A Non-Iterative Problem-Dependent Formula for Stiff Dynamic Problems

A novel one-step formula is proposed for solving initial value problems based on a concept of eigenmode. It is characterized by problem dependency since it has problem-dependent coefficients, which are functions of the product of the step size and the initial physical properties to define the problem under analysis. It can simultaneously combine A-stability, explicit formulation and second order accuracy. A-stability implies no limitation on step size based on stability consideration. An explicit formulation implies no nonlinear iterations for each step. The second order accuracy with an appropriate step size can have a good accuracy in numerical solutions. Thus, it seems promising for solving stiff dynamic problems. Numerical tests affirm that it can have the same performance as that of the trapezoidal rule for solving linear and nonlinear dynamic problems. It is evident that the most important advantage is of high computational efficiency in contrast to the trapezoidal rule due to no nonlinear iterations of each step.

Maximum Allowable Dynamic Load of Mobile Manipulators with Stability Consideration

High payload to mass ratio is one of the advantages of mobile robot manipulators. In this paper, a general formula for finding the maximum allowable dynamic load (MADL) of wheeled mobile robot is presented. Mobile manipulators operating in field environments will be required to manipulate large loads, and to perform such tasks on uneven terrain, which may cause the system to reach dangerous tip-over instability. Therefore, the method is expanded for finding the MADL of mobile manipulators with stability consideration. Moment-Height Stability (MHS) criterion is used as an index for the system stability. Full dynamic model of wheeled mobile base and mounted manipulator is considered with respect to the dynamic of non-holonomic constraint. Then, a method for determination of the maximum allowable loads is described, subject to actuator constraints and by imposing the stability limitation as a new constraint. The actuator torque constraint is applied by using a speed-torque characteristics curve of a typical DC motor. In order to verify the effectiveness of the presented algorithm, several simulation studies considering a two-link planar manipulator, mounted on a mobile base are presented and the results are discussed.