Take-off analysis and pre-take-off stance control of a simple hopping leg mechanism

Legged robotics has gained prominence as a form of locomotion in robots offering distinct advantages such as terrain adaptation and isolation of foot contact. Hopping leg mechanisms in robotics have focussed mainly on distal revolute joints or prismatic actuation. This work investigates the take-off and pre-take-off stance dynamics of a revolute ankle joint-actuated simple vertical hopping leg mechanism with two links through analysis of the normal force on the base hinge. A controller for triggering the hopper take-off by applying a squat hop take-off strategy is simulated by applying proportional control action. Also, simulated is the counter-movement hop strategy for comparison with the squat hop strategy. We also examine the need for a feedforward support torque to add to the proportional control action for counteracting gravity and a torsional hinge spring. The broader objective in this line of work is to develop an analysis of learning algorithms to adapt and learn hopping transitions, that is, take-off and landing on rigid and flexible surfaces of varying properties. We observe in this ankle-actuated hopping mechanism, take-off in counter-movement hop strategy is executed with significantly less input torque magnitude requirement than squat hop strategy in pre-take-off stance phase in absence of a hinge stiffness. In presence of hinge-stiffness however, the input torque magnitude requirement for take-off in countermovement hop strategy increases, making it comparable to the input torque requirement from squat hop strategy and almost equal in presence of a support torque.