This paper presents an optimal motion planning framework to generate versatile energy-optimal quadrupedal jumping motions automatically (e.g., flips, spin). The jumping motions via the centroidal dynamics are formulated as a 12-dimensional black-box optimization problem subject to the robot kino-dynamic constraints. Gradient-based approaches offer great success in addressing trajectory optimization (TO), yet, prior knowledge (e.g., reference motion, contact schedule) is required and results in sub-optimal solutions. The new proposed framework first employed a heuristics-based optimization method to avoid these problems. Moreover, a prioritization fitness function is created for heuristics-based algorithms in robot ground reaction force (GRF) planning, enhancing convergence and searching performance considerably. Since heuristics-based algorithms often require significant time, motions are planned offline and stored as a pre-motion library. A selector is designed to automatically choose motions with user-specified or perception information as input. The proposed framework has been successfully validated only with a simple continuously tracking PD controller in an open-source Mini-Cheetah by several challenging jumping motions, including jumping over a window-shaped obstacle with 30 cm height and left-flipping over a rectangle obstacle with 27 cm height.
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