Kinetostatic Optimization for Kinematic Redundancy Planning of Nimbl’Bot Robot

Abstract

In manufacturing industry, Computer Numerical Control (CNC) machines are often preferred over Industrial Serial Robots (ISR) for machining tasks. Indeed, CNC machines offer high positioning accuracy, which leads to slight dimensional deviation on the final product. However, these machines have a restricted workspace generating limitations in the machining work. Conversely, ISR are typically characterized by a larger workspace. ISR have already shown satisfactory performance in tasks like polishing, grinding and deburring. This paper proposes a kinematic redundant robot composed of a novel two degrees-of-freedom mechanism with a closed-loop kinematic chain. After describing a task priority inverse kinematic control framework used for joint trajectory planning exploiting the robot kinematic redundancy, the paper analyses the kinetostatic performance of this robot depending on the considered control tasks. Moreover, two kinetostatic tasks are introduced and employed to improve the robot performance. Simulation results show how the robot better performs when the optimization tasks are active.

Workspace Determination of Kinematic Redundant Manipulators Using a Ray-Based Method

“…The employed kinematic control algorithm is called Task Priority Inverse Kinematic (TPIK) and is presented in [19][20][21][22]. It can find the robot configuration that solves a set of tasks with different priority levels.…”

“…There exist two types of control objectives, equality and inequality. More details are given in [22]. Each control objective is associated with a feedback reference rate ẋ that drives x(q) to the desired point x * with the linked rate ẋ * .…”

“…Then, lower priority tasks are solved if enough degrees of freedom remains. These concepts were fully described in [22] With the previous definitions, the control action A taken as input by the TPIK algorithm can be defined as a series of priority levels composed of [22]:…”

“…Dexterity The dexterity η(J w ) characterizes the kinematic performance of a manipulator in a given configuration [25]. In [22], the analytical expression of η is computed using the Frobenius norm of…”

“…Moreover, η can be defined as the ratio between the smallest and the highest singular values of J w indicating how close the manipulability hyper-ellipsoid is to being a hyper-sphere [26]. The derivative of the dexterity as a function of the joint variables is described in [22],…”