Feedback Control of Multiple Nonholonomic Mechanical Systems: Geometry, Passivity, and Communication

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The main goal of this project is to provide a systematic feedback control synthesis methodology for multiple nonholonomic mechanical systems. This project will substantially advance the state of current technology by providing ways to exploit the Lagrangian structure of the nonholonomic mechanical systems for their feedback control, rather than unnecessarily cancel them out as usually done (or assumed) so far. In particular, this project will rely on the two fundamental, yet, very intuitive, concepts/properties of the nonholonomic mechanical systems: geometry and passivity. The resultant feedback control law will then be more robust with less cancellation of the open-loop Lagrangian dynamics; intuitively compelling, since it is based on energy-related passivity property and visualizable geometric concepts; and able to provably ensure interaction stability with a wide class of humans/environments by using the powerful passivity-argument. This project will also address constraints on the inter-agent communication topology (i.e. who communicates with whom) and provide ways to synthesize distributed (or decentralized) feedback control for each agent according to the underlying communication topology (i.e. information graph). We will also build an experimental test-bed consisting of three mobile manipulators to validate/demonstrate/stimulate theoretical results. This project will also combine several powerful concepts together, which have been often used disjointly: geometric mechanics, passivity, switching control, and communication. By doing so, it would also generate new research directions situated at their interface.Nonholonomic mechanical systems encompass many practically important systems: wheeled mobile robots (e.g. automobile), mobile manipulators (i.e. dexterous manipulator on the top of wheeled mobile platform), and (under-actuated) satellites, to name just a few. A group of multiple of them would make even more compelling applications such as teleoperated rescue of a human victim from disastrous sites using multiple mobile manipulators, collaborative patient transport in hospitals by multiple nurse robots; cooperative robotic flexible material handling in manufacturing/construction, and cooperative air-borne transport of a heavy object using multiple autonomous satellites. This project will lay theoretical foundations for such powerful applications, which, although having potentials to greatly benefit our daily life, have not been materialized yet, mainly due to the lack of ways to precisely and safely feedback control them with full considerations on the robots' open-loop Lagrangian dynamics, communication constraints, and safe-interaction with humans/environments. This project will also exhibit the obtained results to the public in the form of some interesting demonstrations and actively pursue students from under-represented groups in the science and technology fields to involve them into its research activities.