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1. Introduction
degree of freedomMany industrial applications are defined as end-effector motions, such as assembling, welding and polishing. In these circumstances, the industrial robots should not only follow the specified end-effector paths but also fulfill some secondary tasks, such as avoiding singularity and collision objects.
degree of freedomdegree of freedomThe redundant robots are built to accomplish these objectives. As shown in Figure 1, Motoman SDA has two 7-DOF arms, which have a similar configuration as human. The human-like configuration is designed for human-level dexterity. In the traditional way, this kind of tasks is realized by human teaching; however, the teaching process of SDA is much more difficult and more time-consuming than 6-DOF robots because of the kinematics complexity.
We want to replace this teaching process with motion planning method and to provide better usability of redundant robots. As the end-effector path can be generated with CAM (computer-aided manufacturing), we focus on finding feasible joint path with given end-effector paths.
2. Related works
If we only consider the end-effector tasks, the joint path between two end-effector waypoints can be simply generated with pseudo-inverse of Jacobian matrix. This method can find the least norm joint path but cannot deal with other secondary tasks.
Interestingly, there is a null space for redundant robots’ Jacobian matrix and the self-motion in the null space will not affect the end-effector pose. Many researches have been done on projecting secondary task motions into the null space of the robots’ Jacobian matrix. The secondary tasks can be joint limits avoidance (Dubey et al., 1991), singularity avoidance (Yoshikawa, 1984) or collision avoidance (Maciejewski and Klein, 1985; Shen et al., 2015). Besides, Sadeghian et al. realized null-space compliance (Sadeghian et al., 2014) and Flacco et al. extended it into acceleration level (Flacco et al., 2012).
Similarly, Khatib proposed another control based method, named operational space formulation (OSF) (Khatib, 1987) The OSF can deal with multi-constraints in torque-level control, and Yosuke et al. (Kamiya et al., 2013) introduced this method to industrial robot with forward dynamics calculation. These local optimization approaches can be run in real-time but cannot deal with local minimum.
As the control based methods cannot guarantee completeness, some researchers turned to sampling based methods, such as RRT (LaValle,...