An Optimal Trajectory Planning Method Based On Spline Theory And Its Application

Trajectory planning is an unavoidable problem in many modern engineering fields.At present,the numerical direct method is one of the most effective methods for solving the optimal trajectory planning problem.The focus of the numerical direct method is mainly how to realize the transformation from trajectory planning problem to parameter optimization problem.Aiming at the trajectory planning problem of single-input single-output system with special model,this paper proposes a collocation method based on spline approximation to realize the parameterization of state trajectory and control law,and then transform the original problem into parameter optimization problem.The method is applied to a class of trajectory planning problems with path constraints.Compared with most collocation methods,this method can be applied to the trajectory planning problem of the given model system more effectively.The advantage is that the accuracy of the result is higher,and the parameter optimization problem of transformation is simpler and more convenient for quick solution.The main research contents and innovations of the theoretical part of this paper are as follows:1.For the single-input single-output system of the special model,based on the spline fitting,combined with the initial conditions,the parameterization of the state,output trajectory and control law is realized.In this paper,the derivation process is given,which proves that under the spline fitting,the variable trajectory satisfies the given parameter form and is the necessary and sufficient condition to satisfy the initial condition.A supplementary explanation was given by simulation.2.For the trajectory planning problem of this type of single input single output system,the termination condition is transformed into the parameter constraint.In this paper,the derivation process is given,and the necessary and sufficient conditions for the termination condition to be established after the parameterization are proved,and the processing means that the given condition is not satisfied,that is,the termination condition cannot be strictly met,is introduced.A supplementary explanation was given by simulation.3.For a class of trajectory planning problems with path constraints,the path constraints are discretized.In this paper,the derivation process is given,and it is proved that after the parameterization,there are sufficient conditions for the corresponding parameters to make the termination condition and the discretized path constraint simultaneously.A supplementary explanation was given by simulation.4.For the brushless DC motor starting process,the three-and six-order polynomial fitting methods and the method of this paper are used to solve the planning results.The planning results are better and the accuracy is better.high.Then simulate the starting process of the motor under the action of the tracking controller,using the step,slope and the planning trajectory of the method as the tracking object,and compare the output results-from the perspective of tracking control,the planning trajectory in this method As a tracking object,the output can better satisfy the constraint and is less affected by the controller parameter adjustment.5.Experiment to explore the influence of discrete points on the path to the planning effect.A specific trajectory planning problem with path constraints is given.The trajectory is planned by the method described in this paper.The degree of deviation of the planning trajectory from the path constraints is observed.The conclusion is drawn that the more the number of discrete paths,the path of the planned trajectory is given.The lower the deviation of the fixed path,the slower the solution speed of the nonlinear algorithm,and the smaller the number of discrete points on the index.