The Use of Asymmetric Polynomial Profiles for Planning a Smooth Trajectory

Abstract

This paper presents planning of smooth trajectories using the asymmetric profiles of displacement, velocity, acceleration and jerk of described higher degree polynomials. The presented way of determination of polynomial and asymmetry coefficients as well as motion time includes the procedure at both constraints of single kinematic quantities, i.e., velocity, acceleration, jerk and introducing a few constraints simultaneously. Moreover, the paper presents a method of planning trajectories with intermediate points consisting in concatenation of the analyzed polynomials. The proposed method of trajectory planning was compared to that of using the S-curve. The results in the form of kinematic quantity courses are presented graphically. The discussed method guarantees continuity of displacement, velocity, acceleration and jerk. It can be used for planning trajectories of various technical objects (e.g., manipulators, mobile robots, CNC machine tools, optical disk drives, autonomous vehicles, etc.).

Real-Time Embedded System-Based Approach for Sensing Power Consumption on Motion Profiles

“…Scientists have studied motion profiles extensively for several decades since it has uncountable applications related to motion control, robotics, and commercial machinery, such as robot manipulators [1,2], conveyor belts, computer numerical control (CNC) machinery, 3D printers, and any system that needs to control movement based on electric motors [3][4][5]. The motion profiles define not only the position of the motor shaft but also the velocity, acceleration, and the third derivative of position (jerk) along the path or entire movement [6].…”

“…Jerk minimization has been achieved through the use of degree 7 polynomials, as shown by Wu and Zhang in [4], which is implemented in a robot manipulator. Similarly, Boryga et al use polynomials of degrees 5 to 9 to obtain phases of continuous motion [3]. However, experimental results still need to be presented.…”

A Human-Like Free-Lane-Change Trajectory Planning and Control Method With Data-Based Behavior Decision

“…Compared with traditional theoretical model-based methods, since the inputs are all real-world traffic data, the output lane change decision can be largely similar to real drivers. In terms of trajectory planning of vehicles, the trajectory shapes mainly include trigonometric curves [17], B-spline curves [18], numerical optimization trajectories [19], and polynomial curves [20], etc. Among them, polynomial curve method is currently the most widely used lane change trajectory planning algorithm because it can fully consider the dynamic and kinematic characteristics of vehicle, and can be used in complex driving environments with moving obstacles, and even for some extreme driving conditions.…”