| Summary: | This paper presents a framework for the motion planning and control of redundant manipulators with the added task of collision avoidance. The algorithms that were previously studied and tested by the authors for planar cases are here extended to full mobility redundant manipulators operating in a three-dimensional workspace. The control strategy consists of a combination of off-line path planning algorithms with on-line motion control. The path planning algorithm is used to generate trajectories able to avoid fixed obstacles detected before the robot starts to move; this is based on the potential fields method combined with a smoothing interpolation that exploits Bézier curves. The on-line motion control is designed to compensate for the motion of the obstacles and to avoid collisions along the kinematic chain of the manipulator; this is realized using a velocity control law based on the null space method for redundancy control. Furthermore, an additional term of the control law is introduced which takes into account the speed of the obstacles, as well as their position. In order to test the algorithms, a set of simulations are presented: the redundant collaborative robot KUKA LBR iiwa is controlled in different cases, where fixed or dynamic obstacles interfere with its motion. The simulated data show that the proposed method for the smoothing of the trajectory can give a reduction of the angular accelerations of the motors of the order of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>90</mn><mo>%</mo></mrow></semantics></math></inline-formula>, with an increase of less than <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>15</mn><mo>%</mo></mrow></semantics></math></inline-formula> of the calculation time. Furthermore, the dependence of the on-line control law on the speed of the obstacle can lead to reductions in the maximum speed and acceleration of the joints of approximately <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>50</mn><mo>%</mo></mrow></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>80</mn><mo>%</mo></mrow></semantics></math></inline-formula>, respectively, without significantly increasing the computational effort that is compatible for transferability to a real system.
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