We show dynamic locomotion strategies for wheeled quadrupedal robots, which combine the advantages of both walking and driving. The developed optimization framework tightly integrates the additional degrees of freedom introduced by the wheels. Our approach relies on a zero-moment point based motion optimization which continuously updates reference trajectories. The reference motions are tracked by a hierarchical wholebody controller which computes optimal generalized accelerations and contact forces by solving a sequence of prioritized tasks including the nonholonomic rolling constraints. Our approach has been tested on ANYmal, a quadrupedal robot that is fully torque-controlled including the non-steerable wheels attached to its legs. We conducted experiments on flat and inclined terrains as well as over steps, whereby we show that integrating the wheels into the motion control and planning framework results in intuitive motion trajectories, which enable more robust and dynamic locomotion compared to other wheeled-legged robots. Moreover, with a speed of 4 m/s and a reduction of the cost of transport by 83 % we prove the superiority of wheeled-legged robots compared to their legged counterparts.
We present a trajectory optimizer for quadrupedal robots with actuated wheels. By solving for angular, vertical, and planar components of the base and feet trajectories in a cascaded fashion and by introducing a novel linear formulation of the zeromoment point (ZMP) balance criterion, we rely on quadratic programming only, thereby eliminating the need for nonlinear optimization routines. Yet, even for gaits containing full flight phases, we are able to generate trajectories for executing complex motions that involve simultaneous driving, walking, and turning. We verified our approach in simulations of the quadrupedal robot ANYmal equipped with wheels, where we are able to run the proposed trajectory optimizer at 50 Hz. To the best of our knowledge, this is the first time that such dynamic motions are demonstrated for wheeled-legged quadrupedal robots using an online motion planner.
We present a hierarchical whole-body controller leveraging the full rigid body dynamics of the wheeled bipedal robot Ascento. We derive closed-form expressions for the dynamics of its kinematic loops in a way that readily generalizes to more complex systems. The rolling constraint is incorporated using a compact analytic solution based on rotation matrices. The non-minimum phase balancing dynamics are accounted for by including a linear-quadratic regulator as a motion task. Robustness when driving curves is increased by regulating the lean angle as a function of the zero-moment point. The proposed controller is computationally lightweight and significantly extends the rough-terrain capabilities and robustness of the system, as we demonstrate in several experiments.
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