A New Approach of Dynamic Complexity Analysis for a Planar Manipulator With Clearance and Lubrication in Joint

The existence of clearance in the joint causes positional deviation and reduces the accuracy of robotics, in which nonlinear factors such as friction and lubrication inside the joint seriously affect its dynamic behaviors. On the other hand, the effectiveness of control algorithms is largely dependent on the dynamic complexity of the robotics, while its complexity analysis is an important prerequisite for achieving high-performance control. In this paper, we provide a method for analyzing the dynamic complexity of a planar manipulator with clearance and lubrication in joints based on a nonlinearity measure. The influences of joint parameters such as friction coefficient, lubricant viscosity, and gap radius are quantified on the dynamic complexity of the kinetics, which can identify the collision state of the joints effectively in the robot’s motion. First, a dynamical model of a planar manipulator is established by integrating the contact-separation model and the force model at the joint, and a method for calculating the dynamic complexity based on the nonlinearity measure is proposed. Second, the effects of different joint parameters on the dynamic behaviors of the robotic system are analyzed, and the relationships between the lubricant viscosity, gap radius, and the dynamic complexity under different friction coefficients are established to analyze the impacts of the joint parameters on the dynamic complexities. The results show that the dynamic complexity of the robotic system can be decreased significantly by using the small gap radius and high viscosity of the lubricant, which can help to realize the better control performance. Especially, this method is more sensitive to state changes such as the collision state of the joint relative to the sample entropy method.