Forward and inverse kinematics of a differential drive mobile robot

Abstract

The paper considers the application of a generalized approach to kinematic modeling of wheeled mobile robots to describe the motion of a robotic device on magnetic wheels intended for diagnostics of ferromagnetic surfaces. The magnetic wheels provide holding and adhesion of the device when it moves along horizontal and vertical surfaces. Based on the differential drive model, the geometric parameters of the wheels, the conditions for the absence of lateral slip, as well as forward and inverse kinematics in the local and global coordinate systems are considered. The relationship between the speeds of the driving magnetic wheels and the linear and angular velocities of the robotic device body is established. For the platform under consideration, the wheel position vectors, the unit rolling direction vectors and the coefficients of the kinematic equations are determined, and the Jacobian matrix is formed on their basis. Using the Moore-Penrose pseudoinverse matrix, expressions of forward kinematics in the moving coordinate frame are obtained and the transition to the global coordinate system is performed. It is shown that the use of magnetic wheels does not change the basic structure of the kinematic model; however, the condition of motion without slip is determined by a sufficient magnetic clamping force, which depends significantly on the distance to the ferromagnetic surface. The considered kinematic model can be used for motion simulation, development of control algorithms and trajectory planning of a mobile robot during non-destructive testing of tank equipment.