Trajectory Generation Implemented as a Non-linear Filter

Filter path which is sufficiently well behaved that it can be tracked by a manipulator. However, the creation of good paths becomes somewhat problematic in situations where a manipulator is required to follow a target whose position is varying erratically (for instance, if the target is specified using a position sensor held in an operator's hand). This paper presents a simple solution for such situations, in which the "trajectory generator" is implemented as a non-linear filter which tries to bring its output (manipulator setpoints) to the input (target position) as quickly as possible, subject to constraints on velocity and acceleration. The solution to this problem in one dimension is quite easy. For multiple dimensions, the problem can be handled by applying one-dimensional solutions to a pair of appropriately chosen coordinate axes. An interesting feature of the approach is that it can handle spatial rotations as well as vector quantities.