Online trajectory planner with constraints on velocity, acceleration and torque

Abstract

A filter for trajectories smoothing is presented. The filter provides an output reproducing the input trajectory if this is compliant with given constraints on the velocity, the acceleration and the torque required for tracking it. Otherwise, the filter approximates the input profile guaranteeing that the output trajectory satisfies all the kinematic and dynamic limits. The tracking of the input signal is optimal in the sense that at each time instant the limit value of one among velocity, acceleration and torque is reached. The filter, based on a variable structure controller, is designed in the continuous-time domain but can be implemented by discretization as a sampled system. It can therefore used in mechatronic and robotic applications driven by digital controllers in order to filter trajectories planned without considering the above mentioned constraints or to generate realtime smooth trajectories by simply providing basic inputs such as step or ramp functions.

A Discrete-Time Filter for the Generation of Signals With Asymmetric and Variable Bounds on Velocity, Acceleration, and Jerk

“…Differently from the SS that was proposed in [27], it is able to handle asymmetric jerk bounds. Let us consider a command law that only uses σ 3 , i.e., let us control (6) by means of (8), (15), and (16) and by assuming…”

“…Equations (8), (15), (16), and (23) associate to each point p h,τ,η a planar SS σ 3 and its BL. In particular, as shown in Fig.…”

“…In particular, from any initial state z 0 ∈ B h,τ,η or, equivalently, fromz 0 = [h τ η λ μ ν] T , with h, τ ∈ N + , the origin is certainly reached if system (6) is controlled by means of (8), (15), (16), and (23), according to the following sequence of steps.…”

“…The sole drawback of these approaches is represented by the complexity of the planning algorithm, which can be reduced, still with computational times of microseconds, by adopting indirect planning methods, i.e., by generating trajectories through proper feedback systems. Early works on this topic appeared in [13]- [15] for continuous-time frameworks, and in [16] and [17] for discrete-time frameworks. Given solutions were based on second-order filters that were able to impose bounds on the velocity and on the acceleration signals.…”

An Efficient Algorithm for the Real-Time Generation of Synchronous Reference Signals

“…The solutions proposed over the years have sometimes been conceived for continuous-time environments [15]- [18] or, in other contexts, for discrete-time applications [19]- [22].…”