Employing Symmetry in Dynamics and Motion Control of Robotic Mechanisms

Land, sea, air and space- Across all the media, robotic mechanisms are in service of human endeavour. Among them, floating-base robotic mechanisms, e.g., orbital robots, humanoids etc., have recently gained prominence due to their mobility. These mobile mechanisms are uniquely characterized by conservation of momentum if the effect of gravity is removed. This property follows from the in variance of the mechanism’s kinetic energy w.r.t. its spatial location, as stated by Noether’s theorem. Such a system is an Euler-Lagrange system with symmetry (invariance), or a Lagrange-Poincaré system. For such mobile mechanisms, the floating-base and the articulated mechanism are equipped with sensors and actuators that differ in their underlying principles. This negatively affects control performance while employing traditional methods which disregard its symmetry. Likewise, simulation of its dynamics without considering symmetry can be detrimental in critical applications, e.g., on-ground simulation of orbital robotic missions for validation before launch. Even in robotic mechanisms that do not possess an inherent symmetry, it still appears as a requirement if hierarchical execution of tasks is required for whole-body motion. This means that the motion towards fulfilment of the secondary task should be a symmetry of the primary task. Thus, despite raising its head in many guises, a common theory based on symmetry that unifies the dynamics and control synthesis for this class of problems in robotics is missing. To this end, as the title suggests, this thesis makes its contributions towards employing Lagrangian symmetry for dynamics and motion control of robotic mechanisms. For a floating-base robotic mechanism, a novel computation of its Lagrange-Poincaré dynamics is provided, which reveals advantageous properties for motion control. Using this computation, new geometric aspects of its motion are revealed. The structure of the proposed dynamics is exploited to design a hardware-in-the-loop simulation framework for orbital robots. The proposed framework has lower sensory requirements than the state-of-the-art and also scales according to mission development phases due to the implicit substructuring of the Lagrange-Poincaré dynamics. The symmetry in Lagrange-Poincaré dynamics is exploited to design a control framework that addresses the aforementioned problems arising from the hybrid sensing and actuation of a floating-base robot. This control framework exploits the internal model of the dynamics and uses minimal sensing to achieve full motion stabilization, while being contact-aware in uncertain environments. To achieve hierarchical motion control in robotic mechanisms without any inherent symmetry, two control approaches are proposed to synthesize artificial symmetry. This enables exploiting the control synthesis for Lagrange-Poincaré systems, as for the floating-base robotic mechanisms. Thus, this thesis provides a unified theory based on symmetry for the aforementioned class of problems related to dynamics and motion control in robotics. The methods are validated on state-of-the-art robotic systems and are published in several peer-reviewed conferences and journals. The applicability of the work from this thesis is evidenced by its utility in several projects funded by KUKA AG, EU, ESA and NASA, which are also reported.