Trajectory Planning for High Speed Multiple Axis Contouring Systems

In the high speed coordinated motion of multiple axis linear systems two objectives must be achieved: 1) specified position accuracy and 2) well behaved actuator torque output. Objective (1) can be achieved through the design of an appropriate feedforward controller and (2) is achieved both through feedforward controller design and trajectory planning. Since actuator saturation will result in loss of position accuracy, failure to achieve (2) will also result in the violation of (1). This paper considers the generation of minimum time tracking velocity profiles for multiple axis contouring systems along prespecified spatial curves while subject to hard actuator torque limits. The result is applicable to systems with a general number of axes which may be dynamically coupled. It is also demonstrated that the trajectory generation and controller design problems are interdependent, and a method of selecting a trajectory generation algorithm for a given system under discrete time feedforward/feedback control is described.