On-line Cartesian path trajectory planning for robot manipulators

The authors derive online algorithms that will generate approximate joint paths for any curve in Cartesian space, providing proper knot points are selected. The errors between the desired and approximate paths are required to be within some prescribed tolerance. Two online interpolation schemes, namely simple quartic spline interpolation (SQSI) and modified quartic spline interpolation (MQSI), with quartic spline functions for least-squared error fit, are developed. It is shown that if any curve in Cartesian space is given, the corresponding approximate joint trajectories could be determined in real time. It turns out that MQSI is the better one for tracking the desired path. However, the SQSI algorithm is easier to implement than MQSI. The design of local minimum time trajectories subject to physical constraints is investigated. For the purpose of planning the trajectory in real time, the physical constraints considered are the limits of velocity, acceleration, and jerk of each joint