Kinematic and dynamic analysis of a nonholonomic wheel-legged robot using Gibbs–Appell formulation

In this paper, dynamic modeling of a reconfigurable wheel-legged robot is proposed using a geometric constraint based on independent coordinates. The main contribution of this research is the use of a geometric constraint for the body's rotational angle and using the Gibbs–Appell method instead of traditional modeling approaches to avoid complex constraint equations, significant computational burden, and simulation time. This study necessitates some assumptions in order to develop constraint equations and calculate Gibbs functions due to the presence of nonholonomic constraints on the wheels and the requirement for the robot to move simultaneously in x- and z-directions to execute distinct tasks. With the proposed approach, dynamic equations are obtained without determining the Lagrangian coefficients. In addition, because of the particular form of the Gibbs equations, fewer partial derivatives are necessary to derive the equations from which the joints torques are calculated in terms of the quasi-coordinates. In addition to spatial vector relations, a geometric constraint is used to construct kinematic modeling, requiring other coordinates to be explicitly obtained in terms of quasi-coordinates in the dynamic formulation. Simulation results in various modes of motion to change the height of the robot while proceeding in its course and the associated motor torques, are verified experimentally using a WLRIUST robot. Finally, simulation results for several test scenarios are presented, demonstrating the overall performance of the robot with four double-link legs. Relevant simulation results are also compared to those obtained with the Adams software. The performance of the robot's movements and the torques applied to the motors by relevant changes in the quasi-coordinates are also examined. The results show MATLAB and Adams modeling differ nearly 1%, and with experimental tests differ about 5 to 10%.