Geometric optimization of a self-adaptive robotic leg

Abstract

This paper demonstrates the self-adaptive capabilities of a two-degree-of-freedom Hoeckens-pantograph robotic leg (inspired by underactuated mechanical fingers) as well as its optimization, allowing it to overcome unexpected obstacles during its swing phase. A multi-objective optimization of the mechanism’s geometric parameters is performed using a genetic algorithm to highlight the trade-off between two conflicting objectives and select an appropriate compromise. The first of those objective functions measures the leg’s passive adaptation capability through a calculation of the input torque required to initiate the desired sliding motion along an obstacle. The second objective function evaluates the free-space trajectory followed by the leg endpoint using three criteria: linearity, stance ratio, and height-to-width ratio. In comparison with the initial geometry based on the Hoecken’s linkage, the selected final mechanism chosen from the Pareto front shows an important improvement of the adaptation capabilities, at the cost of a slight decrease in the stance phase duration. This paper expands on mechanical self-adaptive design philosophy, which has recently attracted a lot of attention in the field of grasping, to legged locomotion and paves the way for subsequent experimental validation of this approach.