With the rapid development of unmanned aerial vehicle technology, unmanned aerial vehicles (UAVs) have been widely used in the field of agricultural plant protection. Compared with fuel-driven UAVs, electrically driven rotorcrafts have many advantages such as lower cost, simpler operation, good maneuverability and cleaner power, which them popular in the plant protection. However, electrical rotorcrafts still face battery problems in actual operation, which limits its working time and application. Aiming at this issue, this paper studied the influence of rotorcraft flight parameters on energy consumption through series of carefully designed flight experiments. First of all, the linear motion experiments have been designed that the rotorcraft was made to perform speed tests and acceleration test with the speed varied from 2∼9 m/s. Secondly, the turning maneuver experiments are carried out under the different circular routes, a rotorcraft was made to conduct successive steering maneuvers at a certain speed of 2 m/s. With the collected tests data, the relation of the energy consumption and the flight dynamic parameter are analyzed through correlation analysis, and the test results of different pairs of experiments have been compared. The research results of this paper would encourage the agricultural rotorcraft to make less maneuvers during operation, which can also provide practical experience and data support for subsequent optimization of flight parameters and reduction of energy consumption.

With fast development of automation technology, agricultural plant protection with UAVs is gradually replacing traditional methods of manual operation [

Scholar all over the world have been investigated the issue in decades. Aleksandrov et al. [

Abeywickrama et al. [

There are many factors that could affect the energy consumption of rotorcraft, such as the weight, flight speed, flight status, and battery performance [

The organization of this paper is as follows. Section 2 reviews the principle and theory of linear regression, including the estimation of model parameters, significance test and goodness of fit test. Section 3 describes the experimental platform with hardware configuration and the flight scheme for the analysis of energy consumption factors. Section 4 presents correlation analysis of experimental results. Section 5 concludes the paper.

In practical problems, there are a large number of non-deterministic relations between variables. Although there are close relations between them, their closeness cannot be described by the exact relations. We summarize this relationship as: there is a close relationship between variables, but it is not close enough that one variable can be used to confirm another variable. There is a non-deterministic relationship between them. We call this relationship a statistical relationship or relationship. And regression analysis is a statistical method to discuss the statistical relationship between variables [

Linear regression can be divided into unary linear regression and multiple linear regression. Unary linear regression is a linear regression problem with only one explanatory variable, which is a special case of multiple regression. Multiple linear regression model refers to a regression model containing multiple independent variables, and is used to explain the linear relationship between the dependent variable and other multiple independent variables. The general form of the multiple linear regression model is as follows:

In _{1}, _{2}, …, _{k}_{1}, _{2}, …, _{k}_{i}_{1i}, _{2i}, …, _{ki}

Finally, the least square method is used to estimate the parameters, and the parameter estimated value of the regression model is obtained:

After completing the parameter estimation to obtain the regression model, a significance test is required. Significance test is a statistical process to examine whether the independent variable of the model has a remarkable effect on the dependent variable under a certain level, that is, it is used to evaluate closeness of the relationship between all independent variables and the dependent variable From the perspective of the regression model, even if the linear relationship of the overall regression equation is significant, it does not mean that each independent variable has a significant impact on the dependent variable. Therefore, a significance test is required to screen the independent variables and eliminate them. If the impact is not significant, a simpler and more reasonable multiple linear regression model should be established. The commonly used inspection methods are t-test and F-test.

The necessary goodness-of-fit test comes after the significance test, to determine the fitting effect of the regression equation. The difference between the observed values of the explained variables in the regression equation is mainly caused by two reasons: one is the influence of different value changes on the explanatory variable, and the other is caused by random factors. After all, the explained sum of squares (ESS) and the residual sum of squares (RSS) make up the variance sum of squares.

Then, the sum of squared deviations of the dependent variable is equal to the sum of the regression sum of squares and the remaining sum of squares, which is recorded as total sum of squares (TSS), which is:

In statistics, the total variation of the dependent variable in multiple linear regression is defined as the coefficient of determination ^{2}, which is the amount of variance explained by the line equation, and its calculation formula is:

In ^{2} is the proportion of the regression sum of squares in the total deviation of squares, reflecting the proportion of variation that can be explained by the regression equation. Its value is between 0∼1. The larger the value, the greater the higher the goodness of fit of the regression equation to the sample data points, and vice versa, the smaller the value, indicating that the regression equation has a lower goodness of fit to the sample data points.

The basic components of the rotorcraft used in the experiment include frame, motor, propeller, electronic speed control (ESC), global position system (GPS), battery, flight control, remote control receiver, digital antennae, as shown in

The rotorcraft can be control mainly through the ground station and the remote, as shown in

This paper mainly studies the influence of rotorcraft's motion parameters on its energy consumption. Among all the motion parameters, the flight speed and maneuvering acceleration have been selected to perform the correlation analysis.

Flight speed

The flight speed of the rotorcraft is closely related to the motor speed, air density, propeller diameter and pitch, and the output power of the battery is different at different flight speeds. For a rotorcraft flies at different speeds within the same distance, the output power is different, so that it is used to study the energy consumption during operation.

Maneuvering acceleration

During the flight of a rotorcraft, there are certainly maneuvers such as the accelerative movement, decelerating movement or turning maneuvers, every time the flight status is changed. According to the control principle of rotorcraft, when the flight status is about to change, the control system would adjust the speed of the motors to generate an acceleration, which would cause changes on the output current and voltage of the battery. That is to say, the energy consumption is easily affected by the maneuvering acceleration.

Based on the analysis and the influential parameters’ selection of the Section 3.2, a serial of experiments had been carefully designed to test the relation between those parameters and the energy cost of the rotorcraft. The rotorcraft is set to autonomous flight mode during tests, which operates at a certain height and track the waypoints uploaded from the ground station before takeoff. Two scenarios of flight tests were carried out that included the uniform motion flight, acceleration maneuvers and turning movements, the details are given below:

linear flight with fixed distance

In this scenario, the rotorcraft is instructed to fly straightly from start point to the end point, and then get back from end to the start, as shown in

Turning flight tests

In order to study the influence of turning maneuvers on the energy consumption of rotorcrafts, four sets of turning flights were carried out with same constant speed of 2 m/s. As shown in

After the experiment, the flight log stored in the secure digital (SD) card is converted into a csv format file. Based on MATLAB, the files had been read to analyze how did the energy consumption change with the selected dynamic parameters. Furthermore, the correlation between energy consumption and flight parameters has been studied with linear regression.

In this section, data analysis and the linear regression are carried out with respect to all kinds of the experimental scenarios, the details are present in the subsections.

The experimental results of the linear flights are shown in

Designed speed/(m/s) | Accelerating energy consumption /(KJ) | Energy consumption at uniform speed/(KJ) | Decelerating energy consumption/(KJ) | Total energy consumption/(KJ) |
---|---|---|---|---|

2 | 0.26424 | 10.14133 | 1.23509 | 11.64066 |

3 | 0.43156 | 6.04758 | 1.56194 | 8.04108 |

4 | 0.54902 | 4.38416 | 1.68948 | 6.62266 |

5 | 0.69679 | 2.99476 | 1.71034 | 5.40189 |

6 | 0.82278 | 2.41502 | 1.91739 | 5.15519 |

7 | 0.90285 | 2.10046 | 2.16517 | 5.16848 |

8 | 1.09627 | 1.26969 | 2.40266 | 4.76862 |

9 | 1.13856 | 0.99888 | 2.33568 | 4.47312 |

First of all, the energy consumption of different constant speeds per distance is shown in

A regression model was established using unary linear regression, as in _{us}

Correlation analysis of energy consumption and speed is also carried out and the results to test how much they are correlated. The correlation coefficient

Besides, the average power consumption is also applied to analysis for eliminating the impact of flight time.

Correlation analysis also shows that average power and flight speed are negatively correlated, as shown in

Generally speaking, the operation speed of the agricultural rotorcraft is 4∼6 m/s with respect to different model size. Faster speed may cause inadequate spraying, while slower speed might affect operation efficiency, waste chemicals and result in pollution [

The energy consumption of the maneuver accelerating scenarios and the deceleration are shown in _{a}_{d}_{a} _{d} _{a}^{2}) and _{d}^{2}) are acceleration and deceleration respectively.

It can be seen that in the regression model of maneuver acceleration, both the acceleration coefficient and the flight-time coefficient are over zero, which means that the energy consumption in the accelerating stage is positively correlated with the acceleration and the flight time. In other words, the greater the acceleration, the longer the flight time, and the more the energy consumption. For the decelerating stage, the flight time coefficient is over zero, while the deceleration coefficient is negative, suggesting that the energy consumption in the deceleration phase is positively correlated with the flight time, and negatively correlated with deceleration. Besides, the absolute value of deceleration coefficient is very small, so that the flight time in the deceleration stage has a greater impact on energy consumption.

In order to compare the energy consumption of the acceleration scenario and the uniform motion scenario, the acceleration is integrated with maneuver time to approximate a speed, named as the equivalent speed. Then the power consumption of the equivalent speed is calculated by

From

The actual flight trajectory turning flight experiment is shown in

First of all, from

The power consumption of different turning tests is also studied that average power with the corresponding turning rate

Turning radius | Angular rate (rad/s) | Average power (W) |
---|---|---|

5 m | 0.4342 | 272.7242 |

10 m | 0.1968 | 271.9105 |

20 m | 0.097 | 268.6976 |

50 m | 0.039 | 265.9615 |

Correlation analysis on the average power and turning rate shows that the two factors are negatively correlated. The correlation coefficient is

In this paper, the author studied the relations of the energy consumption and the flying dynamical parameters of the rotorcraft. From the engineering point of view, various testing scenarios were design to analyze the impact of the flight speed, maneuver acceleration and maneuver turns on the energy change. From the tests results, it is found that, the greater the speed, the shorter the time and the lower the energy consumption. Compared with uniform motion, the maneuver accelerating movement and turning motion will cause more energy consumption. Therefore, for agricultural rotorcraft operations, the waypoints should be arranged in a straight line as far as possible, and the distance between the waypoints should be as large as possible to avoid turning and acceleration. As for the operating speed, it is related to the distance between the waypoints and the distribution of the waypoints, and which should be carefully designed. In the follow-up work, the author will further study the way to optimize the operation speed between the waypoints.