CN116382271A - Swing arm type track unmanned vehicle path planning method - Google Patents
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Abstract
The invention discloses a swing arm type track unmanned vehicle path planning method, which comprises the following steps: acquiring swing arm type crawler unmanned aerial vehicle parameters, and constructing a swing arm type crawler unmanned aerial vehicle kinematic model based on the swing arm type crawler unmanned aerial vehicle parameters; refining the kinematic model to obtain a refined collision model; and calculating the refined collision model based on an improved DWA algorithm to obtain an optimal running path. The method improves the traditional DWA algorithm, improves the trafficability of the swing arm type crawler unmanned vehicle in an indoor scene, and can plan a better running path.
Description
Technical Field
The invention belongs to the technical field of route planning, and particularly relates to a swing arm type track unmanned vehicle path planning method.
Background
The swing arm type track unmanned aerial vehicle is additionally provided with a group of track swing arms on the basis of the traditional track unmanned aerial vehicle, so that the swing arm type track unmanned aerial vehicle not only has the advantages of high mobility and high stability of the common track unmanned aerial vehicle, but also can use the maneuver of the front swing arm to cross obstacles. Therefore, the swing arm type crawler unmanned vehicle not only can stably run in the scene inside the building, but also can climb stairs by utilizing the front swing arm. The purpose of local path planning is to enable an unmanned vehicle to reach a specified local target point without collision. Compared with the global path planning algorithm, the local path planning algorithm is executed more frequently and depends more on real-time environment perception information. In the process of exploring the interior of the unmanned vehicle, the local path planning algorithm needs to output a collision-free path according to the perceived passable area and the obstacle information, and control the movement of the unmanned vehicle in real time to track the path. The narrow and complex indoor space provides higher requirements for local path planning, and the obstacle avoidance function can make it difficult for the unmanned vehicle to enter the narrow space. Therefore, unmanned vehicles are required to have higher trafficability in the scenes facing narrow doors, long and narrow hallways and the like.
Disclosure of Invention
In order to solve the technical problems, the invention provides a swing arm type track unmanned vehicle path planning method for solving the problem of limited reachable area.
In order to achieve the above purpose, the invention provides a swing arm type track unmanned vehicle path planning method, which comprises the following steps:
acquiring swing arm type crawler unmanned aerial vehicle parameters, and constructing a swing arm type crawler unmanned aerial vehicle kinematic model based on the swing arm type crawler unmanned aerial vehicle parameters;
refining the kinematic model to obtain a refined collision model;
and calculating the refined collision model based on an improved DWA algorithm to obtain an optimal running path.
Preferably, the method for constructing the swing arm type crawler unmanned vehicle kinematic model comprises the following steps:
constructing a global coordinate system and a vehicle body coordinate system, wherein the vehicle advancing direction is the positive direction of the x axis of the vehicle body coordinate system, and the origin of the vehicle body coordinate system is coincident with the mass center of the swing arm type crawler unmanned vehicle;
calculating to obtain the relation between the crawler running speed, the angular speed and the crawler speeds on two sides based on the global coordinate system, the vehicle body coordinate system and the swing arm type crawler unmanned vehicle posture;
through an in-situ rotation experiment, the swing arm type crawler unmanned aerial vehicle is calibrated, the equivalent differential theory interval is obtained, and a kinematic model of the swing arm type crawler unmanned aerial vehicle is built.
Preferably, the method for obtaining a refined collision model comprises:
decomposing the swing arm type crawler unmanned aerial vehicle model into a disc, calculating the distance between the radius and the circle center of the disc, and covering the calculated disc on the kinematic model of the swing arm type crawler unmanned aerial vehicle to obtain a refined collision model.
Preferably, the method for calculating the distance between the radius and the center of the circle of the disc comprises the following steps:
the distance between the radius of the disc and the circle center is calculated by the length of the swing arm type track unmanned vehicle, the width of the swing arm type track unmanned vehicle, the number of the longitudinally arranged discs and the number of the transversely arranged discs.
Preferably, the process of obtaining the optimal travel path includes:
firstly, carrying out speed sampling through an improved DWA algorithm, and increasing constraint on the sampling speed to obtain constraint speed;
traversing a speed space in the constraint speed range, generating a combination of speed and angular speed, and generating a track which can be tracked by the vehicle in a prediction time through a swing arm type crawler unmanned vehicle kinematic model based on the combination of speed and angular speed;
and finally, carrying out normalization processing on the track, and carrying out evaluation value calculation on the track subjected to normalization processing through an objective function to obtain an optimal running path.
Preferably, the method for obtaining the constraint speed comprises the following steps:
based on the maximum linear speed and the maximum angular speed of the swing arm type track unmanned aerial vehicle, the range constraint is carried out on the speed of the swing arm type track unmanned aerial vehicle;
adding maximum acceleration and deceleration constraint to the swing arm type track unmanned vehicle through an improved DWA algorithm according to the maximum acceleration and the angular acceleration of the swing arm type track unmanned vehicle;
performing allowable speed constraint of the swing arm type crawler unmanned vehicle through the single planned distance evaluation value;
and obtaining the constraint speed based on the range constraint, the maximum acceleration and deceleration constraint and the allowable speed constraint.
Preferably, the normalization method comprises:
and taking the distance function, the target orientation function and the speed function as molecules, adding the evaluation values of all the tracks planned at present as denominators, and calculating to obtain the proportion of the designated track evaluation value to the whole track evaluation value.
Preferably, the evaluation value is calculated by the formula:
G(v，ω)＝β he ·σ(heading(v，ω))+β dist ·σ(SEP dist(v，ω))+β vel ·σ((velocity(v，ω))；
where head (v, ω) represents the target orientation function, SEPdist (v, ω) represents the distance function, and velocity (v, ω) represents the velocity function, β he ，β dist ，β vel And the weighting coefficients of the three objective function evaluation values are respectively.
Compared with the prior art, the invention has the following advantages and technical effects:
the method comprises the steps of firstly analyzing a plane kinematics model of the swing arm type crawler unmanned aerial vehicle and optimizing a collision model of the unmanned aerial vehicle. And then, according to the optimized collision model of the unmanned vehicle, the traditional DWA algorithm is improved, the trafficability of the swing arm type crawler unmanned vehicle in an indoor scene is improved, and a better running path can be planned.
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The accompanying drawings, which are included to provide a further understanding of the application, illustrate and explain the application and are not to be construed as limiting the application. In the drawings:
FIG. 1 is a flow chart of a method for planning a path of a swing arm type crawler unmanned vehicle according to an embodiment of the invention;
fig. 2 is a kinematic model coordinate diagram of a swing arm type crawler unmanned vehicle according to an embodiment of the present invention;
FIG. 3 is a diagram of a refined collision model of a swing arm type crawler unmanned vehicle according to an embodiment of the invention;
FIG. 4 is a graph of the calculation of the distance evaluation value of the DWA algorithm according to an embodiment of the present invention;
FIG. 5 is a graph of the distance evaluation calculation of an improved DWA algorithm according to an embodiment of the present invention;
FIG. 6 is a schematic diagram of a trackable trace according to an embodiment of the invention;
FIG. 7 is a schematic diagram of a planning result according to an embodiment of the present invention;
FIG. 8 is a partial path test comparison chart of an embodiment of the present invention;
fig. 9 is a comparison of a narrow gate pass through according to an embodiment of the present invention.
Detailed Description
It should be noted that, in the case of no conflict, the embodiments and features in the embodiments may be combined with each other. The present application will be described in detail below with reference to the accompanying drawings in conjunction with embodiments.
It should be noted that the steps illustrated in the flowcharts of the figures may be performed in a computer system such as a set of computer executable instructions, and that although a logical order is illustrated in the flowcharts, in some cases the steps illustrated or described may be performed in an order other than that illustrated herein.
Example 1
The invention discloses a swing arm type track unmanned vehicle path planning method as shown in fig. 1, which comprises the following steps:
acquiring swing arm type crawler unmanned aerial vehicle parameters, and constructing a swing arm type crawler unmanned aerial vehicle kinematic model based on the swing arm type crawler unmanned aerial vehicle parameters;
refining the kinematic model to obtain a refined collision model;
and calculating the refined collision model based on an improved DWA algorithm to obtain an optimal running path.
Further optimizing scheme, the process of constructing the swing arm type crawler unmanned vehicle kinematic model is as follows:
when the swing arm movement is not involved, the swing arm type crawler unmanned vehicle is the same as the common crawler vehicle in the kinematic model. Therefore, the embodiment firstly builds a kinematic model of the ordinary tracked vehicle moving in the plane. It is now assumed that the crawler is rigid and that the crawler does not slide with the ground while in motion.
The global coordinate system is Oxy as shown in fig. 2; the coordinate system of the vehicle body is O' x b y b The forward direction of the vehicle is the positive x-axis direction of the vehicle body system, C b The origin O' of the vehicle body coordinate system and the vehicle centroid C are the centroids of the vehicles b And (5) overlapping. Vehicle forward speed v c ，C i The instantaneous center of the rotational movement of the tracked vehicle is the rotational angular velocity omega of the vehicle c . The coordinates of the crawler in the global coordinate system are represented by (x c ,y c ) Representing the included angle phi between the positive direction of the X axis of the crawler system and the positive direction of the X axis of the global system c And (3) representing. The kinematic model of the crawler can be obtained by the method that:
the output speed of the left caterpillar band is v l The output of the right caterpillar is v r . When v 1 ＝v r The tracked vehicle is in a motion state of linear motion along the x-axis direction of the vehicle body system. When v 1 ＝-v r Instant center C of rotary motion of crawler i Coinciding with the origin O 'of the vehicle body coordinate system, the tracked vehicle motion state appears to rotate about O', i.e. in-situ. Of course v l >v r Or v l <v r The movement of the crawler is then shown as about instant C i And (5) rotating. Width of vehicle body W b The width of the single-side crawler belt is W cb Let the crawler radius of rotation be R, and the crawler be the rigid body can obtain the angular velocity of automobile body everywhere equal, therefore have the equation:
the radius of rotation R of the crawler is obtained simultaneously:
wherein (W) b -W cb ) Is equivalent to the differential wheel spacing L diff And further deduce the running speed v of the crawler c The relationship between the angular velocity and the crawler belt velocities at the left side and the right side is as follows:
therefore, the motion state of the tracked vehicle is calculated by the speed output of the left and right tracks, and the tracked vehicle can be controlled by controlling the speed of the tracks. When the swing arm type crawler unmanned vehicle runs on the flat ground, the swing arms are clung to the two sides of the vehicle, and at the moment, L is the same diff The structural parameters of the unmanned swing arm type unmanned aerial vehicle cannot be directly calculated and obtained through direct calculation, and the swing arm type unmanned aerial vehicle is required to be calibrated through multiple in-situ rotation experiments to obtain the equivalent differential theory interval L diff And establishing a kinematic model of the swing arm type crawler unmanned vehicle.
According to a further optimization scheme, as shown in fig. 3, a swing arm type crawler unmanned aerial vehicle model is decomposed into discs, the distance between the radius and the circle center of the discs is calculated, the calculated discs are covered on a kinematic model of the swing arm type crawler unmanned aerial vehicle, a refined collision model is obtained, and the calculation method of the circle center distance and the radius of the discs is as follows:
longitudinally arranging n circles, transversely arranging m circles, and the radius of the circles:
distance d between circle centers of longitudinal arrangement and transverse arrangement l And d w The calculation method of (2) is as follows:
the comparison of the model refinement effect using different numbers of circles is shown in table 1.
TABLE 1
Compared with a simplified model method using only one circle to cover the rectangle, the unmanned vehicle model using 2 circles, 3 circles and 8 circles to cover the rectangle reduces the width of the vehicle by 23.2%,33.1% and 41.1% respectively. It is theoretically known that the greater the number of circles covering the vehicle body, the lower the vehicle body width.
Further optimizing scheme, the calculation process for calculating the refined collision model based on the improved DWA algorithm is as follows:
the DWA algorithm performs velocity sampling in a velocity space (V, ω) consisting of velocity and angular velocity, the sampled velocity being in vector V i ＝(v i ,ω i ) Is then added to the constraint for the speed of sampling.
Maximum linear velocity of vehicle motion v max Maximum angular velocity is ω max The range constraint of vehicle speed is V s ：
V s ＝{v∈[0，v max ]，ω∈[-ω max ，ω max ]}
According to the maximum acceleration and the angular acceleration of the vehicle, the algorithm can add the maximum acceleration and deceleration constraint V to the vehicle d ：
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]}
Wherein Δt is the two sampling time interval, a max And alpha max The maximum acceleration and the angular acceleration of the vehicle, respectively. Due to maximum acceleration and deceleration constraint V d The shape in the velocity space is a rectangle, resembling a window, thus V d Also known as a sliding window, the sliding window method is called a name. The actual speed Vactual of the vehicle is the center of the sliding window.
In order to ensure the running safety of the vehicle, the algorithm adds an allowable speed constraint V to the vehicle according to the obstacle information in the environment, the maximum acceleration and the maximum angular acceleration of the vehicle a ：
Where dist (v, ω) is a distance evaluation value of the track, representing the closest distance to the corresponding track and the obstacle.
Assuming that the algorithm plans q tracks at a time, the calculation method of the distance evaluation value of the ith track is shown in fig. 4.
Wherein,,
dist(v i ，ωi)＝arg min||obs(x，y)-T i (x，y)||
wherein ob (x, y) is a discretized storage list of perceived obstacles in the unmanned vehicle environment, T i (x, y) track T i Each position of (3)Is a discretized stored list of (2), the distance evaluation value is:
dist(v，ω)＝arg max{dist(v i ，ω i )|1≤i≤q}
under the combined action of three constraints, the practically reachable speed range V of the vehicle can be obtained r ：
V r ＝V s ∩V d ∩V a
When the rectangular unmanned vehicle is covered by a plurality of circles, n circles are longitudinally distributed, m circles are transversely distributed, and the coordinates of the centers of the longitudinal jth and transverse kth circles in the vehicle system are (x) j,k ,y j,k ) From rigid body kinematics, the center locus of each circle in the locus can be calculated, and since the circles have rotational invariance, the center locus can be represented by only (x, y) in the global coordinate system:
the evaluation value is calculated for each circle center track, and the calculation method of the distance evaluation value of the single track is shown in fig. 5.
Wherein,,
SEPdist(v i ，ω i )＝arg min{||obs(x，y)-T i (x j，k ，y j，k )||1≤j≤n，1≤k≤m}
if q tracks are planned for a single time, the distance evaluation value of the single time planning is as follows:
SEPdist(v，ω)＝argmax{SEPdist(v i ，ω i )|1≤i≤q}
allowable speed constraint V of vehicle a ' is:
restraint speed V r ' is:
V r ′＝V s ∩V d ∩V a ′
at aboutBeam velocity V r In the' range, the whole speed space is discretized and traversed at a certain speed and angular speed resolution, a plurality of groups of combinations of speed and angular speed are generated, and then tracks which can be tracked by the vehicle in a certain prediction time are generated one by one through a vehicle kinematic model according to the combinations of the speed and the angular speed:
x c，t+1 ＝x c，t +v c，t ·cosθ c，t ·Δt
y c，t+1 ＝y c，t +v c，t ·sinθ c，t ·Δt
ψ c，t+1 ＝ψ c，t +ω c，t ·Δt
wherein x is c，t+1 ，y c，t+1 ，ψ c，t+1 Representing the pose of the vehicle under a global coordinate system at the time t+ 1, x c，t ，y c，t ，ψ c，t Representing the pose of the vehicle under a global coordinate system at the moment t, v c，t+1 ，ω c，t+1 The speed and the angular speed v of the vehicle at the time t+ 1 c，t ，ω c，t The coordinates of the vehicle at the current moment are known for the speed and angular speed of the vehicle at the moment t, and the pose at any moment in the track can be calculated through integration. The predicted current time can trace the track as shown in fig. 6.
Then the algorithm enters an optimization stage, and an objective function G (v, omega) is introduced to calculate the evaluation value of each track.
G(v，ω)＝β he ·σ(heading(v，ω))+β dist ·σ(SEP dist(v，ω))+β vel ·σ((velocity(v，ω))
Wherein,,
heading(v，ω)＝π-ψ p
the target orientation function head (v, omega) is used for measuring whether the gesture of the unmanned vehicle is consistent with the target direction, and the larger the function value is, the closer the unmanned vehicle running direction is to the target point direction, and the phi is p To predict the attitude angle of the end-of-track vehicle. SEPdist (v, omega) measures the distance between the operation track of the unmanned vehicle and the obstacle, and the larger the function value is, the safer the unmanned vehicle is operated. The velocity function velocity (v, ω) is the vehicle in the trackThe larger the function value is, the faster the unmanned vehicle is, and the faster the target point can be obtained. And the track with the highest evaluation value can be obtained in a summary manner, and is the optimal track calculated by the current algorithm. Beta in he ，β dist ，β vel The weighting coefficients of the three objective function evaluation values can be respectively adjusted according to the sizes of the different application scenes, so that different motion states of the unmanned aerial vehicle can be realized. In the formula, sigma is a smooth function, because the unit and the magnitude of each objective function value are different, when the overall evaluation value is calculated, normalization processing is needed to be carried out on each track objective function, and the aim of preventing the influence of a single objective function on the overall evaluation value is achieved. If the evaluation value of the ith track needs to be calculated, the normalization method is as follows:
and n is the number of all tracks planned at the moment, and the normalization principle is to add the evaluation values of all tracks planned at present as denominators, and calculate the proportion of the designated track evaluation value to the total track evaluation value.
The planning result is shown in fig. 7. The final objective function G (v, ω) takes the trajectory with the highest evaluation value as the optimal travel path.
Example two
Firstly, the shape of the unmanned vehicle is rectangular, the length is 1m, the width is 0.6m, and the length-width ratio is 5:3.
And establishing a collision model of the unmanned vehicle, and respectively establishing the collision model of the unmanned vehicle in a mode of an original disc and three refined discs. The centers of the three discs of the refinement model are respectively positioned at (0.33,0), (0, 0), (0, -0.33) in the vehicle body coordinate system, and the radius r=0.78 m of the circle. Each grid in the figure is a square with a side length of 1 m.
Firstly, testing the trafficability of a local path, wherein important parameters are as follows:
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 beta he :10.0, obstacle distance rating coefficient beta dist :5.0, speed evaluation coefficient beta vel ：5.0。
The method comprises the steps that barriers are arranged in a scene, the barriers on two sides form a gradually narrowed channel, the advancing distance of the unmanned aerial vehicle in the narrowed channel is used as the trafficability of the unmanned aerial vehicle, each time the unmanned aerial vehicle advances in the channel for 2m, and the channel is narrowed by 0.2m. And setting a local target point in front of the vehicle, so that the unmanned vehicle continuously advances on the premise of meeting the obstacle avoidance requirement until the algorithm output speed is 0.
Then simulating corridor and narrow door scenes, and testing the traffic capacity of the unmanned vehicle in the building. The corridor width was set to 2m and the narrow gate width was set to 1.4m. The drone is moved in the corridor and then through a narrow door on one side of the corridor.
As can be seen from fig. 8, the maximum of the drone using the original DWA algorithm can pass through only a 1.8m wide channel, while the narrowest of the drone applying the modified DWA algorithm can pass through a 1.2m channel. It can be concluded that the improved algorithm has a greater improvement in the trafficability of the unmanned vehicle. Fig. 9 shows the trafficability of DWA algorithms before and after modification in the building interior scene, both the algorithms before and after modification can make the unmanned vehicle move in the corridor, but the unmanned vehicle cannot pass through the narrow gate in the corridor due to the limitation of the obstacle avoidance function. The unmanned vehicle applying the improved DWA algorithm can pass through the narrow door, and the vehicle body does not collide with the obstacle, so that the improved DWA algorithm is reflected to have excellent trafficability in the internal scene of the building.
In conclusion, the DWA algorithm improved by the refined collision model can enable the unmanned vehicle to have higher trafficability and obtain a better driving path.
The foregoing is merely a preferred embodiment of the present application, but the scope of the present application is not limited thereto, and any changes or substitutions easily conceivable by those skilled in the art within the technical scope of the present application should be covered in the scope of the present application. Therefore, the protection scope of the present application shall be subject to the protection scope of the claims.
Claims (8)
1. The swing arm type track unmanned vehicle path planning method is characterized by comprising the following steps of:
acquiring swing arm type crawler unmanned aerial vehicle parameters, and constructing a swing arm type crawler unmanned aerial vehicle kinematic model based on the swing arm type crawler unmanned aerial vehicle parameters;
refining the kinematic model to obtain a refined collision model;
and calculating the refined collision model based on an improved DWA algorithm to obtain an optimal running path.
2. The swing arm type tracked unmanned aerial vehicle path planning method based on claim 1, wherein the method for constructing the swing arm type tracked unmanned aerial vehicle kinematic model comprises the following steps:
constructing a global coordinate system and a vehicle body coordinate system, wherein the vehicle advancing direction is the positive direction of the x axis of the vehicle body coordinate system, and the origin of the vehicle body coordinate system is coincident with the mass center of the swing arm type crawler unmanned vehicle;
calculating to obtain the relation between the crawler running speed, the angular speed and the crawler speeds on two sides based on the global coordinate system, the vehicle body coordinate system and the swing arm type crawler unmanned vehicle posture;
through an in-situ rotation experiment, the swing arm type crawler unmanned aerial vehicle is calibrated, the equivalent differential theory interval is obtained, and a kinematic model of the swing arm type crawler unmanned aerial vehicle is built.
3. The swing arm type crawler unmanned aerial vehicle path planning method according to claim 1, wherein the method for obtaining the refined collision model comprises the following steps:
decomposing the swing arm type crawler unmanned aerial vehicle model into a disc, calculating the distance between the radius and the circle center of the disc, and covering the calculated disc on the kinematic model of the swing arm type crawler unmanned aerial vehicle to obtain a refined collision model.
4. A method for planning a path of a swing arm type crawler unmanned aerial vehicle according to claim 3, wherein the method for calculating the distance between the radius and the center of the circle of the disc comprises the following steps:
the distance between the radius of the disc and the circle center is calculated by the length of the swing arm type track unmanned vehicle, the width of the swing arm type track unmanned vehicle, the number of the longitudinally arranged discs and the number of the transversely arranged discs.
5. The swing arm type tracked unmanned vehicle path planning method according to claim 1, wherein the process of obtaining the optimal driving path comprises the following steps:
firstly, carrying out speed sampling through an improved DWA algorithm, and increasing constraint on the sampling speed to obtain constraint speed;
traversing a speed space in the constraint speed range, generating a combination of speed and angular speed, and generating a track which can be tracked by the vehicle in a prediction time through a swing arm type crawler unmanned vehicle kinematic model based on the combination of speed and angular speed;
and finally, carrying out normalization processing on the track, and carrying out evaluation value calculation on the track subjected to normalization processing through an objective function to obtain an optimal running path.
6. The swing arm type track unmanned vehicle path planning method according to claim 5, wherein the method for obtaining the constraint speed comprises the following steps:
based on the maximum linear speed and the maximum angular speed of the swing arm type track unmanned aerial vehicle, the range constraint is carried out on the speed of the swing arm type track unmanned aerial vehicle;
adding maximum acceleration and deceleration constraint to the swing arm type track unmanned vehicle through an improved DWA algorithm according to the maximum acceleration and the angular acceleration of the swing arm type track unmanned vehicle;
performing allowable speed constraint of the swing arm type crawler unmanned vehicle through the single planned distance evaluation value;
and obtaining the constraint speed based on the range constraint, the maximum acceleration and deceleration constraint and the allowable speed constraint.
7. The swing arm type tracked unmanned vehicle path planning method according to claim 5, wherein the normalization processing method comprises the following steps:
and taking the distance function, the target orientation function and the speed function as molecules, adding the evaluation values of all the tracks planned at present as denominators, and calculating to obtain the proportion of the designated track evaluation value to the whole track evaluation value.
8. The swing arm type tracked unmanned vehicle path planning method according to claim 5, wherein the evaluation value calculation formula is:
G(v，ω)＝β he ·σ(heading(v，ω))+β dist ·σ(SEPdist(v，ω))+β vel ·σ((velocity(v，ω))；
where head (v, ω) represents the target orientation function, SEPdist (v, ω) represents the distance function, and velocity (v, ω) represents the velocity function, β he ，β dist ，β vel And the weighting coefficients of the three objective function evaluation values are respectively.
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| CN117002479A (en) * | 2023-09-18 | 2023-11-07 | 上海联适导航技术股份有限公司 | Track following method of tracked vehicle based on yaw rate |
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2023
- 2023-03-16 CN CN202310253642.1A patent/CN116382271A/en active Pending
Cited By (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN117002479A (en) * | 2023-09-18 | 2023-11-07 | 上海联适导航技术股份有限公司 | Track following method of tracked vehicle based on yaw rate |
| CN117002479B (en) * | 2023-09-18 | 2024-04-26 | 上海联适导航技术股份有限公司 | Track following method of tracked vehicle based on yaw rate |
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