**7. References**


**1. Introduction**

One of the goals of robotics research is to provide control algorithms that allow robotic manipulators to move in an environment with objects. The contacts with these objects may be part of the task, e.g. in the assembly operations, or they may be undesired events. If the task involves some contacts with the environment it is necessary to control the resulting forces. For that purpose, different control approaches have been proposed like hybrid position/force control (Raibert & Craig, 1981) or impedance control (Hogan, 1985), which have also been applied to redundant manipulators (Khatib, 1987; Park et al., 1996; Woernle, 1993; Yoshikawa, 1987). However, in most cases the contact is supposed to occur between the end-effector or the handling object and the object in the workspace. Except in some special cases all other contacts along the body of the robot manipulator are not desired and have to be avoided. In the case when the contacts are not desired, the main issue is how to accomplish the assigned task without any risk of collisions with the workspace objects. A natural strategy to avoid obstacles would be to move the manipulator away from the obstacle into a configuration where the manipulator is not in contact with the obstacle. Without changing the motion of the end-effector, the reconfiguration of the manipulator into a collision-free configuration can be made only if the manipulator has redundant degrees-of-freedom (DOF). The flexibility depends on the degree-of-redundancy, i.e., on the number of redundant DOF. A high degree-of-redundancy is important, especially when the manipulator is working in an

**Obstacle Avoidance for Redundant** 

**Manipulators as Control Problem** 

Leon Žlajpah and Tadej PetriĀ *Jožef Stefan Institute, Ljubljana* 

**11**

*Slovenia* 

Generally, the obstacle-avoidance (or collision-avoidance) problem can be solved with two classes of strategies: global (planning) and local (control). The global ones, like high-level path planning, guarantee to find a collision-free path from the initial point to the goal point, if such a path exists. They often operate in the configuration space into which the manipulator and all the obstacles are mapped and a collision-free path is found in the unoccupied portion of the configuration space (Lozano-Perez, 1983). However, these algorithms are very computationally demanding and the calculation times are significantly longer than the typical response time of a manipulator. This computational complexity limits their use for practical obstacle avoidance just to simple cases. Furthermore, as global methods do not usually rely on any sensor feedback information, they are only suitable for static and well-defined environments. On the other hand, local strategies treat obstacle avoidance as a control problem. Their aim is not to replace the higher-level, global, collision-free path planning but to make use of the capabilities of low-level control, e.g., they can use the sensor information

environment with many potential collisions with obstacles.

