Insectomorphic robot maneuvering on freely rolling balls

Abstract

The influence of the position of the center of mass of a multilegged robot that moves along the surface of a freely rolling ball on the direction of rolling of this ball over a horizontal plane is studied. The case when the center of mass of this robot is shifted (in the plane that is perpendicular to the velocity vector) from the vertical axis that goes through the ball center is analyzed. Approximation formulas that allow one to estimate the radius of curvature of the trajectory of the center of a ball during turn are obtained under certain simplifying assumptions. It is found that a shift of the center of mass from the vertical axis that goes through the ball center inevitably produces a certain spin of the ball about this axis, complicating the task of maneuvering on this ball. The problem of insectomorphic robot maneuvering with two freely rolling balls on a horizontal plane is solved in the model formulation. The problem consists in moving a robot from a horizontal plane over to a movable ball, rolling this ball close to another free ball, and making the robot climb from the first ball to the second one and then back to the horizontal plane. The difficulty is that the mechanical system under consideration is highly unstable and is thus strongly influenced by execution errors. It is demonstrated constructively that the problem of the indicated interaction between a robot and two balls is fundamentally solvable, and a model robot is able to perform this task, although it is forced to shift its center of mass from the vertical axis in the process.