Soft-Computing Techniques for the Trajectory Planning of Multi-Robot Manipulator Systems

The planning of the motion of robots has become increasingly more complex as robots are used in a wide spectrum of applications, from extremely repetitive tasks in assembly lines to assistance in delicate surgical procedures (Tombropoulos et al., 1999; Coste-Maniere et al., 2003). Whichever scenario, the planning has to consider the fact that the robot will be interacting with other elements in its environment avoiding collision with other objects, whether these remain static or in motion, while executing a given task. In planning the motion for robots, it is a common misassumption that path planning and trajectory planning are synonymous. Motion planning, as defined by Sugihara and Hwang in (Hwang & Ahuja, 1992; Sugihara & Smith, 1997), is subdivided into path planning and trajectory planning. (Fraichard & Laugier, 1992) state the following distinction: path planning is the search of a continuous sequence of collision-free configurations between a start and a goal configuration, whereas trajectory planning is also concerned with the time history or scheduling of this sequence of configurations as well. Considering that the motion of the elements that form the kinematic chain of robot manipulators is described by a system of non-linear equations that relate the motion in the Cartesian space of the end-effector as a consequence of the individual variations of the links of the manipulator due to the angular displacements at each joint. When solving for a particular position of the end-effector in the Cartesian space, the inverse kinematics problem, a set of configurations has to be calculated to position the tip of the manipulator at that desired point. Due to the natural dexterity of robot manipulators, the space of solution is non-linear and multidimensional, where more than a single solution exists to solve a particular point in the Cartesian space and choosing the appropriate solution requires an optimisation approach. Taking this into consideration, the solution of the motion planning problem of robot manipulators is an ideal candidate for the use of soft-computing techniques such as genetic algorithms and fuzzy logic, as both approaches are known to perform well under multidimensional non-linear spaces without the need for complex mathematic manipulation to find a suitable solution (Zadeh, 1965; Mamdani, 1974; Goldberg, 1983; Bessiere et al., 1993; Doyle, 1995; Doyle & Jones, 1996).