A laser scanning track planning method for obtaining uniform laser cleaning effect

Abstract

This invention proposes a laser scanning trajectory planning method for achieving uniform laser cleaning results. By acquiring the boundary contour of the workpiece surface to be cleaned, the stopping points of the robotic arm are determined. An optimized ant colony algorithm is used to plan the global motion path of the robotic arm traversing all stopping points. Then, for each stopping point, the geometric parameters of the concentric circle scanning trajectory executed by the galvanometer are determined. The robotic arm is then controlled to move sequentially to each stopping point, and the concentric circle scanning action is performed by the galvanometer. During the concentric circle scanning process at each stopping point, after completing one concentric circle scan, the starting point of the next concentric circle is controlled to deflect around the center by a preset angle. This invention organically combines global path optimization of the robotic arm with local scanning path optimization of the galvanometer. Macroscopically, it optimizes the movement sequence of the robotic arm and reduces ineffective movement time; microscopically, by dynamically changing the starting point of the concentric circles, it breaks the periodicity of energy distribution, thereby improving cleaning efficiency and surface uniformity.

Description

Technical Field

[0001] This invention relates to the field of laser cleaning technology, and in particular to a laser scanning trajectory planning method for achieving uniform laser cleaning effect. Background Technology

[0002] Laser cleaning technology, as a highly efficient and precise surface treatment method, relies heavily on the planning of the laser scanning trajectory for its cleaning effectiveness. In automated cleaning scenarios, robotic arms carrying laser scanning galvanometers are commonly used. However, existing trajectory planning methods have significant limitations when applied to this platform. Traditional straight-line or "bow"-shaped scanning trajectories are lengthy and involve frequent turns, which not only reduces cleaning efficiency but also makes it difficult to adapt to the contours of complex workpieces, leading to frequent overtravel of the robotic arm's movement path or missed areas during cleaning.

[0003] To address the uniformity issue, existing technologies employ concentric circle scanning patterns, which possess the potential for isotropic energy distribution. However, traditional concentric circle scanning trajectories have an inherent drawback: the starting point of each circle remains fixed. When performing repeated scans to improve cleanliness, the fixed starting point causes the laser energy to periodically overlap in the initial region of the path, easily leading to overheating or even ablation of the material in that area, thus failing to meet high standards of non-destructive cleaning.

[0004] Therefore, there is an urgent need for a laser cleaning trajectory control method that can optimize the global path and adaptively adjust local scanning parameters and paths according to the site location. Summary of the Invention

[0005] This invention proposes a laser scanning trajectory planning method to achieve uniform laser cleaning effect, which solves the problems of low cleaning efficiency, difficulty in adapting to the contour boundaries of complex workpieces, and difficulty in meeting high-standard non-destructive cleaning requirements in existing laser cleaning trajectory control methods.

[0006] The technical solution of this invention is implemented as follows:

[0007] The first aspect of this invention provides a laser scanning trajectory planning method for obtaining a uniform laser cleaning effect, comprising the following steps:

[0008] S1, Obtain the boundary contour of the workpiece surface to be cleaned, and determine a series of robot arm stopping points based on the boundary contour;

[0009] S2, based on multiple pause points, uses an optimized ant colony algorithm to plan the global motion path of the robot arm to traverse all pause points;

[0010] S3, for each pause point, determine the geometric parameters of the concentric circle scanning trajectory performed by the galvanometer;

[0011] S4, control the robotic arm to move sequentially to each stopping point, and control the galvanometer to perform concentric circle scanning at each stopping point until the scanning task of all stopping points is completed; during the concentric circle scanning at each stopping point, after each concentric circle scan is completed, control the starting point of the next concentric circle to deflect around the center by a preset angle. .

[0012] Specifically, in step S1, the method for determining a series of robot arm stopping points based on the boundary contour includes the following steps:

[0013] S1.1, Set a safety margin inside the workpiece boundary to define the robot's motion boundary;

[0014] S1.2, the motion boundary is discretized into a uniform grid using a grid method, with a grid side length of... The calculation formula is:

[0015] ;

[0016] in, This is the maximum effective scanning radius of the galvanometer; k This is the overlap rate coefficient, with a value ranging from 0.7 to 0.9;

[0017] S1.3, define all grids whose center points are located within the motion boundary as valid grids, and set the center point of the valid grid as the initial stopping point of the robot arm.

[0018] Furthermore, step S1 also includes:

[0019] S1.4, Identify the grids that intersect with the original boundary of the workpiece in the effective grid as boundary grids;

[0020] S1.5, generate an auxiliary stopping point for each of the boundary grids to replace the original initial stopping point of the robot arm, and the coordinates of the auxiliary stopping point are... Calculated using the following formula:

[0021] ;

[0022] in, The center coordinates of the boundary grid. The shortest distance from the center of the boundary mesh to the original boundary of the workpiece. This is the unit direction vector pointing from the center of the boundary grid to the nearest boundary point.

[0023] Specifically, in step S2, the method of planning the global movement path using the optimized ant colony algorithm includes the following steps:

[0024] S2.1, Initialization: Abstract each robot arm's stopping point into a path node, and initialize the pheromone concentration on the path segments between each node;

[0025] S2.2, Parallel Path Search: In each iteration, multiple virtual ants are dispatched from random nodes to select the next unvisited node according to the state transition probability formula, in order to construct a complete site visit path; the state transition probability formula is as follows:

[0026] ;

[0027] ;

[0028] in, It's an ant. k exist t From the node i Transfer to node j The probability of; yes t Time Side The concentration of pheromones on the surface; It is a heuristic message used to guide ants to prioritize stopping points that are closer and have smaller deflection angles; The pheromone heuristic factor indicates the importance of pheromones; The expected heuristic factor represents the importance of the heuristic information; It's an ant. k The set of currently accessible nodes; It is a node i and j The Euclidean distance between them; It is the angle that the robotic arm needs to turn from the previous path segment to the current path segment; and These are the weighting coefficients of the distance factor and the smoothness factor, respectively. A constant greater than 0;

[0029] S2.3, Pheromone Update: After all ants have completed path construction, the global pheromone level is updated according to the following formula:

[0030] ;

[0031] ;

[0032] in, It is a pheromone volatile factor; For ants k In this iteration, on the edge The amount of pheromones left on it; m The total number of ants; It is the pheromone intensity constant; It's an ant. k The total length of the constructed path; It's an ant. k Construct the sum of all steering angles along the path;

[0033] S2.4, Optimal Path Output: Iteratively execute steps S2.2 and S2.3. When the maximum number of iterations is reached or the quality of the solution is stable, output the optimal path as the global motion path of the robot.

[0034] Specifically, in step S3, determining the geometric parameters of the concentric circle scanning trajectory includes:

[0035] radius of the inner circle of concentric circles r Must meet: ;

[0036] in, V The linear velocity of the galvanometer scanning is... This is the highest scanning frequency of the galvanometer;

[0037] outer radius of concentric circles R Must meet: ;

[0038] in, The maximum effective scanning radius of the galvanometer. This represents the shortest distance from the current stopping point of the robot arm to the workpiece boundary.

[0039] Number of concentric circle scans N for: , ;

[0040] in, d The spacing between adjacent concentric circles. D The diameter of the light spot; This is the floor function.

[0041] Specifically, in step S4, the preset angle The calculation formula is:

[0042] ;

[0043] in, N This represents the number of concentric circle scans.

[0044] Furthermore, in step S4, the laser is turned off during the process of the galvanometer jumping from the end point of one concentric circle to the beginning point of the next concentric circle, and during the process of the robot moving between different stopping points; the laser is turned on again after the galvanometer or robot is stably positioned.

[0045] Furthermore, in step S4, after completing all concentric circle scans at a pause point, if multiple scans are preset, the entire galvanometer scanning field is controlled to deflect around the center by a preset angle. γ , γ The value ranges from 5° to 10°, and then the next scan is performed at that site.

[0046] A second aspect of the present invention provides an electronic device, including a memory and a processor, wherein the memory stores a computer program executable on the processor, and the processor executes the computer program to implement the steps of the trajectory control method.

[0047] A third aspect of the present invention provides a computer-readable storage medium storing a computer program that, when executed by a processor, implements the steps of the trajectory control method.

[0048] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0049] (1) This invention organically combines pause site planning, global path optimization, local parameter calculation and collaborative scanning execution, which macroscopically optimizes the movement sequence of the robot and reduces the invalid movement time; microscopically, by dynamically changing the starting point of the concentric circle, the periodicity of energy distribution is broken, thereby achieving a synergistic improvement in cleaning efficiency and surface uniformity as a whole.

[0050] (2) This invention, through a grid method combined with an adaptive boundary expansion mechanism, not only generates efficient initial stopping points for regular areas, but also intelligently identifies boundary areas and generates auxiliary points. This strategy ensures that the laser scanning range closely fits the original contour of the workpiece, effectively eliminates the cleaning blind spots in the edge areas, and significantly improves the method's adaptability and coverage integrity for workpieces with complex shapes.

[0051] (3) The improved ant colony algorithm used in this invention optimizes both path length and motion smoothness. The planned global motion path of the robot is not only shorter in total distance but also has smoother turns. This directly reduces the overall running time of the robot and the vibration caused by frequent acceleration and deceleration during the motion, thus improving the stability and efficiency of the system.

[0052] (4) By introducing dynamic deflection of the starting point within the concentric circle and an overall deflection mechanism of the scanning field, this invention enables the laser action points of multiple scans to be statistically evenly distributed throughout the processing area. This design effectively breaks down the fixed starting and ending points, avoiding local energy accumulation, and is the core of achieving high uniformity and non-destructive cleaning effect. Attached Figure Description

[0053] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0054] Figure 1 This is a flowchart illustrating a laser scanning trajectory planning method for achieving uniform laser cleaning effects according to the present invention.

[0055] Figure 2 This is a schematic diagram of the process for determining a series of robot stopping points based on the workpiece boundary contour in an embodiment of the present invention.

[0056] Figure 3 This is a schematic diagram illustrating the process of planning a global motion path using an optimized ant colony algorithm in an embodiment of the present invention.

[0057] Figure 4 This is a schematic diagram of the trajectory of multiple concentric circle scans performed at the same pause point in an embodiment of the present invention. Detailed Implementation

[0058] The technical solution of the present invention will be clearly and completely described below with reference to the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative effort are within the scope of protection of the present invention.

[0059] Reference Figures 1 to 4 The first aspect of this invention provides a laser scanning trajectory planning method for obtaining a uniform laser cleaning effect, comprising the following steps:

[0060] S1, obtain the boundary contour of the workpiece surface to be cleaned (by scanning the workpiece with a high-precision 3D vision sensor integrated on the robot arm, or by directly importing the CAD model of the workpiece), and determine a series of robot arm stopping points based on the boundary contour.

[0061] Specifically, such as Figure 2 As shown, the method for determining a series of robot arm stopping points based on boundary contours includes the following steps:

[0062] S1.1, Set a safety margin inside the workpiece boundary to define the robot's movement boundary; The setting of the safety margin needs to take into account the robot's positioning error, vibration and the physical boundary of the galvanometer scanning field, and is usually set to 10-20mm to ensure that the robot's movement and galvanometer scanning process are absolutely safe and will not collide with the workpiece or fixture.

[0063] S1.2, the motion boundary is discretized into a uniform grid using a grid method, with a grid side length of... The calculation formula is:

[0064] ;

[0065] in, This is the maximum effective scanning radius of the galvanometer; k This is the overlap coefficient, with a value ranging from 0.7 to 0.9; this coefficient ensures the necessary overlap between adjacent galvanometer scanning areas, thereby avoiding areas missed during scanning.

[0066] S1.3, define all grids whose center points are located within the motion boundary as valid grids, and set the center point of the valid grid as the initial stopping point of the robot arm.

[0067] S1.4, Identify the grids that intersect with the original boundary of the workpiece in the effective grid as boundary grids; this step aims to accurately identify those grids located at the edge of the complete scan area that may not be completely covered by the standard circular scan.

[0068] S1.5, generate an auxiliary stopping point for each of the boundary grids to replace the original initial stopping point of the robot arm, and the coordinates of the auxiliary stopping point are... Calculated using the following formula:

[0069] ;

[0070] in, The center coordinates of the boundary grid. The shortest distance from the center of the boundary mesh to the original boundary of the workpiece. This is the unit direction vector pointing from the center of the boundary grid to the nearest boundary point. By introducing auxiliary pause points, the scanning range of the galvanometer can more accurately approximate the original boundary of the workpiece, effectively eliminating cleaning blind spots in the edge region.

[0071] S2, based on multiple pause points, uses an optimized ant colony algorithm to plan the global motion path of the robot arm to traverse all pause points;

[0072] Specifically, such as Figure 3 As shown, the method for planning the global movement path using the optimized ant colony algorithm includes the following steps:

[0073] S2.1, Initialization: Abstract each robot arm's stopping point into a path node, and initialize the pheromone concentration on the path segment between each node to a non-zero constant (e.g., 0.1).

[0074] S2.2, Parallel Path Search: In each iteration, multiple virtual ants (typically 0.5 to 1 times the number of nodes) are dispatched from random nodes to select the next unvisited node according to the state transition probability formula, in order to construct a complete site visit path; the state transition probability formula is as follows:

[0075] ;

[0076] ;

[0077] in, It's an ant. k exist t From the node i Transfer to node j The probability of; yes t Time Side The concentration of pheromones on the surface; It is a heuristic message used to guide ants to prioritize stopping points that are closer and have smaller deflection angles; This is a pheromone heuristic factor, typically taking values ​​in the range [1, 2], representing the importance of the pheromone; The expected heuristic factor typically takes values ​​in the range [2, 5], representing the importance of the heuristic information; It's an ant. k The set of currently accessible nodes; It is a node i and j The Euclidean distance between them; It is the angle that the robotic arm needs to turn from the previous path segment to the current path segment; and These are the weighting coefficients for the distance factor and the smoothness factor, respectively. Their specific values ​​can be adjusted based on the actual emphasis placed on path length or motion stability. , ; A constant greater than 0 (e.g., 1e) -5 (), used to prevent the denominator from being zero.

[0078] S2.3, Pheromone Update: After all ants have completed path construction, the global pheromone level is updated according to the following formula:

[0079] ;

[0080] ;

[0081] in, It is the pheromone evaporation factor, which typically takes values ​​in the range of [0.1, 0.5]. For ants k In this iteration, on the edge The amount of pheromones left on it; m The total number of ants; It is the pheromone intensity constant, which can be set according to the path size; It's an ant. k The total length of the constructed path; It's an ant. k The sum of all turning angles along the path is constructed; this update rule takes into account both path length and smoothness, guiding the algorithm to find a superior path with a shorter total distance and smoother turns.

[0082] S2.4, Optimal Path Output: Iteratively execute steps S2.2 and S2.3. When the maximum number of iterations is reached (e.g., 100-500 times) or the optimal solution no longer improves after several consecutive generations, output the comprehensive evaluation of the optimal path (i.e., the best path). The path with the smallest value is used as the global motion path of the robot.

[0083] S3, for each pause point, determine the geometric parameters of the concentric circle scanning trajectory performed by the galvanometer;

[0084] Before determining the geometric parameters, core laser process parameters need to be set and verified to ensure cleaning effectiveness and control thermal effects. For example, through preliminary process experiments, a set of effective parameters suitable for the current workpiece material and coating can be determined: laser power... P Set to 240W, repetition frequency f Set to 50kHz, pulse width The setting is 80ns. Based on this, the energy of a single pulse... This energy value is controlled near a safe and effective cleaning threshold. Simultaneously, the diameter of the focused laser spot needs to be measured. D These are the basic geometric parameters.

[0085] Specifically, in step S3, determining the geometric parameters of the concentric circle scanning trajectory includes:

[0086] radius of the inner circle of concentric circles r Must meet: ;

[0087] in, V The linear velocity of the galvanometer scanning needs to be matched with the laser parameters. For example, it can be set in the range of 1000 mm / s to 2000 mm / s according to the cleaning threshold and efficiency requirements. This is the maximum scanning frequency of the galvanometer, and this limitation ensures that the galvanometer can still keep up with the trajectory command when scanning the smallest circle.

[0088] outer radius of concentric circles R Must meet: ;

[0089] in, The maximum effective scanning radius of the galvanometer. This is the shortest distance from the current robot arm's stopping point to the workpiece boundary, avoiding the galvanometer scanning outside the workpiece boundary and ensuring the safety of the scanning process.

[0090] Number of concentric circle scans N for: , ;

[0091] in, d The spacing between adjacent concentric circles. D The diameter of the light spot; This is the floor function.

[0092] S4, control the robotic arm to move sequentially to each stopping point, and control the galvanometer to perform concentric circle scanning at each stopping point until the scanning task of all stopping points is completed; during the concentric circle scanning at each stopping point, after each concentric circle scan is completed, control the starting point of the next concentric circle to deflect around the center by a preset angle. .

[0093] Specifically, in step S4, the preset angle The calculation formula is:

[0094] ;

[0095] in, N The number of concentric circle scans; by sequentially deflecting the starting point of each concentric circle, the periodic energy superposition that may be caused by a fixed trajectory starting point can be broken up, significantly improving the uniformity of cleaning.

[0096] Furthermore, in step S4, the laser is turned off during the process of the galvanometer jumping from the end point of one concentric circle to the beginning point of the next, and during the process of the robot moving between different stopping points; the laser is then turned back on after the galvanometer or robot has been stably positioned. This interlocking control mechanism effectively avoids accidental laser emission in non-processing positions, preventing damage to the workpiece or equipment.

[0097] Furthermore, in step S4, after completing all concentric circle scans at a pause point, if multiple scans are preset, the entire galvanometer scanning field is controlled to deflect around the center by a preset small angle. γ , γThe value ranges from 5° to 10°, and then the next scan is performed at that point. Combined with the deflection of the starting point of each circle, this overall deflection mechanism of the scanning field further enables a more statistically uniform distribution of laser energy across multiple scans, which is key to achieving highly uniform and non-destructive cleaning results. In this embodiment, to achieve higher cleanliness requirements, four concentric circle scans are set at each stopping point, with the scanning trajectory as shown... Figure 4 As shown, the black concentric circles represent the scanning path when the laser is on, and the blue broken line represents the deflection path of the starting point of the concentric circles when the laser is off; from Figure 4 As can be seen, for the same pause point, after each complete concentric circle scan, the starting point of the entire concentric circle will deflect around the center by a small angle.

[0098] A second aspect of the present invention provides an electronic device, including a memory and a processor, wherein the memory stores a computer program executable on the processor, and the processor executes the computer program to implement the steps of the trajectory control method.

[0099] A third aspect of the present invention provides a computer-readable storage medium storing a computer program that, when executed by a processor, implements the steps of the trajectory control method.

[0100] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A laser scanning trajectory planning method for achieving uniform laser cleaning effect, characterized in that, Includes the following steps: S1, Obtain the boundary contour of the workpiece surface to be cleaned, and determine a series of robot arm stopping points based on the boundary contour; S2, based on multiple pause points, uses an optimized ant colony algorithm to plan the global motion path of the robot arm to traverse all pause points; S3, for each pause point, determine the geometric parameters of the concentric circle scanning trajectory performed by the galvanometer; S4, control the robotic arm to move sequentially to each stopping point, and control the galvanometer to perform concentric circle scanning at each stopping point until the scanning task of all stopping points is completed; during the concentric circle scanning at each stopping point, after each concentric circle scan is completed, control the starting point of the next concentric circle to deflect around the center by a preset angle. .

2. The laser scanning trajectory planning method for obtaining uniform laser cleaning effect as described in claim 1, characterized in that, In step S1, the method for determining a series of robot arm stopping points based on the boundary contour includes the following steps: S1.1, Set a safety margin inside the workpiece boundary to define the robot's motion boundary; S1.2, the motion boundary is discretized into a uniform grid using a grid method, with a grid side length of... The calculation formula is: ； in, This is the maximum effective scanning radius of the galvanometer; k This is the overlap rate coefficient, with a value ranging from 0.7 to 0.9; S1.3, define all grids whose center points are located within the motion boundary as valid grids, and set the center point of the valid grid as the initial stopping point of the robot arm.

3. The laser scanning trajectory planning method for obtaining uniform laser cleaning effect as described in claim 2, characterized in that, Step S1 also includes: S1.4, Identify the grids that intersect with the original boundary of the workpiece in the effective grid as boundary grids; S1.5, generate an auxiliary stopping point for each of the boundary grids to replace the original initial stopping point of the robot arm, and the coordinates of the auxiliary stopping point are... Calculated using the following formula: ； in, The center coordinates of the boundary grid. The shortest distance from the center of the boundary mesh to the original boundary of the workpiece. This is the unit direction vector pointing from the center of the boundary grid to the nearest boundary point.

4. The laser scanning trajectory planning method for obtaining uniform laser cleaning effect as described in claim 1, characterized in that, In step S2, the method of planning the global movement path using the optimized ant colony algorithm includes the following steps: S2.1, Initialization: Abstract each robot arm's stopping point into a path node, and initialize the pheromone concentration on the path segments between each node; S2.2, Parallel Path Search: In each iteration, multiple virtual ants are dispatched from random nodes to select the next unvisited node according to the state transition probability formula, in order to construct a complete site visit path; the state transition probability formula is as follows: ； ； in, It's an ant. k exist t From the node i Transfer to node j The probability of; yes t Time Side The concentration of pheromones on the surface; It is a heuristic message used to guide ants to prioritize stopping points that are closer and have smaller deflection angles; The pheromone heuristic factor indicates the importance of pheromones; The expected heuristic factor represents the importance of the heuristic information; It's an ant. k The set of currently accessible nodes; It is a node i and j The Euclidean distance between them; It is the angle that the robotic arm needs to turn from the previous path segment to the current path segment; and These are the weighting coefficients of the distance factor and the smoothness factor, respectively. A constant greater than 0; S2.3, Pheromone Update: After all ants have completed path construction, the global pheromone level is updated according to the following formula: ； ； in, It is a pheromone volatile factor; For ants k In this iteration, on the edge The amount of pheromones left on it; m The total number of ants; It is the pheromone intensity constant; It's an ant. k The total length of the constructed path; It's an ant. k Construct the sum of all steering angles along the path; S2.4, Optimal Path Output: Iteratively execute steps S2.2 and S2.

3. When the maximum number of iterations is reached or the quality of the solution is stable, output the optimal path as the global motion path of the robot.

5. The laser scanning trajectory planning method for obtaining uniform laser cleaning effect as described in claim 1, characterized in that, In step S3, determining the geometric parameters of the concentric circle scanning trajectory includes: radius of the inner circle of concentric circles r Must meet: ; in, V The linear velocity of the galvanometer scanning is... This is the highest scanning frequency of the galvanometer; outer radius of concentric circles R Must meet: ; in, The maximum effective scanning radius of the galvanometer. This represents the shortest distance from the current stopping point of the robot arm to the workpiece boundary. Number of concentric circle scans N for: , ; in, d The spacing between adjacent concentric circles. D The diameter of the light spot; This is the floor function.

6. The laser scanning trajectory planning method for obtaining uniform laser cleaning effect as described in claim 1, characterized in that, In step S4, the preset angle is... The calculation formula is: ； in, N This represents the number of concentric circle scans.

7. The laser scanning trajectory planning method for obtaining uniform laser cleaning effect as described in claim 1, characterized in that, In step S4, the laser is turned off while the galvanometer jumps from the end point of one concentric circle to the beginning point of the next concentric circle, and while the robot moves between different stopping points; the laser is turned back on after the galvanometer or robot is stably positioned.

8. The laser scanning trajectory planning method for obtaining uniform laser cleaning effect as described in claim 1, characterized in that, In step S4, after completing all concentric circle scans at a pause point, if multiple scans are preset, the entire galvanometer scanning field is controlled to deflect around the center by a preset angle. γ , γ The value ranges from 5° to 10°, and then the next scan is performed at that site.

9. An electronic device comprising a memory and a processor, wherein the memory stores a computer program executable on the processor, characterized in that, When the processor executes the computer program, it implements the steps of the trajectory control method as described in any one of claims 1 to 8.

10. A computer-readable storage medium storing a computer program, characterized in that, When the computer program is executed by a processor, it implements the steps of the trajectory control method as described in any one of claims 1 to 8.

Images