• Optimization
• Quadrotor
• TLBO
• Trajectory

Most of the optimization algorithms are characterized by a large number of parameters that must be well tuned to have a good working algorithm. This limitation is avoided in Teaching-Learning-Based Optimization (TLBO) algorithm, where a few numbers of parameter needs to be well settled.
TLBO is a recent developed evolutionary algorithm based on two elementary concepts of education, namely teaching phase and learning phase. At first, learners improve their knowledge through the teaching methodology of teacher and finally learners increase their knowledge by interactions among themselves.
Lately, the TLBO algorithm has been widely used in the scientific fields and compared with the other existing technique it demonstrates its superiority. Despite this, few applications of the method to the trajectory planning problem have been made.
Two different problem have been addressed using the proposed TLBO method in this work. A simple trajectory planning problem for a terrestrial vehicle and trajectory planning problem for a quadrotor in urban environment. Literature investigation shows that the modelling work in trajectory planning through TLBO technique, especially on delivery task in urban environment, is insufficient. Hence, the validity of TLBO algorithm in solving trajectory planning problem with multiple constraints need to be still verified.
The principles of TLBO algorithm are described first, and how TLBO algorithm is integrated into the trajectory planning problem is further explained.
First, the dynamic, the constraints and the goals is presented for a terrestrial vehicle. Results show that in order to get optimal solutions, with satisfied constraints, the TLBO’s parameters have to be well settled. It means the parameters have to be tuned in a way that the number of discarded solutions, due to the constraints, are minimized. Hence, TLBO’s parameters must be as much as possible close to the one that reflect a real situation. It can be concluded that m_subjects=5 and n_students=40 can result in solutions good enough in this problem.
Second, the dynamic of quadrotor, the constraints of quadrotor manoeuvrability, urban environment and delivery task are considered in the trajectory planning model, and the goals are to minimize the deviation between the destination targets and the relative quantities at the quadrotor final position. To test the proposed algorithm three different scenarios are analysed, which represent the main phase of a delivery task: Take-off cruise path, cruise path and landing path.
Results show that, once the TLBO’s parameters are well settled, the algorithm is able to reach the targets with respect to all the constraints. In particular for the first two phases of the trajectory the TLBO’s parameters match; for the landing phase a reduction of the control variable u_1 must be realized. This represent a well settling procedure of the parameters, indeed in a real landing situation a reduction of the range power is realized.
In the future, there are different constraints and target that could be considered.
As no constraint on the control inputs rate are taken into account in this work, the obtained control input can result in an over power consumption considering that the energy requested by the vehicle during the mission is ∝(ω ̇_i (t),ω_i^2 (t),ω_i (t))∙ω_i (t) as reported in literature. Hence, a third cost function should be added in order to generate trajectories with minimum energy. Besides, also the wind can affect the energy consumption, a much real environment could be realized therefore adding a wind field.