentally demonstrating their effectiveness on mobile robotic manipulators. Mobile robotic manipulators that can work co-operatively are well suited to re-configurable, flexible manufacturing systems. Solving the fundamental problems considered in this proposal related to the design of nonlinear control algorithms promises to help enable the 'internet of things' in manufacturing.