A Path Planning Method for a Swing-Arm Tracked Unmanned Vehicle

Abstract

The present invention discloses a path planning method for a swing-arm tracked unmanned vehicle, comprising the following steps: collecting parameters of the swing-arm tracked unmanned vehicle and constructing a kinematic model for the vehicle based on the parameters; refining the kinematic model to obtain a refined collision model; and calculating the refined collision model using an improved DWA algorithm to obtain an optimal driving path. This method improves the conventional DWA algorithm, enhancing the maneuverability of the swing-arm tracked unmanned vehicle in indoor scenarios and enabling the planning of a better driving path.

Description

Technical Field

[0001] The present invention belongs to the technical field of route planning, and in particular relates to a path planning method for a swing-arm type crawler unmanned vehicle. Background Art

[0002] A swing-arm tracked unmanned vehicle (UAV) incorporates a set of tracked swing arms, enhancing the high maneuverability and stability of conventional tracked vehicles. This allows it to utilize the maneuverability of its front swing arms to traverse obstacles. This allows UAVs to operate stably within buildings and even climb stairs using their front swing arms. The goal of local path planning is to enable the UAV to reach a designated local target point without collision. Compared to global path planning algorithms, local path planning algorithms are executed more frequently and rely more heavily on real-time environmental perception. During indoor exploration, the local path planning algorithm must output a collision-free path based on perceived traversable areas and obstacles, and control the vehicle's movement in real time to track the path. Narrow and complex indoor spaces place higher demands on local path planning, and obstacle avoidance can make it difficult for UAVs to navigate confined spaces. Therefore, UAVs must possess enhanced maneuverability through narrow doors and long corridors. Summary of the Invention

[0003] In order to solve the above technical problems, the present invention proposes a path planning method for a swing-arm tracked unmanned vehicle to solve the problem of limited reachable area.

[0004] To achieve the above object, the present invention provides a path planning method for a swing-arm tracked unmanned vehicle, comprising the following steps:

[0005] collecting parameters of the swing-arm tracked unmanned vehicle, and constructing a kinematic model of the swing-arm tracked unmanned vehicle based on the parameters of the swing-arm tracked unmanned vehicle;

[0006] Refining the kinematic model to obtain a refined collision model;

[0007] The refined collision model is calculated based on the improved DWA algorithm to obtain the optimal driving path.

[0008] Preferably, the method for constructing a kinematic model of a swing-arm tracked unmanned vehicle comprises:

[0009] Construct a global coordinate system and a vehicle coordinate system. The vehicle's forward direction is the positive direction of the x-axis of the vehicle coordinate system, and the origin of the vehicle coordinate system coincides with the center of mass of the swing-arm tracked unmanned vehicle.

[0010] Based on the global coordinate system, the vehicle body coordinate system and the posture of the swing-arm tracked unmanned vehicle, the relationship between the tracked vehicle's running speed, angular velocity and the speed of the tracks on both sides is calculated;

[0011] Through the in-situ rotation experiment, the swing-arm tracked unmanned vehicle was calibrated, the equivalent differential theory spacing was obtained, and the kinematic model of the swing-arm tracked unmanned vehicle was established.

[0012] Preferably, the method for obtaining a refined collision model includes:

[0013] The swing-arm tracked unmanned vehicle model is decomposed into a disk, and the distance between the radius and the center of the disk is calculated. The calculated disk is overlaid on the kinematic model of the swing-arm tracked unmanned vehicle to obtain a refined collision model.

[0014] Preferably, the method for calculating the distance between the radius of the disk and the center of the disk comprises:

[0015] The radius of the disc and the distance between the center of the circle are calculated by the length of the swing-arm tracked unmanned vehicle, the width of the swing-arm tracked unmanned vehicle, the number of longitudinally arranged discs, and the number of transversely arranged discs.

[0016] Preferably, the process of obtaining the optimal driving path includes:

[0017] First, the speed is sampled by the improved DWA algorithm, and constraints are added to the sampled speed to obtain the constrained speed.

[0018] Then, the velocity space is traversed within the constrained velocity range to generate a combination of velocity and angular velocity, and a trackable trajectory of the vehicle within a prediction time is generated based on the combination of velocity and angular velocity using a kinematic model of the swing-arm tracked unmanned vehicle;

[0019] Finally, the trajectory is normalized, and an evaluation value is calculated for the normalized trajectory using an objective function to obtain an optimal driving path.

[0020] Preferably, the method for obtaining the constraint velocity includes:

[0021] Based on the maximum linear velocity and maximum angular velocity of the swing-arm tracked unmanned vehicle, the speed of the swing-arm tracked unmanned vehicle is constrained within a range;

[0022] According to the maximum acceleration and angular acceleration of the swing-arm tracked unmanned vehicle, the improved DWA algorithm is used to add maximum acceleration and deceleration constraints to the swing-arm tracked unmanned vehicle;

[0023] The permissible speed constraint of the swing-arm tracked unmanned vehicle is set through the distance evaluation value of a single planning;

[0024] A constrained speed is obtained based on the range constraint, the maximum acceleration / deceleration constraint, and the allowable speed constraint.

[0025] Preferably, the normalization method includes:

[0026] The distance function, target orientation function, and speed function are used as the numerator, and the evaluation values of all currently planned trajectories are added as the denominator to calculate the ratio of the evaluation value of the specified trajectory to the evaluation value of all trajectories.

[0027] Preferably, the formula for calculating the evaluation value is:

[0028] G(v,ω)=β he σ(heading(v,ω))+β dist σ(SEP dist(v, ω))+β vel σ((velocity(v,ω))

[0029] In the formula, heading(v,ω) represents the target heading function, SEPdist(v,ω) represents the distance function, velocity(v,ω) represents the speed function, and β he , β dist , β vel are the weighting coefficients of the three objective function evaluation values.

[0030] Compared with the prior art, the present invention has the following advantages and technical effects:

[0031] This paper first analyzes the planar kinematic model of a swing-arm tracked unmanned vehicle and optimizes its collision model. Based on this optimized collision model, the traditional DWA algorithm is then improved, enhancing the vehicle's maneuverability in indoor scenarios and enabling the planning of a more optimal driving path. BRIEF DESCRIPTION OF THE DRAWINGS

[0032] The accompanying drawings, which constitute part of this application, are intended to provide a further understanding of this application. The exemplary embodiments and descriptions of this application are intended to explain this application and do not constitute an improper limitation on this application. In the accompanying drawings:

[0033] Figure 1 This is a flow chart of a path planning method for a swing-arm tracked unmanned vehicle according to an embodiment of the present invention;

[0034] Figure 2 A coordinate diagram of the kinematic model of a swing-arm tracked unmanned vehicle according to an embodiment of the present invention;

[0035] Figure 3 This is a refined collision model diagram of the swing-arm tracked unmanned vehicle according to an embodiment of the present invention;

[0036] Figure 4 This is a distance evaluation value calculation diagram of the DWA algorithm according to an embodiment of the present invention;

[0037] Figure 5 This is a distance evaluation value calculation diagram of the improved DWA algorithm according to an embodiment of the present invention;

[0038] Figure 6 A schematic diagram of a traceable trajectory according to an embodiment of the present invention;

[0039] Figure 7 This is a schematic diagram of planning results according to an embodiment of the present invention;

[0040] Figure 8 This is a comparison diagram of a local path test according to an embodiment of the present invention;

[0041] Figure 9 This is a comparison diagram of the narrow door according to an embodiment of the present invention. DETAILED DESCRIPTION

[0042] It should be noted that, in the absence of conflict, the embodiments and features of the embodiments in this application can be combined with each other. The present application will be described in detail below with reference to the accompanying drawings and in combination with the embodiments.

[0043] It should be noted that the steps shown in the flowcharts of the accompanying drawings can be executed in a computer system such as a set of computer-executable instructions, and that, although a logical order is shown in the flowcharts, in some cases, the steps shown or described can be executed in an order different from that shown here.

[0044] Example 1

[0045] like Figure 1 The present invention provides a path planning method for a swing-arm tracked unmanned vehicle, comprising the following steps:

[0046] collecting parameters of the swing-arm tracked unmanned vehicle, and constructing a kinematic model of the swing-arm tracked unmanned vehicle based on the parameters of the swing-arm tracked unmanned vehicle;

[0047] Refining the kinematic model to obtain a refined collision model;

[0048] The refined collision model is calculated based on the improved DWA algorithm to obtain the optimal driving path.

[0049] The process of further optimization and constructing the kinematic model of the swing-arm tracked unmanned vehicle is as follows:

[0050] When swing arm motion is not involved, the kinematic model of a swing arm tracked unmanned vehicle is the same as that of a conventional tracked vehicle. Therefore, this embodiment first establishes a kinematic model for a conventional tracked vehicle in planar motion. It is assumed that the tracked vehicle is a rigid body and that the tracks do not slip against the ground during motion.

[0051] like Figure 2 The global coordinate system shown is Oxy; the vehicle coordinate system is O'x b y b , the vehicle's forward direction is the positive direction of the x-axis of the vehicle system, Cb is the center of mass of the vehicle, the origin of the vehicle coordinate system O' and the center of mass of the vehicle C b The vehicle's forward speed is v c , C i is the instantaneous center of the tracked vehicle's rotational motion, and the vehicle's rotational angular velocity is ω c The coordinates of the tracked vehicle in the global coordinate system are (x c ,y c ) represents the tracked vehicle posture, which is the angle ψ between the positive x-axis of the vehicle system and the positive x-axis of the global system. c Thus, the kinematic model of the tracked vehicle can be obtained as follows:

[0052]

[0053]

[0054]

[0055] The speed of the left track output is v l , the right crawler output is v r When v1=v r When v1=-v r When the tracked vehicle rotates, the instantaneous center C i Coincident with the origin O' of the vehicle coordinate system, the crawler vehicle's motion state is represented by rotation around O', that is, rotation in place. l >v r or v l <v r When the tracked vehicle moves around the instantaneous center C i Rotation. The width of the vehicle is W b , the width of the track on one side is W cb , assuming that the tracked vehicle's rotation radius is R, and the tracked vehicle is a rigid body, the angular velocity of each part of the vehicle body is equal, so there is an equation:

[0056]

[0057] The rotation radius R of the crawler vehicle can be obtained by combining the following equations:

[0058]

[0059] Among them (W b -W cb ) is equivalent to the differential wheel spacing L diff , and then derive the tracked vehicle running speed v c , the relationship between the angular velocity and the track speed on the left and right sides is:

[0060]

[0061]

[0062] It can be seen that the motion state of the crawler vehicle is calculated by the speed output of the left and right crawlers. By controlling the speed of the crawlers, the crawler vehicle can be controlled. When the swing arm crawler unmanned vehicle of the present invention is running on flat ground, the swing arm is close to the two sides of the vehicle. At this time, L diff It cannot be directly calculated from the structural parameters of the vehicle. It is necessary to calibrate the swing arm unmanned vehicle through multiple in-situ rotation experiments to obtain its equivalent differential theory spacing L diff , establish the kinematic model of the swing-arm tracked unmanned vehicle.

[0063] Further optimization solutions, such as Figure 3 As shown in the figure, the swing-arm tracked unmanned vehicle model is decomposed into a disk, and the radius of the disk and the distance between the center are calculated. The calculated disk is overlaid on the kinematic model of the swing-arm tracked unmanned vehicle to obtain a refined collision model. The center distance and radius of the disk are calculated as follows:

[0064] Arrange n circles vertically and m circles horizontally. The radius of the circle is:

[0065]

[0066] The distance d between the centers of the circles arranged vertically and horizontally l and d w The calculation method is as follows:

[0067]

[0068]

[0069] Table 1 compares the model refinement effects using different numbers of circles.

[0070] Table 1

[0071]

[0072] Compared to a simplified model using only one circle covering a rectangle, autonomous vehicle models using two, three, and eight circles covering the rectangle reduced the vehicle's width by 23.2%, 33.1%, and 41.1%, respectively. Theoretically, the greater the number of circles covering a vehicle, the narrower the vehicle.

[0073] A further optimization scheme is to calculate the refined collision model based on the improved DWA algorithm. The calculation process is as follows:

[0074] The DWA algorithm performs velocity sampling in the velocity space (v, ω) composed of velocity and angular velocity. The sampled velocity is represented by the vector V i =(v i ,ω i ), and then add constraints on the sampling speed.

[0075] The maximum linear velocity of the vehicle is v max , the maximum angular velocity is ω max , the range of vehicle speed is constrained to V s :

[0076] V s ={v∈[0,v max ],ω∈[-ω max ,ω max ]}

[0077] According to the maximum acceleration and angular acceleration of the vehicle, the algorithm can add a maximum acceleration and deceleration constraint V to the vehicle. d :

[0078] V d ={(v,ω)|v∈[v c -a max Δt,v c +a max Δty]∩ω∈[ω c -α max Δt,ω c +α max Δt]}

[0079] Where Δt is the time interval between two samplings, a max and α max are the maximum acceleration and angular acceleration of the vehicle respectively. Due to the maximum acceleration and deceleration constraint V d The shape in velocity space is a rectangle, like a window, so V d It is also called a sliding window, hence the name of the sliding window method. The actual speed of the vehicle, Vactual, is the center of the sliding window.

[0080] In order to ensure the safety of vehicle operation, the algorithm adds an allowable speed constraint V to the vehicle based on the obstacle information in the environment, as well as the maximum acceleration and maximum angular acceleration of the vehicle. a :

[0081]

[0082] Where dist(v,ω) is the distance evaluation value of the trajectory, which indicates the closest distance between the corresponding trajectory and the obstacle.

[0083] Assuming that the algorithm plans q trajectories at a time, the distance evaluation value of the i-th trajectory is calculated as follows: Figure 4 shown.

[0084] in,

[0085] dist(v i ,ωi)=arg min||obs(x,y)-T i (x, y)||

[0086] Where obs(x,y) is the discretized storage list of obstacles perceived in the unmanned vehicle environment, T i (x,y) trajectory T i The discretized storage list of each position in , the distance evaluation value is:

[0087] dist(v,ω)=arg max{dist(v i ,ω i )|1≤i≤q}

[0088] Under the combined effect of the three constraints, the actual speed range V that the vehicle can reach can be obtained. r :

[0089] V r =V s ∩V d ∩V a

[0090] When a rectangular unmanned vehicle is decomposed and covered by multiple circles, it is assumed that there are n circles distributed longitudinally and m circles distributed transversely. The coordinates of the center of the jth longitudinal circle and the kth transverse circle in the vehicle system are (x j,k ,y j,k ), according to rigid body kinematics, the center trajectory of each circle in the trajectory can be calculated, and because the circle is rotationally invariant, the center trajectory can be represented only by (x, y) in the global coordinate system:

[0091]

[0092] The evaluation value is calculated for each center trajectory. The distance evaluation value calculation method for a single trajectory is as follows: Figure 5 shown.

[0093] in,

[0094] SEPdist(v i ,ω i )=arg min{||obs(x,y)-T i (x j，k ,y j，k )||1≤j≤n,1≤k≤m}

[0095] If q trajectories are planned in a single time, the distance evaluation value of the single planning is:

[0096] SEPdist(v,ω)=argmax{SEPdist(v i ,ω i )|1≤i≤q}

[0097] The vehicle's permissible speed constraint V a 'for:

[0098]

[0099] Constraint speed V r 'for:

[0100] V r ′=V s ∩V d ∩V a '

[0101] At the constraint speed V r ' range, the entire velocity space is discretized with a certain speed and angular velocity resolution to generate several sets of speed and angular velocity combinations. Then, based on the speed and angular velocity combinations, the vehicle kinematic model is used to generate trajectories that can be tracked by the vehicle within a certain prediction time:

[0102] x c，t+1 =x c，t +v c，t cosθ c，t ·Δt

[0103] y c，t+1 =y c，t +v c，t sinθ c，t ·Δt

[0104] ψ c，t+1 =ψ c，t +ω c，t ·Δt

[0105] Among them, x c，t+1 ,y c，t+1 , ψ c，t+1 represents the vehicle's position in the global coordinate system at time t+1, x c，t ,y c，t , ψ c，t represents the vehicle's position in the global coordinate system at time t, v c，t+1 ,ω c，t+1 is the speed and angular velocity of the vehicle at time t+1, v c，t ,ω c，tis the speed and angular velocity of the vehicle at time t. Knowing the coordinates of the vehicle at the current moment, the position at any moment in the trajectory can be calculated by integration. The predicted current moment can be tracked as Figure 6 shown.

[0106] Then the algorithm enters the optimization stage and introduces the objective function G(v, ω) to calculate the evaluation value of each trajectory.

[0107] G(v,ω)=β he σ(heading(v,ω))+β dist σ(SEP dist(v, ω))+β vel σ((velocity(v,ω))

[0108] in,

[0109] heading(v,ω)=π-ψ p

[0110] The target heading function heading(v,ω) is used to measure whether the posture of the unmanned vehicle is consistent with the target direction. The larger the function value, the closer the direction of the unmanned vehicle is to the target point. p is the attitude angle of the vehicle at the end of the predicted trajectory. SEPdist(v,ω) measures the distance between the unmanned vehicle's trajectory and the obstacle. The larger the function value, the safer the unmanned vehicle's operation. The velocity function velocity(v,ω) is the projection of the vehicle's linear velocity in the trajectory in the target direction. The larger the function value, the faster the unmanned vehicle runs and the faster it can reach the target point. In summary, the trajectory with the highest evaluation value can be deduced as the optimal trajectory calculated by the current algorithm. Where β he , β dist , β vel These are the weighted coefficients for the three objective function evaluation values. The coefficients can be adjusted according to different application scenarios to achieve different motion states for the unmanned vehicle. Here, σ is a smoothing function. Since the units and magnitudes of each objective function are different, when calculating the overall evaluation value, it is necessary to normalize the objective function for each trajectory to prevent a single objective function from having too large an impact on the overall evaluation value. If the evaluation value of the i-th trajectory needs to be calculated, the normalization method is as follows:

[0111]

[0112]

[0113]

[0114] Where n is the number of all planned trajectories at that moment. The principle of normalization is to add the evaluation values of all currently planned trajectories as the denominator and calculate the ratio of the evaluation value of a specific trajectory to the evaluation values of all trajectories.

[0115] Planning results such as Figure 7 As shown in Figure 2, the final objective function G(v,ω) takes the trajectory with the highest evaluation value as the optimal driving path.

[0116] Example 2

[0117] First, set the shape of the unmanned vehicle to a rectangle with a length of 1m and a width of 0.6m, with an aspect ratio of 5:3.

[0118] A collision model for the autonomous vehicle is constructed using a single original disk and three refined disks. The centers of the three disks in the refined model are located at (0.33, 0), (0, 0), and (0, -0.33) in the vehicle coordinate system, respectively, with a radius of r = 0.78m. Each grid cell in the figure is a square with a side length of 1m.

[0119] First, test the passability of the local path. The important parameters are as follows:

[0120] Target speed (m / s): 1.5, speed resolution (m / s): 0.05, angular velocity resolution (rad / s): 0.01, maximum acceleration (m / s): 2.0, maximum speed (m / s 2 ):2.0、Maximum angular velocity (rad / s): 1.0、Prediction time (s): 6.0、Target orientation evaluation coefficient β he : 10.0, obstacle distance rating coefficient β dist : 5.0, speed evaluation coefficient β vel :5.0.

[0121] Obstacles are placed in the scene, forming a gradually narrowing channel on both sides. The distance the unmanned vehicle travels in the narrowing channel is used as a measure of the vehicle's maneuverability. For every 2 meters the unmanned vehicle advances in the channel, the channel narrows by 0.2 meters. A local target point is set in front of the vehicle, forcing the unmanned vehicle to continue moving forward while meeting the obstacle avoidance requirements until the algorithm outputs a speed of 0.

[0122] Next, we simulated a corridor and narrow door scenario to test the autonomous vehicle's ability to navigate within the building. We set the corridor width to 2 meters and the narrow door width to 1.4 meters. We had the autonomous vehicle move through the corridor and then pass through a narrow door on one side of the corridor.

[0123] according to Figure 8As can be seen, the unmanned vehicle using the original DWA algorithm can only pass through a channel as wide as 1.8m, while the unmanned vehicle using the improved DWA algorithm can pass through a channel as narrow as 1.2m. This shows that the improved algorithm significantly improves the unmanned vehicle's ability to pass through. Figure 9 The DWA algorithm demonstrates its ability to navigate interior building scenes. Both algorithms enable the autonomous vehicle to navigate corridors, but due to its obstacle avoidance capabilities, the original DWA algorithm prevents the vehicle from passing through narrow doors in corridors. The improved DWA algorithm allows the vehicle to navigate narrow doors without colliding with obstacles, demonstrating the superior ability of the improved DWA algorithm to navigate interior building scenes.

[0124] In summary, it can be concluded that the DWA algorithm improved by the refined collision model can make the unmanned vehicle have higher passability and obtain a better driving path.

[0125] The above are merely preferred embodiments of the present application, but the scope of protection of the present application is not limited thereto. Any changes or substitutions that can be easily conceived by a person skilled in the art within the technical scope disclosed in this application should be included in the scope of protection of the present application. Therefore, the scope of protection of the present application should be based on the scope of protection of the claims.

Claims

1. A path planning method for a swing-arm tracked unmanned vehicle, characterized in that: The following steps are involved: collecting parameters of the swing-arm tracked unmanned vehicle, and constructing a kinematic model of the swing-arm tracked unmanned vehicle based on the parameters of the swing-arm tracked unmanned vehicle; Refining the kinematic model to obtain a refined collision model; Calculating the refined collision model based on the improved DWA algorithm to obtain an optimal driving path; The process of obtaining the optimal driving path includes: First, the speed is sampled by the improved DWA algorithm, and constraints are added to the sampled speed to obtain the constrained speed. Then, the velocity space is traversed within the constrained velocity range to generate a combination of velocity and angular velocity, and a trackable trajectory of the vehicle within a prediction time is generated based on the combination of velocity and angular velocity using a kinematic model of the swing-arm tracked unmanned vehicle; Finally, the trajectory is normalized, and an evaluation value is calculated for the normalized trajectory using an objective function to obtain an optimal driving path; The method for obtaining the constraint velocity comprises: Based on the maximum linear velocity and maximum angular velocity of the swing-arm tracked unmanned vehicle, the speed of the swing-arm tracked unmanned vehicle is constrained within a range; According to the maximum acceleration and angular acceleration of the swing-arm tracked unmanned vehicle, the improved DWA algorithm is used to add maximum acceleration and deceleration constraints to the swing-arm tracked unmanned vehicle; The permissible speed constraint of the swing-arm tracked unmanned vehicle is set through the distance evaluation value of a single planning; A constrained speed is obtained based on the range constraint, the maximum acceleration / deceleration constraint, and the allowable speed constraint.

2. The path planning method for the swing arm tracked unmanned vehicle according to claim 1 is characterized in that: The method for constructing a kinematic model of a swing-arm tracked unmanned vehicle comprises: Construct a global coordinate system and a vehicle coordinate system. The vehicle's forward direction is the positive direction of the x-axis of the vehicle coordinate system, and the origin of the vehicle coordinate system coincides with the center of mass of the swing-arm tracked unmanned vehicle. Based on the global coordinate system, the vehicle body coordinate system and the posture of the swing-arm tracked unmanned vehicle, the relationship between the tracked vehicle's running speed, angular velocity and the speed of the tracks on both sides is calculated; Through the in-situ rotation experiment, the swing-arm tracked unmanned vehicle was calibrated, the equivalent differential theory spacing was obtained, and the kinematic model of the swing-arm tracked unmanned vehicle was established.

3. The path planning method for the swing arm type crawler unmanned vehicle according to claim 1 is characterized in that: The method for obtaining the refined collision model includes: The swing-arm tracked unmanned vehicle model is decomposed into a disk, and the distance between the radius and the center of the disk is calculated. The calculated disk is overlaid on the kinematic model of the swing-arm tracked unmanned vehicle to obtain a refined collision model.

4. The path planning method for the swing arm type crawler unmanned vehicle according to claim 3 is characterized in that: The method for calculating the distance between the radius of the disk and the center of the disk includes: The radius of the disc and the distance between the center of the circle are calculated by the length of the swing-arm tracked unmanned vehicle, the width of the swing-arm tracked unmanned vehicle, the number of longitudinally arranged discs, and the number of transversely arranged discs.

5. The path planning method for the swing arm tracked unmanned vehicle according to claim 1 is characterized in that: The normalization method includes: The distance function, target orientation function, and speed function are used as the numerator, and the evaluation values of all currently planned trajectories are added as the denominator to calculate the ratio of the evaluation value of the specified trajectory to the evaluation value of all trajectories.

6. The path planning method for the swing arm tracked unmanned vehicle according to claim 1 is characterized in that: The formula for calculating the evaluation value is: ； In the formula, heading(v,ω) represents the target heading function, SEPdist(v,ω) represents the distance function, velocity(v,ω) represents the speed function, and β he , β dist , β vel are the weighting coefficients of the three objective function evaluation values.

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