Concise method to the dynamic modeling of climbing robot

Abstract

With the aim of dynamic modeling of the climbing robot with dual-cavity structure and wheeled locomotion mechanism, a succinct and explicit equation of motion based on the Udwadia-Kalaba equation is established. The trajectory constraint of the climbing robot, which is regarded as the external constraint of the system, is integrated into the dynamic equation dexterously. A modified numerical method is considered to reduce the errors because the numerical results obtained by integrating the constrained dynamic equation yield the errors. The trajectories are almost coincident by comparing the modified numerical value and the theoretical value. The driving torques required to guarantee the climbing robot to move along the given trajectory are obtained explicitly, which overcomes the disadvantage of obtaining dynamical equation from traditional Lagrange equation by Lagrange multiplier. The simulations are performed to demonstrate that the dynamical equation established by this method with brevity and accuracy is in accordance with reality status.

Determination of Stability Correction Parameters for Dynamic Equations of Constrained Multibody Systems

“…However, in the simulation process, the integral error ofq in formula (5) increases with the time, and the motion trajectory of the mechanical system obtained eventually deviates from the given trajectory from (2). Therefore, the method of Baumgarte constraint violation stability can be used to correct (3). The corrected constraint equation can be written as…”

“…The theory, which was proposed for modeling and analysis of the constrained system dynamics by Udwadia and Kalaba, has been applied more and more in mechanical systems [1][2][3][4][5]. However, when the mechanical system is analyzed and simulated with Udwadia and Kalaba method, the results of numerical integration of system dynamics equation will deviate from requirements of constraint equations over time and eventually lead to constraint violation.…”

Dynamic modeling and analysis of wheeled wall-climbing robot

“…However, the modeling process introduces process parameters such as ''partial velocities,'' 24 ''quasi-coordinates,'' 25 and ''quasi-accelerations,'' 26 that do not have clear physical significance. Although the dynamic model of a wallclimbing robot could be constructed concisely by Udwadia-kalaba equation, 27 the constraint construction and the constraint treatment of the inherent structural and physical characteristics of the robot system are still important contents in the modeling process, and few scholars focus on these parts.…”