Barghi Jond, H., V. Nabiyev, V., Benveniste, R. (2016). Trajectory Planning Using High Order Polynomials under Acceleration Constraint. Journal of Optimization in Industrial Engineering, 10(21), 1-6. doi: 10.22094/joie.2016.255
Hossein Barghi Jond; Vasif V. Nabiyev; Rifat Benveniste. "Trajectory Planning Using High Order Polynomials under Acceleration Constraint". Journal of Optimization in Industrial Engineering, 10, 21, 2016, 1-6. doi: 10.22094/joie.2016.255
Barghi Jond, H., V. Nabiyev, V., Benveniste, R. (2016). 'Trajectory Planning Using High Order Polynomials under Acceleration Constraint', Journal of Optimization in Industrial Engineering, 10(21), pp. 1-6. doi: 10.22094/joie.2016.255
Barghi Jond, H., V. Nabiyev, V., Benveniste, R. Trajectory Planning Using High Order Polynomials under Acceleration Constraint. Journal of Optimization in Industrial Engineering, 2016; 10(21): 1-6. doi: 10.22094/joie.2016.255
Trajectory Planning Using High Order Polynomials under Acceleration Constraint
1Young Researchers and Elite Club, Ahar Branch, Islamic Azad University, Ahar, Iran
2Department of Computer Engineering, Karadeniz Technical University, Trabzon, Turkey
3Department of Electrical and Electronic Engineering, Avrasya University, Trabzon, Turkey
Abstract
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 robot’s acceleration as the constraint. Also, initial and final conditions for the robot’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.
Highlights
Presenting a trajectory formulation and a procedure to arrange the suitable trajectories for applications.
Formulating three trajectory problems using 3rd, 4th and 5th degree of polynomials.
Using the high-degree polynomials because of providing of smoothness.
Simplifying the acceleration constraint to reduce the complexity of finding the high-degree polynomial coefficients.
Solving the polynomial coefficients by Genetic Algorithm (GA).
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