A prototype of an autonomous controller for a quadrotor UAV

Question

1. What are the contributions mentioned in the paper "A prototype of an autonomous controller for a quadrotor uav" ?

2. What are the future works in "A prototype of an autonomous controller for a quadrotor uav" ?

3. What is the simplest way to determine the optimal trajectory?

4. What is the function of the LQR problem?

Accepted Answer

The paper proposes a complete real-time control algorithm for autonomous collision-free operations of the quadrotor UAV.. The developed control system incorporates both trajectory planning and path following.. The paper presents the results of simulations to demonstrate the suitability of the proposed control algorithm.

Accepted Answer

Future work will look at extending the developed controller to make it more robust and capable of handling collision-free flight in presence of multiple vehicles.

Accepted Answer

Assuming that the running costs (fuel consumption) are proportional to the average velocity, the objective function can be defined as:2 2 2 2 1 2 301 = (1 ) ( )f tf fw P x P y P z dt w t T t Φ − + + + − , (23)where w, 1P , 2P , and 3P are the weighting factors (for more flexibility, the last three of them are not necessarily equal to each other), and T is the predetermined time of arrival.

Accepted Answer

A. Formulation of the LQR Problem For a linear state-space model of the plant dynamics( ) = ( ) ( )t t t+x Ax Bu (15) a control input( ) = ( )ct t−u K x (16) is determined such that the closed loop system= [ ] ( )c t−x A BK x (17) is stable and a performance measure where( )

Accepted Answer

B. Stability AnalysisThe control gains cK were designed with the plant linearized at hover with the weighting matrices5 12 12= 10 − ×Q The authorand 5 8 8 8= diag(10 ,10 ,10 ,10 )−R (20) ensuring that the actuator constraints are maintained [43].

Accepted Answer

The components of the control input, u , can be easily expressed in terms of the states and their derivatives from (10-12) and (9)2 2 2 1234= ( ) = = = u x y g z u u u φ θ ψ + + −(24)From (10)-(12) it also follows that the rotational part of the state vector can be expressed as a function of the output vector and it’s derivatives as= arctan x g z θ − −(25)and2 2 2 = arcsin( )yx y g z φ + + − . (26)Singularities in (25) and (26) can only appear when =g z , in other words when the vehicle is in free fall.

Accepted Answer

to determine the optimal (reference) trajectory, an optimization within the control space is performed subject to some constraints placed within the output space and the state space.

Accepted Answer

The obstacle is modeled as a sphere of a 1m radius centered at (3, 0, 0)m; – The third mission assumes a horizontal flight to (10, 0, 0)m followed by a decent down a mineshaft of a 2m radius to its bottom (10, 0, -5)m.

Accepted Answer

The total thrust is given by 1 1 2 3 4= ( )u τ τ τ τ+ + + ; (1) a roll moment is achieved by varying the left (#4) and right (#3) rotor speeds 2 4 3= ( )u l τ τ− ; (2) a pitch moment is produced by varying the ratio of the front (#1) and back (#2) rotor speeds 3 1 2= ( )u l τ τ− ; (3) and finally, a yaw moment is obtained from the torque resulting from the subtracting counterclockwise (front and back) from the clockwise (left and right) speeds

Accepted Answer

It should be noted though that while time tf is 1.5 times greater than the optimal one (obtained for the simplified dynamics) all boundary conditions (including those imposed on the rotor fans’ dynamics) are satisfied, the reference trajectory and nominal control are feasible and (which is probably the most important) the solution can be obtained in the real-time.

Accepted Answer

Wind can be modeled as a drift in the translational position, more precisely a velocity of 0.1m/s along the x axis (this can further be improved with a gusting model of random noise in the same direction).

Accepted Answer

For the second mission (obstacle avoidance), as the optimal trajectory is measured by the flight time, it follows, that the optimal trajectory is the shortest path (and the thrust control looks pretty much the same as in the previous task).

Accepted Answer

The control vector, u , is therefore defined as[ ]1 2 3 4= , , , Tu u u uu , (5) where the last three control inputs govern the rotational dynamics directly:234p uq ur u=.

Accepted Answer

This is because the speed is unambiguously related to the Cartesian coordinates via2 2 2( ) ( ) ( ) ( )V t x t y t z t= + + . (39) The only way to separate the trajectory from the speed profile is to use some abstract argument τ that relates to time via the variable speed factor ( ) /d dtλ τ τ= [21].

Accepted Answer

The solution to the first problem (minimum-time vertical climb) is well known [47]: the vehicle applies maximum thrust followed by minimum thrust to slow down.

A prototype of an autonomous controller for a quadrotor UAV

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Most frequently asked questions

1. What are the contributions mentioned in the paper "A prototype of an autonomous controller for a quadrotor uav" ?

2. What are the future works in "A prototype of an autonomous controller for a quadrotor uav" ?

3. What is the simplest way to determine the optimal trajectory?

4. What is the function of the LQR problem?

5. What is the simplest way to calculate the LQR?

6. what is the arctan x g z?

7. What constraints are placed on the output space and the state space?

8. What is the simplest way to simulate a sphere of a 1m radius?

9. what is the torque and thrust of the quadrotor?

10. What is the way to achieve the optimal trajectory?

11. What is the way to model wind and noise?

12. What is the way to avoid obstructions?

13. what is the control vector for the rotor?

14. Why is the trajectory different from the speed profile?

15. What is the solution to the first problem?

Figures

Citations

Overview

Determination of landing zones of quadrotors experiencing in-flight failures

Trajectory generation for quadrotors using Galerkin projection and fuzzy inference

Trajectory tracking of a Quadcopter using Supertwisting Sliding Mode Control

CTFF: An Efficient Strategy for Continuously Targeting Fire Fighting with Quadrotor

References

Survey of Numerical Methods for Trajectory Optimization

PID vs LQ control techniques applied to an indoor micro quadrotor

Direct trajectory optimization using nonlinear programming and collocation

Aircraft trajectory planning with collision avoidance using mixed integer linear programming

Direct and indirect methods for trajectory optimization

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