Sensitivity analysis of flexible joint nonholonomic wheeled mobile manipulator in singular configuration

This paper proposes a method for decreasing jerk and increasing Maximum Allowable Load (MAL) of nonholonomic Wheeled Mobile Manipulator (WMM) considering flexibility of joints in singular conditions. The full dynamic model of nonholonomic WMM contains simultaneous operation of mobile base and manipulator with joint flexibility (in wheels and manipulator) which is presented here. The problem is formulated in terms of the optimal control which leads to a two point boundary value problem. Then Sobol's sensitivity analysis method is applied to determine the optimal values of flexible joint constants subject to the jerk minimization. To illustrate the proposed method, two categories of conditions are considered: conditions containing non-singular configuration and the singular conditions. An example is explained for non-singular condition of nonholonomic WMM in presence of obstacle in which a complex path is generated but there is no singularity in robot configuration. Some examples of occurring singular configuration in final point and moving boundary condition is also presented. The results show that flexibility of the joints near to singular configuration normalizes the sudden movement and jerk implied to actuators. That is why using a rotational spring with a low stiffness coefficient could be helpful to decrease the high jerk and increase the maximum allowable load in mobile robots.