Constrained Hopping Traversability Analysis on Non-Uniform Polygonal Chains

We analyze the existence of constrained ballistic hopping paths on a nonuniform polygonal chain. This analysis has practical significance in constrained path planning applications for jumping robots where robot dynamic constraints, uneven surface structure, and non-uniform surface properties are considered. We derive closed-form conditions to satisfy i) damage-free robot landing ii) non-sliding of the robot iii) actuator saturation, and iv) intermediate terrain avoidance constraints. Using the closed-form conditions, we propose a traversability algorithm to determine the path existence between two given points on the polygonal chain. Correspondingly, a path generation approach is discussed to generate an optimal constrained hopping path with minimum number of intermediate hops and least take-off speed per hop. Applicability and viability of the proposed algorithms are demonstrated through computer simulations in a realistic terrain scenario with robot jumping motion uncertainties and disturbances.