In this paper kinematics model of a nonholonomic mobile manipulator is formulated. The kinematics equations for a mechanical mobile manipulator are developed in such a way that the kinematics interaction between the mobile platform and mechanical manipulator explicitly appears in the equations. In both conditions the motion constraints and kinematics redundancy are considered and analyzed. These concepts are expanded in general cases by using special subjects, on linear algebra and functional analysis. A useful and unique kinematics model for redundancy resolution of mobile manipulators is introduced by defining specified variables. Finally, the application of the model is verified by simulation results in order to find the maximum allowable load of a mobile manipulator.

This paper proposes an efficient algorithm based on memetic algorithm (MA) for a redundancy allocation problem without component mixing (RAPCM) in a series-parallel system when the redundancy strategy can be chosen for individual subsystems. Majority of the solution methods for the general RAPCM assume that the type of a redundancy strategy for each subsystem is pre-determined and known a priori. In general, active redundancy has traditionally received greater attention; however, in practice both active and cold-standby redundancies may be used within a particular system design. The choice of the redundancy strategy then becomes an additional decision variable. Thus, the problem is to select the best redundancy strategy, component and redundancy level for each subsystem in order to maximize the system reliability under system-level constraints. Due to its complexity and NP-hardness, it is so difficult to optimally solve such a problem by using traditional optimization tools. To validate the performance of the proposed MA in terms of solution quality, a number of test problems are examined and the robustness of this algorithm is then discussed. Finally, the related results are reported and it is shown that the proposed MA performs well.

To increase the reliability of a specific system, using redundant components is a common method which is called redundancy allocation problem (RAP). Some of the RAP studies have focused on k -out-of- n systems. However, all of these studies assumed predetermined active or standby strategies for each subsystem. In this paper, for the first time, we propose a k -out-of-n system with a choice of redundancy strategies. Therefore, a k-out-of- n series–parallel system is considered when the redundancy strategy can be chosen for each subsystem. In other words, in the proposed model, the redundancy strategy is considered as an additional decision variable and an exact method based on integer programming is used to obtain the optimal solution of the problem. As the optimization of RAP belongs to the NP-hard class of problems, a modified version of genetic algorithm (GA) is also developed. The exact method and the proposed GA are implemented on a well-known test problem and the results demonstrate the efficiency of the new approach compared with the previous studies.