An Improved Adaptive Kinematics Jacobian Trajectory Tracking of a Serial Robot Passing Through Singular Configurations

In real time applications, the trajectory which has to be followed and the task that has to be performed during motion planning of multi-axis non-linear mechanical systems, such as robot manipulators are of great importance. Due to the non-linear transformation between the task space and the joint space coordinates, singularities and uncertainties in the arm configuration occur, the unplanned occurrence of such problems drive the end-effector out of the desired path which may cause collision of the robot arm with objects located in its work cell (Koker, 2005; Antonelli et al., 2003). Depending on different tasks operation requirements and circumstances, motion control algorithms can be developed either at the kinematics level or at the dynamic level (Graca & Gu, 1993; Karilk & Aydin, 2000). To develop a dynamic control algorithm, torque limits of the joint actuators are to be handled, two typical approaches were introduced which are the Computed-torque and Resolved-acceleration approach, both approaches are based on the inverse dynamic model of the robot system (Asada & Soltin,1986; Sopng & Vinyasagar,1998; Faiz & Agrawal ,2000). A problem with these algorithms is the remarkable computational load required to handle the dynamics of a full-sized manipulator, which is seldom affordable by current industrial control units. In addition, implementation of torque-based control laws requires replacement of the low-level joint servos typically available in industrial robots with custom control loops. Aimed at overcoming the above drawbacks, a different approach to path tracking based on the kinematics control was proposed. In detail, kinematics control consists in an inverse kinematics transformation which sends to the joint servos the reference values corresponding to an assigned end-effector trajectory; as a first advantage, this allows simple interfacing with the standard control architecture of industrial robots. In the framework of kinematics-based methods for path tracking, the counterpart of the physically meaning joint torque limits is played by acceleration constraints and the use of full dynamic models can be avoided; this typically leads to computationally light algorithms that allow real-time implementation on standard numerical hardware even for robot arms of many Degrees of