In this paper, we aim to improve the robustness of dynamic quadrupedal locomotion through two aspects: 1) fast model predictive foothold planning, and 2) applying LQR to projected inverse dynamic control for robust motion tracking. In our proposed planning and control framework, foothold plans are updated at 400 Hz considering the current robot state and an LQR controller generates optimal feedback gains for motion tracking. The LQR optimal gain matrix with non-zero offdiagonal elements leverages the coupling of dynamics to compensate for system underactuation. Meanwhile, the projected inverse dynamic control complements the LQR to satisfy inequality constraints. In addition to these contributions, we show robustness of our control framework to unmodeled adaptive feet. Experiments on the quadruped ANYmal demonstrate the effectiveness of the proposed method for robust dynamic locomotion given external disturbances and environmental uncertainties.
The vast majority of state-of-the-art walking robots employ flat or ball feet for locomotion, presenting limitations while stepping on obstacles, slopes, or unstructured terrain. Moreover, traditional feet for quadrupeds lack sensing systems that are able to provide information about the environment and about the foot interaction with the surroundings. This further diminishes their value. Inspired by our previous work on soft feet for bipedal robots, we present the SoftFoot-Q, an articulated adaptive foot for quadrupeds. This device is conceived to be robust and able to overcome the limitations of currently employed feet. The core idea behind our adaptive foot design is first introduced and validated through a simplified mathematical formulation of the problem. Subsequently, we present the chosen mechanical implementation to attempt overcoming current limitations. The realized prototype of adaptive foot is integrated and tested on the compliantly actuated quadrupedal robot ANYmal together with an ROS-based real-time foot pose reconstruction software. Both extensive field tests and indoor experiments show noticeable performance improvements, in terms of reduced slippage of the robot, with respect to both flat and ball feet.
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