Exponential trajectory generation for point to point motions

This paper presents a new method to generate point-to-point (PTP) trajectories, such as the ones used by robots or CNC machines, using an exponential function as the basis for the trajectory profile. The method is based on adding a series of time-delayed third-order exponential functions to generate an approximation to the trapezoidal velocity profile commonly used in time-optimal motions. The exponential velocity has zero-starting and ending values as well as continuous derivatives (acceleration and jerk). The proposed algorithm has several advantages over conventional trajectory planning methods such as those using S-curve and trapezoidal velocity profiles. These include: (i) the generated trajectory is continuous up to the third derivative, i.e. jerk, resulting in smooth machine motions (ii) only two control parameters, a gain and a delay, are required simplifying trajectory planning, and (iii) allows for simple blending of consecutive trajectories. The method has been tested experimentally on an industrial six Degree-of-Freedom (DOF) robot, a KUKA KR5 sixx R650. The results show position accuracy improvements over conventional S-curve and time-optimal (trapezoidal) velocity methods. The implementation is based on a simple look-up table which enables its real-time implementation.