Trajectory Planning Using High-Order Polynomials under Acceleration Constraint

The trajectory planning, known as a movement from starting point to ending point by satisfying the constraints along the path, is an essential part of robot motion planning. A common way to create trajectories is to deal with polynomials which have independent coefficients. This paper presents a trajectory formulation as well as a procedure to arrange the suitable trajectories for applications. Created trajectories are aimed to be used for safe and smooth navigation in mobile robots. First, a trajectory problem is formulized by considering a border on the robot’s acceleration as the constraint. Also, initial and final conditions for the robot’s velocity along the straight path are settled. To investigate the idea that suggested trajectories perform motions with continuous velocity and smooth acceleration, three trajectory problems are formulated using 3rd, 4th, and 5th degrees of polynomials. The high-degree polynomials are used because of providing of smoothness, but there is complexity in the calculation of additional coefficients. To reduce the complexity of finding the highdegree polynomial coefficients, the acceleration constraint is simplified and this process is based on certain scenarios. Afterwards, the coefficients of the used polynomials are found by taking into account the acceleration constraint and velocity conditions. Additionally, to compare the obtained solutions through proposed scenarios, the polynomials` coefficients are solved numerically by Genetic Algorithm (GA). The computer simulation of motions, as well as acceleration constraint, shows that the velocity conditions at the beginning and at the end of motion are fulfilled.