Unit Dual Quaternion Based Attitude And Position Integrated Control For Quadrotor

The mismatch between the output of the controller and the output of the actuator caused by the saturated nonlinearity of actuators is a gap between designed controller that does not consider the constrainted control inputs and its application on real vehicles.For a general rigid body,its rotation affects its translation which shows the coupling relationship between attitude and position.Considering the feedback control,when both the position loop and the attitude loop have control input constraints,the traditional decoupled control method for the position and attitude is difficult to realize the control tasks.Therefore,it is urgent to study the simutaneous control method of position and attitude for the constraints of control input.The unit dual quaternion(UDQ)is the most concise and computationally efficient mathematical tool in three-dimensional space,and can simultaneously describe position and attitude without singularity.However,the previous studies based on unit dual quaternion mainly takes general rigid bodies as the research object to design ideal controllers.As far as we know,there has no UDQ based research considering of control input.This paper takes the quadrotor as research object.is explored Based on the unit dual quaternion,the solution to the problem of limited control input.The main results and contributions of this paper are as follows:(1)To deal with the input constraints of quadrotor,an attitude and position coupled set-point control law based on unit dual quaternion is proposed and proved,which realizes the set-point control of quadrotor in both simulation and real experiment.This paper makes the description of the control input constraints of quadrotor in math format.Then it establishes constrained error kinematic model and design position and attitude coupled setpoint control law based on unit dual quaternion.And also it gives the proof of the stability of this control law by Lyapunov method with the velocity saturation conditions.Numerical simulation and quadrotor simulation present the evolution of control inputs and pose of the quadrotor in control process.The experiment on real quadrotor shows the proposed control method can complete the set-point control task successfully.(2)For tracking control of quadrotor with the input constraints,an constrained tracking control law based on unit dual quaternion is proposed and proved,which successfully makes quadrotor track the moving target configuration in both simulation and real experiment.In order to make the quadrotor track the desired and moving target configuration,we update the math description of input constraints of quadrotor and establish corresponding error kinematic model.Then we design the corresponding constrained tracking control law and give the proof of the stability of this control law by Lyapunov method with the velocity saturation conditions.To make comparison with decoupled control law,the quadrotor simulation and the experiment on real quadrotor have been done and their results show the advantage of the proposed method in tracking performance and energy consumption.