Automatic Trajectory Generation using Redundancy Resolution Scheme Based on Virtual Mechanism

In recent times, while markets are reaching their saturation limits and customers are becoming more demanding, a paradigm shift has been taking place from mass production to customized mass production. The concept of customization focuses on satisfying a customer’s unique needs with the help of new technologies. Typically, the products are similar but they differ in some parameters which make manual teaching and manual preparation of the manufacturing programs not acceptable. The customized mass production requires that all production phases are prepared in advance during the design phase of the specific product. This requires that standard production procedures are modified and prepared for each specific product. It is also required that the adaptation is done automatically without any human intervention. In modern production systems, CAD models of the product are used to generate specific machining programs. In the case of industrial robots, automatically generated programs have to consider various limitations, such as joint limits, wrist singularity and possible collisions of the robot with the environment. Although the off-line programming enables detection of such situations during the program preparation, it does not solve the basic goal the automatic generation of feasible collision free trajectories. One of the most promising approaches to solving these problems is based on redundancy resolution control schemes, where the primary task is assigned to the trajectory tracking while the secondary task optimizes robot trajectories using various optimization goals, such as obstacle and singularity avoidance, staying within the available join limits, etc.. The basic definition of the kinematic redundancy is that the robot has more degrees of freedom than needed to accomplish the specific task. In the past, many control schemes were presented which use kinematic redundancy for the optimization of secondary tasks, such as obstacle avoidance, torque optimization, singularity avoidance, etc. All these schemes rely on a non-square Jacobian, which maps the joint velocities to the task space, which is in most cases described by the Cartesian coordinates. If the redundancy of the task can be easily described in Cartesian coordinates, i.e. the task is redundant in one of the Cartesian coordinates, then the solution is trivial an we can directly apply one of the existing control schemes. But there are tasks, such as brushing, polishing, grinding, sawing, etc. where the kinematic redundancy is hidden. It reveals when the circular shape of the tool is considered. Note that all six Cartesian coordinates are still needed to describe and to accomplish the given task.