QIAU Journal of Optimization in Industrial Engineering 2251-9904 10 21 2016 12 25 Trajectory Planning Using High Order Polynomials under Acceleration Constraint 1 6 255 10.22094/joie.2016.255 EN Hossein Barghi Jond Young Researchers and Elite Club, Ahar Branch, Islamic Azad University, Ahar, Iran Vasif V. Nabiyev Department of Computer Engineering, Karadeniz Technical University, Trabzon, Turkey Rifat Benveniste Department of Electrical and Electronic Engineering, Avrasya University, Trabzon, Turkey Journal Article 2014 12 03 The trajectory planning, which is known as a movement from starting to end 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 aimed to be used for safe and smooth navigation in mobile robots. First, a trajectory problem is formulized by considering a border on the robotâ€™s acceleration as the constraint. Also, initial and final conditions for the robotâ€™s velocity along the straight path are settled. To investigate that suggested trajectories perform motions with continuous velocity and smooth acceleration, three trajectory problems are formulated using 3rd, 4th and 5th degree 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 high-degree polynomial coefficients, the acceleration constraint is simplified and this process is based on a 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 shows that as well as acceleration constraint, the velocity conditions at the beginning and at the end of motion are fulfilled. http://www.qjie.ir/article_255_b370ba94ee22ec4ad288ad84513a92a2.pdf