Virtual Constraints: A New Paradigm for the Control of Motion

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This proposal concerns the investigation of a new paradigm for motion control in nonlinear dynamical systems. The motion control problem involves designing algorithms to make one or more dynamical systems exhibit a prescribed behaviour. Motion control problems abound in all areas of engineering, and include locomotion in multi-legged robots, flight control of autonomous aircrafts, and formation control of terrestrial, aerial, and space vehicles. The traditional motion control methodology has limited robustness against disturbances and uncertainties in the environment, and it is therefore inadequate to address emerging applications such as locomotion in multi-legged robots and coordination of spacecraft formations. In the last decade, a new paradigm for motion control has emerged which has the potential to overcome the limitations of traditional methods, and may enable a new generation of motion control algorithms. This paradigm relies on the concept of virtual constraint, a constraint on the states of a control system that does not physically exist, but can be enforced via feedback control. The notion of virtual constraint has been used with great success to induce stable walking gaits in biped robots, but much research remains to be done to make the virtual constraint paradigm go beyond biped locomotion, and become general enough to be applicable to a vast array of engineering problems. The proposed research program will lay the foundations for a systematic theory of virtual constraints for a class of mechanical systems and autonomous vehicles, and will investigate its applications to the control of satellite formations and robotic teleoperation. The ultimate goal of this research program is a set of general tools to automatically generate a collection of motion primitives. Each motion primitive will be associated with a virtual constraint, and will correspond to a desired behaviour. An inexpert user will then be able to select a sequence of motion primitives to induce complex behaviours in the dynamical system. The outcomes of this research program may have considerable practical implications in areas as diverse as robotics, aerospace engineering, and rehabilitation engineering.