Multi-axis time-synchronized s-shaped trajectory planning algorithm

Abstract

The application discloses a multi-axis time synchronization S-shaped trajectory planning algorithm, and belongs to the field of robot running trajectory algorithm. The original trajectory is properly modified, so that the multi-axis motion time is synchronized, and the problems that the robot speed, acceleration or motor torque may exceed the allowable range of the motor due to the dynamic saturation limitation of the motion system are solved. The application mainly comprises the following steps: judging whether the maximum acceleration can be reached; judging whether there is a uniform speed section; judging whether the maximum acceleration and deceleration of the acceleration section and the deceleration section can be reached; 6-axis motion time adjustment: setting the new motion time of the remaining 5 axes as the longest motion axis time; and synchronously scaling the 6-axis time by using the redefined parameters of each axis in step S2, and re-planning the joint motion trajectory. The application is mainly used for the S-shaped trajectory planning of multi-axis time synchronization of a robot.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of robot trajectory algorithm, in particular, especially relates to a multi-axis time synchronization S-shaped trajectory planning algorithm. BACKGROUND

[0002] At present, industrial robots are widely used in the automation industry and play an important role in it. Robots need to complete specific movements according to the instructions of the controller. Different control strategies will result in different motion characteristics of the robot, and the trajectory planning algorithm of the robot is the core algorithm of the motion control strategy of the robot, which aims to determine the variation law of the position, velocity and acceleration of the robot with time. An excellent trajectory planning algorithm can reduce the vibration of the robot body and achieve smooth motion of the joints. Different trajectory planning algorithms will affect the motion path, time and trend of the joint robot, resulting in differences in the performance of the robot, and different degrees of influence on its accuracy and service life.

[0003] The motion control algorithm of the robot joint mainly includes trapezoidal curve, polynomial trajectory planning and S-shaped curve trajectory planning. The acceleration of trapezoidal curve and polynomial trajectory planning is usually discontinuous or not smooth, which will cause mechanical impact in actual application, thereby causing wear of the mechanical structure of the equipment. Therefore, in the joint robot, the S-shaped trajectory planning can smoothly control the change of velocity and acceleration, and can achieve efficient trajectory planning without sacrificing system performance, so it is widely used in industry to reduce the impact on the mechanical structure, improve the accuracy of the robot and prolong its service life.

[0004] However, the above trajectory planning methods are mostly suitable for trajectory control in the case of single motor. In the joint robot system, multiple axes need to move cooperatively. When the motion time of each axis is not synchronized, the motion trajectory of the end of the mechanical arm may deviate from the predetermined path, thereby reducing the motion accuracy. This error can significantly reduce the product quality in precision manufacturing, assembly and machining applications, so that the product cannot meet the expected design requirements. In addition, the motion time out of synchronization may also cause the speed and acceleration between the axes to be uncoordinated, thereby making the motion not smooth and bearing additional force and torque, causing the mechanical arm to vibrate and shake, affecting its working stability and working efficiency, and increasing mechanical wear. In applications requiring force control, such as assembly and surface polishing, the motion of the axes out of synchronization will cause uneven distribution of force, thereby affecting the actual work effect. Therefore, in order to reduce the impact and vibration on the system and fully utilize the servo performance of the motor, the joint robot needs to synchronize the motion time of the six axes when controlling the motion.

[0005] The existing robot trajectory time synchronization method has various defects:

[0006] Direct programming method, keep the set acceleration under the given constraint, run at the highest speed and extend the uniform velocity time as long as possible, so as to give full play to the performance of the motor. However, this method is difficult to be used among different trajectory planning algorithms, and the trapezoidal synchronous planning derivation is simple and has high calculation efficiency, and the direct programming method has low complexity. However, because the complexity of S type planning is too high, the direct programming method cannot be applied to S type trajectory planning;

[0007] Generalized velocity method, a plurality of displacements are combined into a vector for operation, and then decomposed, but this method is easy to cause the speed and acceleration of the shaft to exceed the limit;

[0008] Double spline method, although multi-axis synchronization can be realized, the same node vector is mostly used for path fitting, the kinematics related constraints are not considered, and the implementation process is complex. SUMMARY

[0009] The purpose of the present application is to provide a multi-axis time synchronous S type trajectory planning algorithm, which realizes the synchronization of multi-axis motion time by appropriately modifying the original trajectory, and solves the problem that the robot speed, acceleration or motor torque may exceed the allowable range of the motor due to the dynamic saturation limit of the motion system.

[0010] The present application is realized by the following technical solutions:

[0011] A multi-axis time synchronous S type trajectory planning algorithm, comprising the following steps,

[0012] S1, a segmented S type trajectory planning method is used to independently plan the trajectory of each axis, comprising the following steps:

[0013] 1) judge whether the maximum acceleration can be reached;

[0014] 2) judge whether there is a uniform velocity section;

[0015] 3) judge whether the acceleration section and the deceleration section can reach the maximum acceleration and deceleration;

[0016] S2, 6-axis motion time adjustment: set the new motion time of the remaining 5 axes to the longest motion axis time;

[0017] S3, using the parameters redefined in step S2, the 6-axis time synchronization scaling is used to re-plan the joint motion trajectory;

[0018] S4, according to the obtained parameters, the position of any trajectory is calculated.

[0019] Further, the step S1 further comprises the following steps: the whole movement process is divided into jerk section, uniform acceleration section, deceleration section, uniform speed section, acceleration-deceleration section, uniform deceleration section, deceleration-deceleration section; q0 is initial position, q1 is terminal position, V0 is initial speed, V1 is terminal speed, V max is maximum speed, a max is maximum acceleration, j max is maximum jerk, T j1 is jerk section time, T a is acceleration section time, T v is uniform speed section time, T j2 is deceleration section time, T d is deceleration section time;

[0020] 1) judging whether maximum acceleration can be reached comprises the following steps:

[0021] supposing that maximum speed V max can be reached, but there is no uniform acceleration section, V0' is speed at the end of the jerk section, at this time, the jerk section is:

[0022]

[0023] a is acceleration at any time in the deceleration section, the deceleration section is:

[0024]

[0025] According to formula 1.1 and formula 1.2, the following can be obtained: If , it indicates that acceleration reaches the maximum value, which will cause the speed in the acceleration stage to exceed the maximum speed limit, at this time, a max needs to be adjusted, the process is as follows:

[0026]

[0027] If , it indicates that maximum acceleration can be reached, there is a uniform acceleration section, the time of the uniform acceleration section is T j1匀 ,

[0028] The parameters are obtained as follows:

[0029]

[0030] S is the total path length of the movement, the calculation of the uniform speed section time is as follows:

[0031]

[0032] T d is solved in the same way as T aSimilarly, the parameters of the deceleration phase of the trajectory planning can be obtained by analogy;

[0033] 2) judging whether there is a uniform speed section includes the following steps:

[0034] When T V >0, it indicates that there is a uniform speed section, and the total time of motion planning T=T a +T V +T d , the state at this time is defined as state 1, State=1, the trajectory is a 7-segment trajectory, and the subsequent multi-axis time synchronization planning will use this state record;

[0035] When T V <0, it indicates that there is no uniform speed section, and the maximum speed cannot be reached; assuming that the maximum acceleration and the maximum deceleration can be reached, the trajectory at this time has a jerk section, a uniform acceleration section, an acceleration-deceleration section, a deceleration-acceleration section, a uniform deceleration section, and a deceleration-deceleration section;

[0036]

[0037] According to formula 1.4 and formula 1.6, the value of V max at this time can be calculated as follows:

[0038]

[0039] V max is brought into the calculation formula of T a and T d , and the values of the two can be obtained;

[0040] 3) judging whether the acceleration section and the deceleration section can reach the maximum acceleration and deceleration includes the following steps:

[0041] In step 2), the values of T a and T d have been obtained, if T a <0, it indicates that there is no acceleration section, only a deceleration section, the state at this time is defined as state 2, State=2, and the trajectory is a 3-segment trajectory; if T d <0, it indicates that there is no deceleration section, only an acceleration section, the state at this time is defined as state 3, State=3, and the trajectory is a 3-segment trajectory; if T a >=2×T j1 &&T d >=2×T j2 , the state at this time is defined as state 4, State=4, and the trajectory has no uniform speed section; when T a <2×T j1 ||T d <2×T j2If the maximum acceleration cannot be reached during the acceleration or deceleration phase, the maximum acceleration value needs to be adjusted to meet the conditions. This can be achieved by using Newton's iteration method to reduce the maximum acceleration value and recalculating V. max T a T d until it satisfies T a >=2×T j1 &&T d >=2×T j2 .

[0042] Furthermore, step S2 specifically includes: using the longest motion axis time T max Based on this, the new motion time T for the remaining 5 axes is... N Set this time to the T value of each axis. a T d T V T j1 T j2 V max a max j max q1 and q0 are passed to step S3.

[0043] Furthermore, step S3 also includes: calculating the motion time and total time of each segment through step S1, using the new motion time as the replanning time, and scaling the acceleration segment, constant speed segment, and deceleration segment respectively using scaling factors. In step S1, when performing single-axis planning, the trajectory has been divided into 4 states, which should be considered separately during scaling.

[0044] State 1 is a 7-segment S-shaped trajectory. Let the scaling factor be... (T N (>=T), multiply the time of each segment by the scaling factor λ to obtain the new acceleration segment time T. aN Uniform speed time T VN Deceleration time T dN At this point, the maximum speed is set to V. maxN Calculate the motion distance S before and after scaling, as shown in Equation 1.8:

[0045]

[0046] According to Equation 1.8, we can solve for V. maxN The value is shown in Equation 1.9:

[0047]

[0048] Find the new V maxN Then, it is necessary to calculate the time interval T of the uniform acceleration. j1N and maximum acceleration a maxNV''0 is the speed at the end of the deceleration section;

[0049]

[0050] According to formula 1.9 and formula 1.10, T can be solved j1N The value is as follows:

[0051]

[0052] At this time, T j1N is negative;

[0053] In order to obtain the parameters of all trajectory re-planning of state 1, as shown in formula 1.12:

[0054]

[0055] State 4 is a trajectory without uniform speed section, and the time scaling calculation method is similar to state 1, and the formula T VN and V maxN The calculation formula is different, and the uniform speed section is removed during operation, and the parameters of state 4 are obtained as shown in formula 1.13:

[0056]

[0057] State 2 is a deceleration section,

[0058]

[0059] The current j max and the value of T2 are solved through formula 1.14.

[0060] State 3 is an acceleration section, T1 is the time of the uniform acceleration section, T2 is the time of the deceleration section,

[0061]

[0062] The current j max and the value of T2 are solved through formula 1.15.

[0063] Further, the curve diagram of the trajectory and the parameters of each section trajectory are brought into the position equation to obtain the position at any time.

[0064] Compared with the prior art, the beneficial effects of the present application are:

[0065] 1. First, S-shaped trajectory planning is performed on six axes respectively, and S-curve data of each independent joint is calculated; then, the axis with the longest motion time is taken as a reference, and time scaling method is used to adjust the motion curves of other axes; in this process, the maximum speed and maximum acceleration of each joint are also adjusted based on the dynamics limit, so as to realize multi-axis synchronous trajectory planning, so that the speed and acceleration will not exceed the limit of dynamics constraint, and the coordination of multi-axis motion and the overall operation precision of the robot are effectively improved.

[0066] 2. Not only the synchronization of multi-axis motion time is realized, but also the problem that the speed, acceleration or motor torque of the robot may exceed the allowable range of the motor due to the dynamics saturation limit of the motion system is solved. BRIEF DESCRIPTION OF DRAWINGS

[0067] Figure 1 is a 7-segment S-shaped trajectory planning diagram of the application;

[0068] Figure 2 is a trajectory planning flowchart of the application;

[0069] Figure 3 is an acceleration segment speed curve diagram of the application;

[0070] Figure 4 is a deceleration segment speed curve diagram of the application;

[0071] Figure 5 is a multi-axis time synchronization trajectory planning algorithm flowchart of the application;

[0072] Figure 6 is a single-axis time scaling motion data curve diagram of the application;

[0073] Figure 7 is a 6-axis non-time synchronization trajectory planning motion data curve diagram of the application;

[0074] Figure 8 is a 6-axis time synchronization trajectory planning motion data curve diagram of the application. DETAILED DESCRIPTION

[0075] The application will be further described and illustrated below with reference to the accompanying drawings.

[0076] Example 1

[0077] A multi-axis time synchronization S-shaped trajectory planning algorithm, comprising the following steps,

[0078] S1, a segmented S-shaped trajectory planning method is used to independently plan the trajectory of each axis, including the following steps:

[0079] 1) judging whether the maximum acceleration can be reached;

[0080] 2) Determine whether there is a uniform section;

[0081] 3) Determine whether the acceleration and deceleration sections can reach the maximum acceleration and deceleration;

[0082] S2, 6-axis motion time adjustment: set the new motion time of the remaining 5 axes to the longest motion axis time;

[0083] S3, using the redefined parameters of each axis in step S2, 6-axis time synchronous scaling, joint motion trajectory re-planning;

[0084] S4, according to the obtained parameters, calculate the position of any trajectory.

[0085] Example 2

[0086] A multi-axis time synchronous S-shaped trajectory planning algorithm, step S1 further includes the following steps: the entire motion process is divided into jerk acceleration section, uniform acceleration section, deceleration section, uniform section, acceleration and deceleration section, uniform deceleration section, deceleration section; under ideal conditions, it can be divided into 7 sections, as shown in Figure 1 q0 is the initial position, q1 is the terminal position, V0 is the initial speed, V1 is the terminal speed, V max is the maximum speed, a max is the maximum acceleration, j max is the maximum jerk, T j1 is the jerk acceleration section time, T a is the acceleration section time, T v is the uniform section time, T j2 is the deceleration and acceleration section time, T d is the deceleration section time; under actual conditions, because of the maximum speed, acceleration, jerk size and torque limit, it is not necessarily to achieve 7 sections, at this time, the motion process needs to be adjusted, for example, discard the uniform section, uniform acceleration section, or reduce the maximum speed, maximum acceleration of single axis, so that it can meet the planning conditions;

[0087] 1) Determine whether the maximum acceleration can be reached, including the following steps:

[0088] Let the maximum speed V max can be reached, but there is no uniform acceleration section, V'0 is the speed at the end of the jerk acceleration section, at this time, the jerk acceleration section is:

[0089]

[0090] a is the acceleration at any time in the deceleration and acceleration section, the deceleration and acceleration section is:

[0091]

[0092] According to formula 1.1 and formula 1.2 If then it means the acceleration reaches the maximum value, which will cause the speed of the acceleration phase to exceed the maximum speed limit, at this time the a max needs to be adjusted, the process is as follows:

[0093]

[0094] If then it means that the maximum acceleration can be reached, there is a uniform acceleration segment, and the time of the uniform acceleration segment is T j1匀 ,

[0095] The parameters are obtained as follows:

[0096]

[0097] S is the total path length of the motion, and the calculation of the uniform speed segment time step is as follows:

[0098]

[0099] T d The solving process of T a is similar to that of T V , and the parameters of the deceleration phase of the trajectory planning can be obtained by the same method;

[0100] 2) Determine whether there is a uniform speed segment, including the following steps:

[0101] Whether there is a uniform speed segment means whether the robot joint can reach the limited maximum speed; when T a >0, it means that there is a uniform speed segment, and the total motion planning time T=T V +T d , define the state at this time as state 1, State=1, and the trajectory is a standard 7-segment trajectory, which will be used in subsequent multi-axis time synchronization planning;

[0102] When T V <0, it means that there is no uniform speed segment and the maximum speed cannot be reached; assuming that the maximum acceleration and the maximum deceleration can be reached, the trajectory at this time has a jerk acceleration segment, a uniform acceleration segment, a jerk deceleration segment, a uniform deceleration segment, and a jerk deceleration segment.

[0103]

[0104] According to formula 1.4 and formula 1.6, the value of V max at this time can be calculated as follows:

[0105]

[0106] Bring V max into T a , Td The values of the two can be obtained in the calculation formula of

[0107] 3) judging whether the acceleration section and deceleration section can reach the maximum acceleration and deceleration includes the following steps:

[0108] The value of T a , T d has been obtained in step 2), if T a <0, it indicates that there is no acceleration section, only deceleration section, the state at this time is defined as state 2, State = 2, and the trajectory is a 3-section trajectory; if T d >0, it indicates that there is no deceleration section, only acceleration section, the state at this time is defined as state 3, State = 3, and the trajectory is a 3-section trajectory; if T a >2*T j1 && T d >2*T j2 , the state at this time is defined as state 4, State = 4, and the trajectory has no uniform speed section; when T a <2*T j1 || T d <2*T j2 , it indicates that the acceleration section or deceleration section cannot reach the maximum acceleration, the maximum acceleration value needs to be adjusted so that it can meet the condition, Newton iteration method is used to reduce the maximum acceleration value, and V max , T a , T d are recalculated until T a >2*T j1 && T d >2*T j2 ;

[0109] The above is the trajectory planning step of step S1, and the flow chart is shown in Figure 2 ;

[0110] Step S2 specifically includes: taking the longest motion axis time T max as the benchmark, setting the new motion time T N of the remaining 5 axes to the time, and transmitting T a , T d , T V , T j1 , T j2 , V max , a man , j max , q1, q0 of each axis to step S3;

[0111] Step S3 further comprises: calculating the motion time and total time of each segment by step S1, taking the new motion time as the time of re-planning, using a scaling factor to scale the acceleration segment, constant speed segment and deceleration segment respectively, and in step S1, the trajectory is divided into four states when single-axis planning is performed, and the scaling is considered respectively;

[0112] State 1 is a standard 7-segment S-shaped trajectory, and a scaling factor (T N > = T) is set, and the time of each segment is multiplied by the scaling factor λ to obtain a new acceleration segment time T aN , constant speed segment time T VN and deceleration segment time T dN , wherein the maximum speed is set as V maxN , and the motion distance S before and after scaling is calculated respectively, as shown in formula 1.8:

[0113]

[0114] According to formula 1.8, the value of V maxN is solved as shown in formula 1.9:

[0115]

[0116] After obtaining the new V maxN , the constant acceleration segment time T j1N and the maximum acceleration a maxN are solved, Figure 3 which is a schematic diagram of an acceleration segment speed curve, V′0 is the speed at the end of the jerk segment, V″0 is the speed at the end of the constant acceleration segment, and V″′0 is the speed at the end of the deceleration segment;

[0117]

[0118] According to formula 1.9 and formula 1.10, the value of T j1N is solved as follows:

[0119]

[0120] At this time, T j1N takes a negative value, and if it takes a positive value, it will result in 2T j1N ≥ T aN , which does not meet the trajectory planning, so the positive value is discarded; to obtain all the trajectory re-planning parameters of state 1, as shown in formula 1.12:

[0121]

[0122] State 4 is a trajectory without constant speed segment, and the time scaling calculation method is similar to that of state 1, and the formulas T VN and VmaxN The calculation formula is different, and the uniform section is removed during operation. The state 4 parameters are shown in formula 1.13:

[0123]

[0124] State 2 and state 3 are only deceleration and only acceleration trajectories. This case is special and cannot be directly scaled in time, which will break the kinematics and dynamics limits. These two cases will not appear in the regular multi-axis synchronous planning, but may appear in multi-segment trajectory fusion and stop motion, so they are handled separately. When planning in step S1, it is already the time-optimal motion state, which can maximize the performance of the motor. When there is only deceleration or only acceleration, if the trajectory planning curve is scaled according to step S1, it will cause kinematic saturation and dynamic saturation, which violates the saturation limit constraint of the drive system. Therefore, when these two states occur, the original planning curve trend cannot be maintained, and the jerk acceleration or deceleration segment needs to be removed, so that it can first accelerate or decelerate at the maximum acceleration, and then decelerate or decelerate. When there is only deceleration or acceleration, there may also be an initial acceleration, for example, when there is only deceleration, the joint has a positive acceleration. At this time, if the acceleration is first reduced to 0 and then gradually increased to the maximum value of the reverse acceleration, it will cause the trajectory to produce an acceleration segment, which conflicts with the only deceleration state. Therefore, when time scaling is performed, the acceleration at this time should be ignored, and a reverse maximum acceleration should be assigned to it, and then gradually reduced to 0, so that the entire planning presents a dense to sparse state, as shown in Figure 4 State 2 is a deceleration segment,

[0125]

[0126] The current j max and T2 values are solved by formula 1.14;

[0127] State 3 is an acceleration segment, T1 is the time of the uniform acceleration segment, T2 is the time of the deceleration acceleration segment,

[0128]

[0129] The current j max and T2 values are solved by formula 1.15;

[0130] Through the above three steps, the curve graph of the trajectory and the parameters of each segment trajectory are brought into the position equation to obtain the position at any time. When executing a segment trajectory, the key parameters are first obtained by multi-axis time synchronization trajectory planning, which can reduce the calculation amount when calculating the trajectory position and improve the system running efficiency. The multi-axis time synchronization trajectory planning algorithm flow is shown in Figure 5 , and the others are the same as in example 1.

[0131] In summary, the present scheme obtains the maximum motion time by independently planning trajectories for the six axes and dividing the robot motion into four states. Based on this time, the trajectory is re-planned by applying time scaling method to the four motion states of the robot, so that it can be synchronized with multiple axes, meeting the requirements of robot kinematics and dynamics.

[0132] The present patent proposes a multi-axis time synchronization trajectory planning algorithm, which can realize multi-axis linkage and fully exert the servo performance of the motor under the premise of reducing system impact and vibration.

[0133] The algorithm analyzes the trajectory planning calculation strategy of the robot in four different states, realizes time synchronization under the premise of reducing calculation amount, modifies the trajectory, avoids violating the system saturation constraint limit, and meets the requirements of robot kinematics and dynamics.

[0134] Figure 6 The effect comparison before and after using the time synchronization trajectory planning algorithm for one axis is shown. It can be observed from the figure that the motion start and end positions of the two planning are the same, the motion time is synchronized from 1.28s to 2s, the motion time is lengthened, the speed and acceleration do not exceed the limit, and the expected effect is achieved.

[0135] Figure 7 With Figure 8 The effect diagram before and after using the multi-axis time synchronization trajectory planning algorithm for six axes is shown. Figure 7 The non-time synchronization trajectory planning motion data curve diagram is shown. It can be seen that the motion times of each axis are different. Figure 8 The time synchronization trajectory planning motion data curve diagram is shown. The motion times of the six axes are unified to one time, and the motion start and end points of each axis have not changed. The acceleration and deceleration segments of each axis are basically concentrated in the front and rear parts of the whole time. Each axis moves simultaneously and stops simultaneously, and has similar motion trend, which meets the expected effect.

Claims

1. A multi-axis time-synchronized S-shaped trajectory planning method, characterized by comprising the following steps, S1, using a segmented S-shaped trajectory planning method to independently plan the trajectory of each axis, comprising the following steps: 1) determining whether the maximum acceleration can be reached; 2) determining whether there is a uniform speed section; 3) determining whether the acceleration and deceleration sections can reach the maximum acceleration and deceleration; S2, 6-axis motion time adjustment: setting the new motion time of the remaining 5 axes to the longest motion axis time; S3, using the redefined axis parameters in step S2, synchronously scaling the 6-axis time, and re-planning the joint motion trajectory; S4, calculating the position of any trajectory according to the obtained parameters; Step S1 further comprises the following steps: the entire motion process is divided into jerk acceleration section, uniform acceleration section, deceleration section, uniform speed section, acceleration and deceleration section, uniform deceleration section, and deceleration section; set as the initial position, as the termination position, as the initial speed, as the termination speed, as the maximum speed, as the maximum acceleration, as the maximum jerk, as the jerk acceleration section time, as the acceleration section time, as the uniform speed section time, as the deceleration section time, as the deceleration section time; 1) determining whether the maximum acceleration can be reached comprises the following steps: set the maximum speed that can just reach the maximum speed but without a uniform acceleration section, as the speed at the end of the jerk acceleration section, at which time the jerk acceleration section is obtained: as the acceleration at any time in the deceleration section, the deceleration section is obtained: 1.2 According to formula 1.1 and formula 1.2, if , it indicates that the acceleration reaches the maximum value, which will cause the speed in the acceleration stage to exceed the maximum speed limit, at which time needs to be adjusted, the process is as follows: 1.3 if , which means that the maximum acceleration can be reached, there is a uniform acceleration segment, and the time of the uniform acceleration segment is The parameters are obtained as follows: 1.4 S is the total path length of the motion, and the time step of the uniform speed segment is calculated as follows: 1.5 The solution process is similar to , and the parameters of the deceleration phase of the trajectory planning can be obtained by the same method; 2) Determine whether there is a uniform speed segment, including the following steps: When , it means that there is a uniform speed segment, and the total time of the motion planning is , the state at this time is defined as state 1, , the trajectory is a 7-segment trajectory, and this state will be used in subsequent multi-axis time synchronization planning; When , it means that there is no uniform speed segment, and the maximum speed cannot be reached; assuming that the maximum acceleration and the maximum deceleration can be reached, the trajectory at this time has a jerk acceleration segment, a uniform acceleration segment, a jerk deceleration segment, a uniform deceleration segment, and a jerk deceleration segment. 1.6 The value of this time according to equation 1.4 and equation 1.6 can be calculated as The values are as follows: 1.7 Bringing into the calculation formula of , , the value of both can be obtained; 3) judging whether the acceleration section and the deceleration section can reach the maximum acceleration and deceleration includes the following steps: The value of , has been calculated in step 2), if , it means there is no acceleration section, only deceleration section, define this state as state 2, , the trajectory is 3-section trajectory; if , it means there is no deceleration section, only acceleration section, define this state as state 3, , the trajectory is 3-section trajectory; if , define this state as state 4, , the trajectory has no uniform section; when , it means the acceleration section or deceleration section cannot reach the maximum acceleration, the maximum acceleration value needs to be adjusted so that it can meet the condition, use Newton iteration method to reduce the maximum acceleration value, recalculate , , , until it meets .

2. The multi-axis time-synchronized S-curve trajectory planning method of claim 1, wherein: Step S2 specifically includes: setting the longest axis of motion time as the reference Setting the longest axis of motion time as the reference, the remaining 5-axis new motion time Setting as the time, the axis of each , , , , , , , , , Transmit to step S3.

3. The multi-axis time-synchronized S-curve trajectory planning method of claim 2, wherein: Step S3 further includes: calculating the motion time of each section and the total time by step S1, taking the new motion time as the time of re-planning, using the scaling factor to scale the acceleration section, the constant speed section and the deceleration section respectively, in step S1, when single-axis planning is performed, the trajectory is divided into four states, which are considered respectively during scaling; State 1 is a 7-segment S-shaped trajectory, set scaling factor , respectively multiply the time of each segment by the scaling factor , get the new acceleration segment time , constant speed segment time , deceleration segment time , at this time the maximum speed is set to , respectively calculate the motion distance S before and after scaling, as shown in equation 1.8: 1.8 According to equation 1.8, we have The value of the function f(x) is given by equation 1.9: 1.9 Find new After that, the time of uniform acceleration section and the maximum acceleration , is the speed at the end of the jerk section, is the speed at the end of the uniform acceleration section, is the speed at the end of the deceleration section; 1.10 From equations 1.9 and 1.10 we can solve for The values are as follows: 1.11 At this time, Take negative values; In order to obtain the re-planned parameters of all trajectories in state 1, as shown in formula 1.12: 1.12 State 4 is a non-uniform trajectory, the time scaling calculation method is similar to state 1, the formula and The calculation formula is different, and the uniform section is removed during operation. The state 4 parameters are shown in formula 1.13: 1.13 State 2 is a deceleration section, 1.14 Solve for the current value of and by equation 1.

14. State 3 is the acceleration segment, is the time for the uniform acceleration segment, is the time for the deceleration segment, 1.15 Solve for the current value of and by equation 1.

15.

4. The multi-axis time-synchronized S-curve trajectory planning method of claim 3, wherein: The curve of the trajectory and the parameters of each section of the trajectory are brought into the position equation to obtain the position at any time.

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