A robot trajectory planning method, system and related components

Abstract

The application discloses a robot trajectory planning method, a system and related components. The robot trajectory planning method comprises the following steps: determining a companion function, the companion function taking a trajectory parameter as an independent variable, and the first derivative and the second derivative of the companion function at the starting point and the ending point thereof being 0; planning a position smooth trajectory according to a position front trajectory, a position rear trajectory and the companion function; and planning a posture smooth trajectory according to a posture front trajectory, a posture rear trajectory and the companion function. The robot trajectory planning method provided by the application is used, the first derivative and the second derivative of the smooth trajectory at a transition point are continuous with those of the front trajectory and the rear trajectory, and the robot does not shake when moving to the transition point. Meanwhile, the position and the posture are synchronized by the companion function, and the one-to-one correspondence of the path in the position and the posture is realized.

Description

Technical Field

[0001] This application relates to the field of robot pose control technology, and more specifically, to a robot trajectory planning method, system, device, and computer-readable storage medium. Background Technology

[0002] In robot motion control, trajectory planning can be divided into CP motion and PTP (Plan-to-Plan) motion. To make the robot's TCP point follow the desired path, multiple CP motions need to be performed continuously. In the planning of a single CP motion, both the initial and final velocities are 0. If the velocity drops to 0 in each segment during multiple continuous CP motions, it will significantly reduce work efficiency, and frequent acceleration and deceleration will also affect the lifespan of the motor and reducer.

[0003] Most methods employ techniques to smoothly transition between two consecutive CP motion segments without reducing the velocity to zero. This is because continuous straight lines or arcs, if not tangent, will have sharp angles; if the velocity is not zero when passing through these angles, vibrations will occur. Therefore, the motion deviates from the original planned trajectory at the end of the first segment and the beginning of the second segment. The end of the first segment has an exit point, and the beginning of the second segment has an entry point; these are the start and end points of the smooth trajectory, also known as the transition points between the smooth trajectory and the first and second segments.

[0004] The motion description of a robot's TCP point can be divided into two parts: path and pose. The path describes the position of the robot's TCP point in the coordinate system, denoted as (X, Y, Z). The pose describes the orientation of the TCP point in the coordinate system, and can be expressed in many ways, including rotation matrices, Euler angles, quaternions, etc.

[0005] In existing technologies, the methods for planning smooth trajectories are mostly vector superposition, circular arc smoothing, and Bezier curves.

[0006] Vector superposition creates a smooth trajectory by superimposing velocity vectors, and its characteristic is that it is velocity-dependent. In robotic applications, the same set of teaching points may be moved at different speeds. Vector superposition can cause different trajectories at different speeds, posing a risk of collision.

[0007] Circular smoothing solves this problem because it's a path planning technique where the path doesn't change with velocity. However, with circular smoothing, since the curvature of a straight line is 0 while the curvature of an arc is 1 / 2 the radius, there's an abrupt change in curvature. Therefore, its drawback is that only the first derivative of the path is continuous, while the second derivative is discontinuous. This abrupt acceleration change at transition points can cause jitter.

[0008] The subsequent Bezier curve, while possessing the advantage of smooth circular arcs, makes the path second-order differentiable, eliminating sudden accelerations along the path. However, the Bezier curve still has a problem. The position and attitude of the Bezier curve are planned separately, and then synchronized by synchronizing them over the same time. This still introduces a velocity term, and under finite conditions, different velocities will cause synchronous changes in position and attitude. Trajectory changes will still occur in axis space.

[0009] In summary, how to achieve a smooth transition of trajectory while ensuring a one-to-one correspondence between the robot's position and posture is a problem that urgently needs to be solved by those skilled in the art. Summary of the Invention

[0010] In view of this, the purpose of this application is to provide a robot trajectory planning method, which, based on second-order differentiability, plans a smooth trajectory through the pose paths of two consecutive trajectories, so that the path corresponds one-to-one in position and orientation. Another purpose of this application is to provide a smooth trajectory planning system, a smooth trajectory planning device, and a computer-readable storage medium.

[0011] To achieve the above objectives, this application provides the following technical solution:

[0012] A robot trajectory planning method, comprising:

[0013] Determine the adjoint function, which takes the trajectory parameters as independent variables, and whose first and second derivatives at the starting and ending points are both 0;

[0014] A position smoothing trajectory is planned based on the preceding position trajectory, the following position trajectory, and the accompanying function; the starting point of the position smoothing trajectory coincides with a path point in the preceding position trajectory, and the ending point of the position smoothing trajectory coincides with a path point in the following position trajectory.

[0015] A smooth attitude trajectory is planned based on the preceding attitude trajectory, the following attitude trajectory, and the accompanying function; the starting point of the smooth attitude trajectory coincides with a path point in the preceding attitude trajectory, and the ending point of the smooth attitude trajectory coincides with a path point in the following attitude trajectory.

[0016] Optionally, the process of planning a smooth position trajectory based on the preceding position trajectory, the following position trajectory, and the adjoint function includes:

[0017] The positional smoothing trajectory is obtained according to the first relational expression; wherein, the first relational expression is: s is the trajectory parameter, r(s) is the positional smoothing trajectory, p(s) is the adjoint function, and the endpoint of the preceding positional trajectory and the starting point of the following positional trajectory intersect at the center of the smoothing sphere. The preceding trajectory is located at the position within the smooth sphere. The trajectory is the one following the position located within the smooth sphere.

[0018] Optionally, the process of planning the smoothed attitude trajectory based on the previous attitude trajectory, the next attitude trajectory, and the adjoint function includes:

[0019] The attitude smoothing trajectory is obtained according to the second relation; wherein, the second relation is: Let p(s) be the attitude smoothing trajectory, and p(s) be the adjoint function. The endpoint of the previous attitude trajectory and the starting point of the next attitude trajectory intersect at the center of the smooth sphere. The attitude front trajectory is located within the smooth sphere. Let θ be the trajectory of the posture located within the smooth sphere, where θ is the included angle.

[0020] Optionally, when the trajectory parameters are located at the starting point, the adjoint function has a value of 0 at its starting point and a value of 1 at its ending point. Optionally, the adjoint function is p(s) = 10s. 3 -15s 4 +6s 5 .

[0021] A smooth trajectory planning system, comprising:

[0022] The adjoint function determination module is used to determine the adjoint function, wherein the adjoint function takes the trajectory parameters as independent variables, and the first and second derivatives of the adjoint function at its starting point and ending point are both 0;

[0023] The position smoothing trajectory planning module is used to plan a position smoothing trajectory based on the previous position trajectory, the next position trajectory, and the adjoint function; the starting point of the position smoothing trajectory coincides with a path point in the previous position trajectory, and the ending point of the position smoothing trajectory coincides with a path point in the next position trajectory;

[0024] The attitude smoothing trajectory planning module is used to plan an attitude smoothing trajectory based on the previous attitude trajectory, the next attitude trajectory, and the adjoint function; the starting point of the attitude smoothing trajectory coincides with a path point in the previous attitude trajectory, and the ending point of the attitude smoothing trajectory coincides with a path point in the next attitude trajectory.

[0025] Optionally, the position smoothing trajectory planning module includes:

[0026] A first determining module is configured to obtain the positional smoothing trajectory according to a first relational expression; wherein, the first relational expression is: s is the trajectory parameter, r(s) is the positional smoothing trajectory, p(s) is the adjoint function, and the endpoint of the preceding positional trajectory and the starting point of the following positional trajectory intersect at the center of the smoothing sphere. The preceding trajectory is located at the position within the smooth sphere. The trajectory is the one following the position located within the smooth sphere.

[0027] Optionally, the attitude smoothing trajectory planning module includes:

[0028] The second determining module is used to obtain the attitude smoothing trajectory according to the second relation; wherein, the second relation is: Let p(s) be the attitude smoothing trajectory, and p(s) be the adjoint function. The endpoint of the previous attitude trajectory and the starting point of the next attitude trajectory intersect at the center of the smooth sphere. The attitude front trajectory is located within the smooth sphere. Let θ be the trajectory of the posture located within the smooth sphere, where θ is the included angle.

[0029] A smooth trajectory planning device, comprising:

[0030] Memory, used to store computer programs;

[0031] A processor is used to implement the steps of any of the above-described robot trajectory planning methods when executing the computer program.

[0032] A computer-readable storage medium storing a computer program that, when executed by a processor, implements the steps of any robot trajectory planning method.

[0033] The beneficial effects of the robot trajectory planning method provided in this application through the above scheme are as follows:

[0034] The robot trajectory planning method provided in this application includes the following steps: determining the adjoint function with trajectory parameters as independent variables; planning a position smoothing trajectory based on the previous position trajectory, the next position trajectory, and the adjoint function; and planning a posture smoothing trajectory based on the previous attitude trajectory, the next attitude trajectory, and the adjoint function.

[0035] First, both position-smoothed trajectories and pose-smoothed trajectories introduce adjoint functions. The same adjoint function corresponds to a specific position and a specific pose; that is, position and pose establish a synchronization relationship through the adjoint function, achieving a one-to-one correspondence between the path and its position and pose. During robot operation, regardless of whether the robot is at high or low speed, the same position corresponds to only one pose, preventing multiple poses from occurring.

[0036] In addition, the first and second derivatives of the adjoint function are both 0 at its starting point and ending point. Therefore, the smooth trajectory is continuous with the first and second derivatives of the previous and subsequent trajectories at the transition point. As a result, the robot will not experience sudden changes in velocity or acceleration when it moves to the transition point, thus achieving a smooth transition effect.

[0037] The smooth trajectory planning system, smooth trajectory planning device, and computer-readable storage medium provided in this application all have the aforementioned beneficial effects. Attached Figure Description

[0038] To more clearly illustrate the technical solutions in the embodiments of this application 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 embodiments of this application. For those skilled in the art, other drawings can be obtained based on the provided drawings without creative effort.

[0039] Figure 1 A flowchart illustrating a robot trajectory planning method provided in this application embodiment;

[0040] Figure 2 This is a schematic diagram of the position preceding trajectory, position following trajectory, and position smoothing trajectory;

[0041] Figure 3 This is a schematic diagram of the structure of a smooth trajectory planning system provided in an embodiment of this application;

[0042] Figure 4 This is a schematic diagram of the structure of a smooth trajectory planning device provided in an embodiment of this application. Detailed Implementation

[0043] The technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, and not all embodiments. Based on the embodiments of this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0044] Please refer to Figure 1The robot trajectory planning method provided in this application is applicable to planning a smooth trajectory connecting the previous and subsequent trajectories when the previous and subsequent trajectories are known, so that the robot moves sequentially along the previous trajectory, the smooth trajectory, and the subsequent trajectory. Two smooth trajectories are planned: one is a position smooth trajectory, and the other is a posture smooth trajectory. The specifications of the position smooth trajectory and the posture smooth trajectory can be performed independently, without distinguishing the order. The smooth trajectory described below can be either the position smooth trajectory or the posture smooth trajectory. This robot trajectory planning method includes the following steps:

[0045] Step S1: Determine the adjoint function. The adjoint function takes the trajectory parameters as independent variables. The first and second derivatives of the adjoint function at its starting and ending points are both 0.

[0046] Specifically, the trajectory parameters are also the independent variables of the smooth trajectory. Since the adjoint function is not a fixed value, but a function of the independent variable that can change, the adjoint function can be regarded as a curve. The starting point of the adjoint function corresponds to the transition point between the previous trajectory and the smooth trajectory, and the ending point of the adjoint function corresponds to the transition point between the smooth trajectory and the subsequent trajectory.

[0047] Step S2: Plan a smooth position trajectory based on the previous position trajectory, the next position trajectory, and the accompanying function.

[0048] Specifically, each trajectory consists of several waypoints. In the design, the preceding and following positions are two known trajectories. A waypoint in the preceding trajectory is the first transition point, and a waypoint in the following trajectory is the second transition point. The planned smoothing trajectory connects these two transition points, with the first transition point in the preceding trajectory being the starting point and the second transition point in the following trajectory being the ending point. During robot operation, it first moves along the preceding trajectory to the first transition point (the starting point of the smoothing trajectory); then it moves along the smoothing trajectory until its ending point (the second transition point); and finally, it moves along the following trajectory.

[0049] The adjoint function assigns corresponding weight coefficients to the preceding and following trajectories, and then superimposes the preceding and following trajectories into a smoothed position trajectory.

[0050] Step S3: Plan the attitude smoothing trajectory based on the attitude front trajectory, attitude back trajectory, and adjoint function.

[0051] Specifically, the attitude trajectory is similar to the position trajectory in step S2. During design, the preceding and following attitude trajectories are two known trajectories. A path point in the preceding attitude trajectory is the third transition point, and a path point in the following attitude trajectory is the fourth transition point. The planned smooth attitude trajectory needs to connect these two transition points. The third transition point in the preceding attitude trajectory is the starting point of the smooth attitude trajectory, and the fourth transition point in the following attitude trajectory is the ending point. During robot operation, it first moves along the preceding attitude trajectory to the third transition point, i.e., to the starting point of the smooth attitude trajectory; then it moves along the smooth attitude trajectory until its ending point, i.e., to the fourth transition point; finally, it moves along the following attitude trajectory.

[0052] The adjoint function assigns corresponding weight coefficients to the attitude front and attitude back trajectories, and superimposes the attitude front and attitude back trajectories into a smooth attitude trajectory.

[0053] The beneficial effects of the robot trajectory planning method provided in this application are as follows:

[0054] First, in existing technologies, the same time is used to synchronize position and posture during smooth segments. Since the position and posture are not described by the same parameter at the same time, there is a risk of misalignment between position and posture in speed planning. The same position may correspond to multiple postures. During use, users may adjust the speed, which may cause the robot to move in different postures at high and low speeds.

[0055] In this application, the smooth trajectory is formed by superimposing two consecutive trajectories according to preset weights. Both the position-smoothed trajectory and the pose-smoothed trajectory are described by adjoint functions. The same adjoint function corresponds to a specific position and a specific pose. That is, position and pose are synchronized through the adjoint function, achieving a one-to-one correspondence between the path in position and pose. During the robot's operation, the adjoint function is independent of speed. Regardless of whether the robot is at high speed or low speed, the same position always corresponds to one pose, and there will be no situation where the position corresponds to other poses.

[0056] Secondly, the adjoint function has zero first and second derivatives at both its starting and ending points. This adjoint function ensures that the position smoothing trajectory is continuous with the first and second derivatives of the preceding and following position trajectories at the two transition points, respectively. Simultaneously, it ensures that the attitude smoothing trajectory is continuous with the first and second derivatives of the preceding and following attitude trajectories at the two transition points. Therefore, the robot will not experience abrupt changes in velocity or acceleration when moving to the transition points, allowing the smoothing trajectory to transition smoothly in a manner consistent with the desired first and second derivatives.

[0057] Furthermore, in one embodiment, the process of planning a smooth position trajectory based on the preceding position trajectory, the following position trajectory, and the adjoint function in step S2 includes:

[0058] The positional smoothing trajectory is obtained based on the first relational expression; where the first relational expression is: p(s) is the adjoint function, s is the trajectory parameter, and s∈[0,1].

[0059] For details, please refer to Figure 2 r1(s1) represents the trajectory before the position, r2(s2) represents the trajectory after the position, r(s) is the position smoothing trajectory, and s1,s2∈[0,1].

[0060] In practical applications, users specify the start and end points of the preceding position trajectory, i.e., the points s1 = 0 and s1 = 1; the starting point of the following position trajectory is s2 = 0, s1 = 1 coincides with s2 = 0, and they intersect at the center of the sphere; the ending point of the following position trajectory is also specified, i.e., the point s2 = 1; and a smoothing radius is also specified. A sphere is drawn using the smoothing radius to obtain a smooth sphere. When a TCP point enters the smooth sphere, it can detach from both the preceding and following position trajectories and move according to the smooth position trajectory. The intersection of the preceding position trajectory and the smooth sphere is a transition point, i.e., s1 = s2 = 0. 1z The intersection of the trajectory after the position and the smooth sphere is a transition point, i.e., s2 = s 2z Clearly, the two transition points are the start and end points of the positional smoothing trajectory.

[0061] Therefore, we can conclude that:

[0062] r1(s 1z )=r(0),r2(s 2z )=r(1)

[0063] r1′(s 1z )=r′(0),r2′(s 2z )=r′(1)

[0064] r1″(s 1z )=r″(0),r2″(s 2z )=r″(1)

[0065] The construction idea is to transform the trajectory before the position into the trajectory after the position based on the adjoint function. The construction method is as follows: Let:

[0066]

[0067] in, Let r1(s1) be the position of the previous trajectory within the smooth sphere, represented by the dashed line segment on the left side of the figure. The independent variable s1 of r1(s1) has a range of [0,1]. A subset belonging to r1(s1), and the range of the independent variable is [s 1z Therefore, the range of the independent variable of r1(s1) is transformed from [0,1] to [s1]. 1z From [,1], we can obtain:

[0068]

[0069]

[0070]

[0071] at the same time, Let r2(s2) be the position of the trajectory within the smooth sphere, represented by the dashed line segment on the right side of the figure. The independent variable s2 of r2(s2) has a range of [0,1]. It belongs to a subset of r2(s2), and the range of the independent variable is [0, s]. 2z Therefore, the range of the independent variable of r2(s2) is changed from [0,1] to [0,s]. 2z From this, we can obtain:

[0072]

[0073] At the same time, it can be determined that:

[0074]

[0075]

[0076]

[0077] It should be noted that r1(s1) can represent any form of the previous trajectory, not limited to the arc shown in the figure; r2(s2) can also represent any form of the next trajectory, not limited to the straight line shown in the figure.

[0078] Furthermore, in one embodiment, step S3, which involves planning the attitude smoothing trajectory based on the preceding attitude trajectory, the following attitude trajectory, and the adjoint function, includes:

[0079] The smoothed trajectory is obtained based on the second relation; where the second relation is: p(s) is the adjoint function, and the endpoint of the previous attitude trajectory and the starting point of the next attitude trajectory intersect at the center of the smooth sphere. Let be the attitude front-line trajectory located within a smooth sphere. Let θ be the attitude trailing trajectory within a smooth sphere, and θ be the angle between two quaternions.

[0080] Specifically, Indicates the trajectory preceding the attitude. Indicates the trajectory after the attitude. Let s1, s2, s∈[0,1] be the attitude smooth trajectory. It describes quaternions.

[0081] The construction process of attitude smoothing trajectory is similar to that of position smoothing trajectory. First, the transition point needs to be determined by the previous attitude trajectory, the next attitude trajectory, and the smoothing radius. Therefore:

[0082]

[0083]

[0084]

[0085] The constructor is as follows:

[0086]

[0087] in,

[0088] Therefore, the attitude smoothing path is:

[0089]

[0090] Furthermore, in one embodiment, the starting value of the adjoint function is 0, and the ending value of the adjoint function is 1.

[0091] Specifically, the adjoint function is essentially a weight adjustment quantity used to adjust the weights of the preceding and subsequent trajectories in the final smoothed trajectory. The starting value of the adjoint function refers to its value when the smoothed trajectory is at the starting point; the ending value refers to its value when the smoothed trajectory is at the ending point.

[0092] More specifically, the positional smoothing trajectory is determined based on the preceding and following positional trajectories. The weights of the preceding and following positional trajectories in the determined positional smoothing trajectory are determined by the adjoint function. The closer the independent variable of the positional smoothing trajectory is to the preceding positional trajectory, the greater the weight the adjoint function should assign to the preceding positional trajectory and the smaller the weight to the following positional trajectory. Conversely, the closer the independent variable of the positional smoothing trajectory is to the following positional trajectory, the greater the weight the adjoint function should assign to the following positional trajectory and the smaller the weight to the preceding positional trajectory.

[0093] For example, for the first relation, i.e. When s = 0, r(s) should be the same as... When s = 1, r(s) should be equal to the value of the adjoint function, and the value of the adjoint function should be as small as possible. They are equal. Therefore, in this embodiment, p(0) = 0 and p(1) = 1.

[0094] Similarly, the attitude smoothing trajectory is determined based on the preceding and following attitude trajectories. The weights of the preceding and following attitude trajectories in the determined attitude smoothing trajectory are determined by the adjoint function. The closer the independent variable of the attitude smoothing trajectory is to the preceding attitude trajectory, the greater the weight the adjoint function should assign to the preceding trajectory and the smaller the weight to the following trajectory. Conversely, the closer the independent variable of the attitude smoothing trajectory is to the following attitude trajectory, the greater the weight the adjoint function should assign to the following trajectory and the smaller the weight to the preceding trajectory.

[0095] For example, for the second relation, i.e. When s = 0 Should be with When they are equal, the value of the adjoint function should be as small as possible. When s = 1, Should be with They are equal. Therefore, in this embodiment, p(0) = 0 and p(1) = 1.

[0096] Furthermore, in one embodiment, the adjoint function is p(s) = 10s. 3 -15s 4 +6s 5 Understandably, in other embodiments, the adjoint function may also use other coefficients that satisfy p(0) = 0, p(1) = 1, p′ (0) =0, p″ (0) =0, p′(1)=0, p″(1)=0 is sufficient.

[0097] Please refer to Figure 3 This application also provides a smooth trajectory planning system, which can be referred to in correspondence with the robot trajectory planning method described above, and the smooth trajectory planning system also has the beneficial effects of the above-described robot trajectory planning method. The smooth trajectory planning system includes:

[0098] The adjoint function determination module 11 is used to determine the adjoint function, which takes the trajectory parameters as independent variables, and the first and second derivatives of the adjoint function at its starting point and ending point are both 0;

[0099] The position smoothing trajectory planning module 12 is used to plan a position smoothing trajectory based on the previous position trajectory, the next position trajectory, and the adjoint function; the starting point of the position smoothing trajectory coincides with a path point in the previous position trajectory, and the ending point of the position smoothing trajectory coincides with a path point in the next position trajectory.

[0100] The attitude smoothing trajectory planning module 13 is used to plan the attitude smoothing trajectory based on the previous attitude trajectory, the next attitude trajectory, and the adjoint function; the starting point of the attitude smoothing trajectory coincides with a path point in the previous attitude trajectory, and the ending point of the attitude smoothing trajectory coincides with a path point in the next attitude trajectory.

[0101] Furthermore, the position smoothing trajectory planning module 12 includes:

[0102] The first determining module is used to obtain the position smoothing trajectory according to the first relation; wherein, the first relation is: r(s) is the positional smoothing trajectory, p(s) is the adjoint function, and the endpoint of the previous positional trajectory and the starting point of the next positional trajectory intersect at the center of the smoothing sphere. Let be the position of the previous trajectory within the smooth sphere. The position of the last line of the trajectory is located within the smooth sphere.

[0103] Furthermore, the attitude smoothing trajectory planning module 13 includes:

[0104] The second determining module is used to obtain the attitude smoothing trajectory according to the second relation; wherein, the second relation is: Let p(s) be the attitude smooth trajectory, and p(s) be the adjoint function. The endpoint of the previous attitude trajectory and the starting point of the next attitude trajectory intersect at the center of the smooth sphere. Let be the attitude front-line trajectory located within a smooth sphere. Let θ be the attitude trailing trajectory located within a smooth sphere, and θ be the included angle.

[0105] Please see Figure 4 This application also provides a smooth trajectory planning device, including a memory 21 and a processor 22. The memory 21 is used to store a computer program; the processor 22 is used to implement the steps of any of the above-described robot trajectory planning methods when executing the computer program. The smooth trajectory planning device also has the beneficial effects of the above-described robot trajectory planning methods.

[0106] This application also provides a computer-readable storage medium storing a computer program, which, when executed by processor 22, implements the steps of any of the above-described robot trajectory planning methods. The computer-readable storage medium also possesses the beneficial effects of the aforementioned robot trajectory planning methods.

[0107] The various embodiments in this specification are described in a progressive manner, with each embodiment focusing on the differences from other embodiments. The same or similar parts between the various embodiments can be referred to each other.

[0108] The robot trajectory planning method, system, apparatus, and computer-readable storage medium provided in this application have been described in detail above. Specific examples have been used to illustrate the principles and implementation methods of this application. The descriptions of the embodiments above are merely for the purpose of helping to understand the method and its core ideas. It should be noted that those skilled in the art can make various improvements and modifications to this application without departing from its principles, and these improvements and modifications also fall within the protection scope of the claims of this application.

Claims

1. A robot trajectory planning method, characterized in that, include: Determine the adjoint function, which takes the trajectory parameters as independent variables. The first and second derivatives of the adjoint function are both 0 at its starting point and ending point. The starting point of the adjoint function corresponds to the transition point between the previous trajectory and the smooth trajectory, and the ending point of the adjoint function corresponds to the transition point between the smooth trajectory and the subsequent trajectory. A position smoothing trajectory is planned based on the preceding position trajectory, the following position trajectory, and the accompanying function; the starting point of the position smoothing trajectory coincides with a path point in the preceding position trajectory, and the ending point of the position smoothing trajectory coincides with a path point in the following position trajectory. A smooth attitude trajectory is planned based on the previous attitude trajectory, the next attitude trajectory, and the adjoint function; the starting point of the smooth attitude trajectory coincides with a path point in the previous attitude trajectory, and the ending point of the smooth attitude trajectory coincides with a path point in the next attitude trajectory. The adjoint function assigns corresponding weight coefficients to the preceding and following trajectories, and superimposes the preceding and following trajectories into a smoothed position trajectory; The adjoint function assigns corresponding weight coefficients to the attitude front and attitude back trajectories, and superimposes the attitude front and attitude back trajectories into a smooth attitude trajectory. The adjoint function starts at 0 and ends at 1.

2. The robot trajectory planning method according to claim 1, characterized in that, The process of planning a smooth position trajectory based on the preceding position trajectory, the following position trajectory, and the adjoint function includes: The positional smoothing trajectory is obtained according to the first relational expression; wherein, the first relational expression is: , The trajectory parameters are... For the smoothed trajectory at the stated position, The adjoint function is such that the endpoint of the preceding trajectory and the starting point of the following trajectory intersect at the center of the smooth sphere. The preceding trajectory is located at the position within the smooth sphere. The trajectory is the one following the position located within the smooth sphere.

3. The robot trajectory planning method according to claim 1, characterized in that, The process of planning the smoothed attitude trajectory based on the previous attitude trajectory, the next attitude trajectory, and the adjoint function includes: The attitude smoothing trajectory is obtained according to the second relation; wherein, the second relation is: ; The smoothed trajectory of the posture. The adjoint function is such that the endpoint of the preceding attitude trajectory and the starting point of the following attitude trajectory intersect at the center of the smooth sphere. The attitude front trajectory is located within the smooth sphere. The trajectory following the posture is located within the smooth sphere. ,and Indicates the trajectory preceding the attitude. Indicates the trajectory after the attitude. and These are the start and end points of the positional smoothing trajectory.

4. The robot trajectory planning method according to any one of claims 1-3, characterized in that, The adjoint function is .

5. A smooth trajectory planning system, characterized in that, include: The adjoint function determination module is used to determine the adjoint function, which takes the trajectory parameters as independent variables. The first and second derivatives of the adjoint function are both 0 at its starting point and ending point. The starting point of the adjoint function corresponds to the transition point between the previous trajectory and the smooth trajectory, and the ending point of the adjoint function corresponds to the transition point between the smooth trajectory and the subsequent trajectory. The position smoothing trajectory planning module is used to plan a position smoothing trajectory based on the previous position trajectory, the next position trajectory, and the adjoint function; the starting point of the position smoothing trajectory coincides with a path point in the previous position trajectory, and the ending point of the position smoothing trajectory coincides with a path point in the next position trajectory; An attitude smoothing trajectory planning module is used to plan an attitude smoothing trajectory based on the previous attitude trajectory, the next attitude trajectory, and the adjoint function; the starting point of the attitude smoothing trajectory coincides with a path point in the previous attitude trajectory, and the ending point of the attitude smoothing trajectory coincides with a path point in the next attitude trajectory. The adjoint function assigns corresponding weight coefficients to the preceding and following trajectories, and superimposes the preceding and following trajectories into a smoothed position trajectory; The adjoint function assigns corresponding weight coefficients to the attitude front and attitude back trajectories, and superimposes the attitude front and attitude back trajectories into a smooth attitude trajectory. The adjoint function starts at 0 and ends at 1.

6. The smooth trajectory planning system according to claim 5, characterized in that, The position smoothing trajectory planning module includes: A first determining module is configured to obtain the positional smoothing trajectory according to a first relational expression; wherein, the first relational expression is: , The trajectory parameters are... For the smoothed trajectory at the stated position, The adjoint function is such that the endpoint of the preceding trajectory and the starting point of the following trajectory intersect at the center of the smooth sphere. The preceding trajectory is located at the position within the smooth sphere. The trajectory is the one following the position located within the smooth sphere.

7. The smooth trajectory planning system according to claim 5, characterized in that, The attitude smoothing trajectory planning module includes: The second determining module is used to obtain the attitude smoothing trajectory according to the second relation; wherein, the second relation is: ; The smoothed trajectory of the posture. The adjoint function is such that the endpoint of the preceding attitude trajectory and the starting point of the following attitude trajectory intersect at the center of the smooth sphere. The attitude front trajectory is located within the smooth sphere. The trajectory following the posture is located within the smooth sphere. ,and Indicates the trajectory preceding the attitude. Indicates the trajectory after the attitude. and These are the start and end points of the positional smoothing trajectory.

8. A smooth trajectory planning device, characterized in that, include: Memory, used to store computer programs; A processor, configured to implement the steps of the robot trajectory planning method as described in any one of claims 1 to 4 when executing the computer program.

9. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores a computer program that, when executed by a processor, implements the steps of the robot trajectory planning method as described in any one of claims 1 to 4.

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