Predicting impact scenarios of a rimless wheel: a geometrical approach

Abstract

The 2D motion of a rigid rimless wheel on an inclined plane has been widely studied as a first simple case of passive walker. Usually, it is modelled as a hybrid dynamical system alternating continuous smooth phases and discrete impact ones. As in other bipedal walkers, the related research is often devoted to the analysis of cyclic motions and assumes that the spoke-ground collision is a single-point one. This work focuses exclusively on the impact problem and explores the possibility of different transitions within the impact interval (single-point to double-point collisions, dynamic jamb, stick-slide transitions and sliding reversal) as a function of the spokes angular aperture, the wheel inertia, the wheel-ground friction coefficient, and the initial conditions. This analysis is done through an innovative geometrical approach based on the Percussion Centre.

MonoBot: A Single-Actuator Walking Robot

“…Passive dynamic walkers, which rely on gravity and their mechanical properties to generate a walking gait. The design and control principles of these walkers are well-established, as seen in examples like the rimless wheel walker [10] and the compass gait walker [11]. Compliant walkers, which incorporate compliant elements in their legs for energy storage and release during walking.…”

Modeling, analysis and control of robot–object nonsmooth underactuated Lagrangian systems: A tutorial overview and perspectives

“…Finally, this class of models has been validated experimentally [120], where normal and tangential local kinematics are carefully analyzed. Contact and impact modeling is still the object of research and validation in Robotics [122,123], and Mechanics [6,107,108,103,124].…”

Stochastic stability analysis of legged locomotion using unscented transformation

“…Higher-order terms are ignored, and the partial derivatives with respect to state and noise should be calculated by numerical methods. Then the forecast value is calculated by substituting (8) into (7),…”

“…Stability can be enhanced by considering the stochastic nature of walking behavior during system identification and controller design. Even though, there exists recent work [7] that focuses on the impact problem and explores the possibility of different transitions within the impact interval with a geometrical approach, in the robotics community, this is a significant but understudied method that is primarily handled as a robust control problem [6,8] rather than an examination of stochastic dynamics.…”