Exploiting variable impedance in domains with contacts
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The control of complex robotic platforms is a challenging task, especially in designs with high levels of kinematic redundancy. Novel variable impedance actuators (VIAs) have recently demonstrated that, by allowing the ability to simultaneously modulate the output torque and impedance, one can achieve energetically more efficient and safer behaviour. However, this adds further levels of actuation redundancy, making planning and control of such systems even more complicated. VIAs are designed with the ability to mechanically modulate impedance during movement. Recent work from our group, employing the optimal control (OC) formulation to generate impedance policies, has shown the potential benefit of VIAs in tasks requiring energy storage, natural dynamic exploitation and robustness against perturbation. These approaches were, however, restricted to systems with smooth, continuous dynamics, performing tasks over a predefined time horizon. When considering tasks involving multiple phases of movement, including switching dynamics with discrete state transitions (resulting from interactions with the environment), traditional approaches such as independent phase optimisation would result in a potentially suboptimal behaviour. Our work addresses these issues by extending the OC formulation to a multiphase scenario and incorporating temporal optimisation capabilities (for robotic systems with VIAs). Given a predefined switching sequence, the developed methodology computes the optimal torque and impedance profile, alongside the optimal switching times and total movement duration. The resultant solution minimises the control effort by exploiting the actuation redundancy and modulating the natural dynamics of the system to match those of the desired movement. We use a monopod hopper and a brachiation system in numerical simulations and a hardware implementation of the latter to demonstrate the effectiveness and robustness of our approach on a variety of dynamic tasks. The performance of model-based control relies on the accuracy of the dynamics model. This can deteriorate significantly due to elements that cannot be fully captured by analytic dynamics functions and/or due to changes in the dynamics. To circumvent these issues, we improve the performance of the developed framework by incorporating an adaptive learning algorithm. This performs continuous data-driven adjustments to the dynamics model while re-planning optimal policies that reflect this adaptation. The results presented show that the augmented approach is able to handle a range of model discrepancies, in both simulation and hardware experiments using the developed robotic brachiation system.