Robot high safety stop planning method based on generalized space and parameter normalization

Abstract

This invention discloses a high-safety stopping planning method for robots based on generalized space and parameter normalization, belonging to the field of robot control. The high-safety stopping planning method for robots based on generalized space and parameter normalization includes the following steps: Step 1: When the robot is in motion and receives a stop command, it immediately acquires the robot's velocity V in the generalized space. g0 and acceleration A g0 Step 2: Perform stopping motion planning in the generalized space, considering the kinematic constraints of maximum acceleration, to obtain the robot's starting motion from velocity V. g0 The stopping velocity curve reduced to 0. The robot high-safety stopping planning method disclosed in this invention, based on generalized space and parameter normalization, has the advantage of eliminating the dependence on caching and directly starting the stopping motion planning from the robot's current motion state, thus eliminating the memory overhead and real-time risks caused by caching.

Description

Technical Field

[0001] This invention belongs to the field of robot control, specifically relating to a high-safety stopping planning method for robots based on generalized space and parameter normalization. Background Technology

[0002] In the field of robot motion control, stopping motion planning is one of the key technologies for achieving safe and reliable robot operation. When a robot receives a stop command, it needs to quickly and smoothly complete the deceleration and stopping process without deviating from the original planned path, in order to avoid safety hazards such as mechanical impact and trajectory deviation.

[0003] The invention patent with publication number CN111015669A, entitled "An Invention Patent on a Method for Planning the Stopping Motion Trajectory of an Industrial Robot," and IPC classification number B25J9 / 16, establishes a cache to store the joint position information output by trajectory interpolation. It uses a cubic spline model to transform discrete joint positions into continuous information in the time domain and employs a time scaling method to achieve stopping planning, ensuring the continuity of the stopping process and preventing deviation from the original trajectory. However, this invention patent has the following shortcomings.

[0004] First, using a cache to store joint positions requires data migration operations in each interpolation cycle, increasing system memory overhead and CPU burden, which may affect the stability of the control cycle in embedded real-time control systems. Second, constructing a cubic spline model requires solving a large number of linear equations, resulting in high computational complexity. Frequent stopping planning leads to a significant increase in computational load, affecting the execution of other real-time response tasks and making it difficult to meet the real-time requirements of high-speed robot control. Cubic spline interpolation is sensitive to the choice of boundary conditions; different boundary conditions may lead to differences in the stopping trajectory shape, affecting the reliability and consistency of the stopping trajectory. More importantly, this invention only guarantees positional continuity. Although its second derivative (acceleration) is continuous, it does not consider kinematic constraints such as joint velocity and acceleration, and cannot guarantee that the motion parameters during the stopping process do not exceed the maximum allowable range of the joint. This poses risks such as joint overload, runaway, and damage, and may even cause serious losses.

[0005] The invention patent with publication number CN118493380A, entitled "A Method for Planning Robot Motion and Stop Instructions," and IPC classification number B25J9 / 16, controls the execution timing of trajectory planning by establishing a cached data queue and setting opening and closing thresholds, and employs a fifth-order polynomial interpolation algorithm for stopping planning. Although this invention patent controls the length of the cached data and improves cache management, it still has fundamental limitations.

[0006] First, this invention still relies on a caching mechanism. The existence of a cached data queue means the system requires additional memory space, and the asynchronous nature of data injection and consumption rates cannot be completely eliminated. When the system load fluctuates, the data queue may become empty or overflow, leading to motion stuttering or data loss. Second, the fifth-order polynomial programming only considers the boundary conditions (position, velocity, acceleration) of the start and end points, without constraining the joint velocities and accelerations during the intermediate stages of the stopping trajectory. This means that although the planned stopping trajectory has continuous endpoint states, the peak velocity at intermediate moments may far exceed the maximum allowable velocity of the joint, and the acceleration may also exceed the physical limits of the joint. Third, this invention performs polynomial fitting independently for each joint, without considering multi-axis kinematic coupling relationships. In multi-joint cooperative motion, this may cause the tool end-effector trajectory to deviate from the original motion path. Fourth, the setting of the stopping position index value depends on the amount of cached data. When the cached data is insufficient, effective stopping planning cannot be executed, limiting the robustness of the system. Fifth, the invention patent uses a multi-threaded communication mechanism, which has problems such as thread synchronization overhead, thread scheduling delay, data competition and priority inversion, which increases the real-time uncertainty of the system. In actual operation, it may cause problems such as control cycle jitter, motion stuttering, trajectory deviation or even system failure, while increasing the complexity of the system and the difficulty of debugging and maintenance.

[0007] In summary, existing stopping planning methods generally suffer from the following technical problems. First, reliance on caching modules leads to memory consumption and real-time performance risks. Second, they lack effective consideration of kinematic constraints such as maximum joint velocity and maximum acceleration, potentially causing stopping trajectories to exceed the physical limits of the joints. Third, the planning models are complex or the constraints are incomplete, making it difficult to balance computational efficiency and motion safety. These problems are particularly prominent in high-speed, heavy-duty robot applications. Therefore, there is an urgent need for a stopping planning method that does not require caching, fully considers joint physical constraints, is computationally efficient, and is safe and reliable. Summary of the Invention

[0008] This invention addresses the shortcomings of existing technologies by providing a high-safety robot stopping planning method based on generalized space and parameter normalization. It eliminates reliance on caching, directly starting stopping motion planning from the robot's current motion state, thus eliminating memory overhead and real-time performance risks associated with caching. Stopping motion planning based on generalized space ensures the time synchronization and consistency of each joint's stopping motion. Simultaneously, by introducing maximum acceleration kinematic constraints, kinematic physical limitations are directly integrated into the planning model, ensuring that the motion parameters of each joint remain within safe ranges throughout the stopping process. The stopping motion planning involves only simple arithmetic operations, eliminating the need for extensive complex calculations and guaranteeing the continuity of position, velocity, and acceleration. Parameter normalization technology achieves smooth stopping while ensuring the end-effector trajectory does not deviate from the original motion path. This invention aims to solve technical problems such as delayed stopping response, kinematic parameter exceeding limits, and trajectory deviation in existing technologies, achieving efficient, safe, real-time, and stable stopping control for industrial robots.

[0009] This invention employs the following technical solution: a robot high-safety stopping planning method based on generalized space and parameter normalization, comprising the following steps: Step 1: When the robot is in motion and receives a stop command, immediately acquire the robot's velocity V in generalized space. g0 and acceleration A g0 ; Step 2: Perform stopping motion planning in the generalized space, considering the kinematic constraints of maximum acceleration, to obtain the robot's starting motion from velocity V. g0 The stopping velocity curve when reduced to 0; Step 2 is specifically implemented as follows: First, let's define the acceleration A in the generalized space. g0 Reduce the velocity to 0, and calculate the corresponding velocity V. ga The details are as follows: (1) Among them, J g For accelerometer in generalized space, A g0 Time T required to reduce to 0 a = |A g0 / J g |;Then according to V ga The size is used to plan the stopping motion; If V ga If J is less than 0, it indicates that reverse behavior will occur, and J needs to be adjusted. g Revised to J gv ; If V ga = 0, which indicates that the J of the robot system itself in the generalized space is 0. g Just meets V gReduce to 0, then stop the exercise plan. If V ga If the value is > 0, it means that the robot's speed has not yet decreased to 0, and further stopping motion planning is needed; Step 3: Based on the stopping velocity curve obtained in Step 2, perform discrete interpolation based on parameter normalization in the generalized space to obtain the discrete interpolation position where the robot stops along the original motion path; Step 4: Project the discrete interpolation positions obtained in Step 3 onto each subspace of the generalized space to obtain the interpolation positions of each joint space; Step 5: Convert the interpolation positions of each joint space into position pulses, send them to the servo, and control the motors to stop moving until the robot speed is reduced to 0.

[0010] As a preferred technical solution to the above technical solutions, in step 1, for a robot with n degrees of freedom, the generalized space is defined as follows: if the robot moves in the task space, the generalized space is a 2-dimensional space composed of the position space and the attitude space; if the robot moves in the joint space, the generalized space is an n-dimensional space composed of n joint spaces.

[0011] As the preferred technical solution to the above technical solutions, if V ga If J is less than 0, it indicates that reverse behavior will occur, and J needs to be adjusted. g Revised to J gv The details are as follows: (2) J after modifying equation (2) gv Substituting into equation (1), it just satisfies V g Reducing it to 0 yields the velocity curve expression for the robot's stopping motion planning, as follows: (3) Where the motion time t∈[0, T] av ], after correction A g0 Time T required to reduce to 0 av = |A g0 / J gv |

[0012] As the preferred technical solution to the above technical solutions, if V ga = 0, which indicates that the J of the robot system itself in the generalized space is 0. g Just meets V g When the value decreases to 0, the motion planning ends, and the velocity curve expression for the robot's stopping motion planning is obtained as follows: (4) Where the motion time t∈[0, T] a].

[0013] As the preferred technical solution to the above technical solutions, if V ga If the value is > 0, it means that the robot's speed has not yet decreased to 0, and further stopping motion planning is needed, as follows: The velocity curve expression based on a cubic polynomial with time parameters in the generalized space is constructed as follows: (5) Wherein, the time parameter x = t / T m T m To from V ga The time to decrease to 0, t∈[0, T] m Taking the derivative of equation (5), we obtain the following expression for the acceleration curve in generalized space: (6) From equation (6), it can be seen that when x = 0.5, the acceleration reaches its maximum value, which is the maximum acceleration A in the generalized space. gmax Substituting into equation (6), we can obtain the result under the maximum acceleration constraint from V ga Deceleration time T to 0 m The calculation is as follows: (7) Substituting equation (7) into equation (5) and combining it with equation (4), we can obtain the result under the maximum acceleration constraint from V g The velocity curve expression for the motion planning to stop when the velocity decreases to 0 is as follows: (8).

[0014] As a preferred technical solution to the above technical solutions, in step 3, the velocity curve expression of the stopping motion plan obtained in step 2 is integrated to obtain the corresponding position curve expression as follows: (9) Among them, S g0 S represents the robot's position in generalized space when the stop command is received; ga For acceleration A g The robot's position when the value decreases to 0; The path length of motion in the generalized space is defined as the L2 norm of the vector whose elements are the path lengths of motion in each subspace. In the generalized space, motion with any path length can be represented by a parameter-normalized form, as follows: (10) Where u is the normalization coefficient, u∈[0,1], S0 is the starting position, S t The target location.

[0015] As the preferred technical solution above, let u be the normalization coefficient corresponding to when the robot receives the stop command. g0 The robot stopped moving in the U-shaped trajectory. g0 Based on this, position interpolation is continued to ensure that the end trajectory does not deviate from the original motion path during the stopping process; during the stopping process, the position increment ΔP(k) of the k-th control cycle is S(k) - S(k-1), where k = 1, 2, 3…n are positive integers; thus, the expression for the normalization coefficient during the stopping process is obtained as follows: (11) The discrete interpolation position is further obtained as follows: (12).

[0016] As the preferred technical solution above, step 4 is specifically implemented as follows: The subspace projection coefficient is defined as the ratio of the subspace motion path length to the generalized space motion path length. If the robot's original planned motion is in the task space, let the projection coefficients for the position space and attitude space be α and α, respectively. c1 and α c2 The discrete interpolation position P(k) in the generalized space is projected onto the position subspace and the attitude subspace as follows: (13) Among them, P c1 (k) represents the interpolation position in the location space, P c2 (k) represents the interpolation position in the attitude space; Then, the discrete interpolation positions of the obtained position subspace and attitude subspace are inversely solved into the corresponding joint space interpolation positions.

[0017] As a preferred technical solution to the above technical solutions, if the robot's original planned motion is in the joint space, let the projection coefficients of each joint subspace be α. j1 α j2 …α jn The discrete interpolation position P(k) in the generalized space is projected onto each joint subspace to obtain the interpolation position of each joint subspace, as follows: (14); Among them, P j1 (k), P j2 (k)…P jn (k) represents the interpolation position of the n joint subspaces.

[0018] The robot high-safety stopping planning method based on generalized space and parameter normalization disclosed in this invention has the following advantages: 1. It abandons the reliance on caching and directly plans the stopping motion based on the robot's current motion state, thus eliminating the memory overhead and real-time performance risks caused by caching.

[0019] 2. Based on generalized space, stop motion planning is performed to ensure the time synchronization and consistency of the stop motion of each joint.

[0020] 3. By introducing maximum acceleration kinematic constraints, kinematic physical limitations are directly integrated into the planning model, ensuring that the motion parameters of each joint are within a safe range throughout the entire stopping process.

[0021] 4. The stopping motion planning only involves simple arithmetic operations, without requiring a lot of complex calculations, and also ensures the continuity of position, velocity, and acceleration.

[0022] 5. By employing parameter normalization technology, a smooth stop is ensured while maintaining the end-effector trajectory within the original motion path, thereby achieving efficient, safe, real-time, and stable stopping control of industrial robots. Attached Figure Description

[0023] Figure 1 This is a flowchart of the present invention.

[0024] Figure 2 This is a graph showing the velocity and acceleration curves of the robot stopping process according to the present invention.

[0025] Figure 3 This is a position trajectory diagram of the robot in Cartesian space according to the present invention. Detailed Implementation

[0026] This invention discloses a high-safety stopping planning method for robots based on generalized space and parameter normalization. The following describes a preferred embodiment (Embodiment 1), with reference to the accompanying drawings. Figures 1 to 3 The specific embodiments of the present invention will be further described below.

[0027] Example 1.

[0028] See attached diagram. Figures 1 to 3 Preferably, the robot high-safety stopping planning method based on generalized space and parameter normalization includes the following steps: Step 1: When the robot is in motion and receives a stop command, immediately acquire the robot's velocity V in generalized space. g0 and acceleration A g0 ; Step 2: Perform stopping motion planning in the generalized space, considering the kinematic constraints of maximum acceleration, to obtain the robot's starting motion from velocity V. g0 The stopping velocity curve when reduced to 0; Step 2 is specifically implemented as follows: First, let's define the acceleration A in the generalized space.g0 Reduce the velocity to 0, and calculate the corresponding velocity V. ga The details are as follows: (1) Among them, J g For accelerometer in generalized space, A g0 Time T required to reduce to 0 a = |A g0 / J g |;Then according to V ga The size is used to plan the stopping motion; If V ga If J is less than 0, it indicates that reverse behavior will occur, and J needs to be adjusted. g Revised to J gv ; If V ga = 0, which indicates that the J of the robot system itself in the generalized space is 0. g Just meets V g Reduce to 0, then stop the exercise plan. If V ga If the value is > 0, it means that the robot's speed has not yet decreased to 0, and further stopping motion planning is needed; Step 3: Based on the stopping velocity curve obtained in Step 2, perform discrete interpolation based on parameter normalization in the generalized space to obtain the discrete interpolation position where the robot stops along the original motion path; Step 4: Project the discrete interpolation positions obtained in Step 3 onto each subspace of the generalized space to obtain the interpolation positions of each joint space; Step 5: Convert the interpolation positions of each joint space into position pulses, send them to the servo, and control the motors to stop moving until the robot speed is reduced to 0.

[0029] In step 1, for a robot with n degrees of freedom, the generalized space is defined as follows: if the robot moves in the task space, the generalized space is a 2-dimensional space composed of the position space and the attitude space; if the robot moves in the joint space, the generalized space is an n-dimensional space composed of n joint spaces.

[0030] Where V ga If J is less than 0, it indicates that reverse behavior will occur, and J needs to be adjusted. g Revised to J gv The details are as follows: (2) J after modifying equation (2) gv Substituting into equation (1), it just satisfies V g Reducing it to 0 yields the velocity curve expression for the robot's stopping motion planning, as follows: (3) Where the motion time t∈[0, T] av ], after correction A g0 Time T required to reduce to 0 av = |A g0 / J gv |

[0031] Where V ga = 0, which indicates that the J of the robot system itself in the generalized space is 0. g Just meets V g When the value decreases to 0, the motion planning ends, and the velocity curve expression for the robot's stopping motion planning is obtained as follows: (4) Where the motion time t∈[0, T] a ].

[0032] Where V ga If the value is > 0, it means that the robot's speed has not yet decreased to 0, and further stopping motion planning is needed, as follows: The velocity curve expression based on a cubic polynomial with time parameters in the generalized space is constructed as follows: (5) Wherein, the time parameter x = t / T m T m To from V ga The time to decrease to 0, t∈[0, T] m Taking the derivative of equation (5), we obtain the following expression for the acceleration curve in generalized space: (6) From equation (6), it can be seen that when x = 0.5, the acceleration reaches its maximum value, which is the maximum acceleration A in the generalized space. gmax Substituting into equation (6), we can obtain the result under the maximum acceleration constraint from V ga Deceleration time T to 0 m The calculation is as follows: (7) Substituting equation (7) into equation (5) and combining it with equation (4), we can obtain the result under the maximum acceleration constraint from V g The velocity curve expression for the motion planning to stop when the velocity decreases to 0 is as follows: (8).

[0033] In step 3, the velocity curve expression of the stopping motion plan obtained in step 2 is integrated to obtain the corresponding position curve expression as follows: (9) Among them, S g0 S represents the robot's position in generalized space when the stop command is received; ga For acceleration A g The robot's position when the value decreases to 0; The path length of motion in the generalized space is defined as the L2 norm of the vector whose elements are the path lengths of motion in each subspace. In the generalized space, motion with any path length can be represented by a parameter-normalized form, as follows: (10) Where u is the normalization coefficient, u∈[0,1], S0 is the starting position, S t The target location.

[0034] Let u be the normalization coefficient corresponding to when the robot receives the stop command. g0 The robot stopped moving in the U-shaped trajectory. g0 Based on this, position interpolation is continued to ensure that the end trajectory does not deviate from the original motion path during the stopping process; during the stopping process, the position increment ΔP(k) = S(k) - S(k-1) in the k-th control cycle, where k = 1,2,3…n are positive integers; thus, the expression for the normalization coefficient during the stopping process is obtained as follows: (11) The discrete interpolation position is further obtained as follows: (12).

[0035] Step 4 is specifically implemented as follows: The subspace projection coefficient is defined as the ratio of the subspace motion path length to the generalized space motion path length. If the robot's original planned motion is in the task space, let the projection coefficients for the position space and attitude space be α and α, respectively. c1 and α c2 The discrete interpolation position P(k) in the generalized space is projected onto the position subspace and the attitude subspace as follows: (13) Among them, P c1 (k) represents the interpolation position in the location space, P c2 (k) represents the interpolation position in the attitude space; Then, the discrete interpolation positions of the obtained position subspace and attitude subspace are inversely solved into the corresponding joint space interpolation positions.

[0036] If the robot's original planned motion is in joint space, let the projection coefficients of each joint subspace be α. j1 α j2 …α jn The discrete interpolation position P(k) in the generalized space is projected onto each joint subspace to obtain the interpolation position of each joint subspace, as follows: (14); Among them, P j1 (k), P j2 (k)…P jn (k) represents the interpolation position of the n joint subspaces.

[0037] Based on this, the overall concept of the robot high-safety stopping planning method based on generalized space and parameter normalization disclosed in this embodiment is further elaborated.

[0038] Specifically, firstly, when the robot receives a stop command while it is in motion, it immediately acquires the robot's velocity V in the generalized space. g0 and acceleration A g0 Then, stopping motion planning considering kinematic constraints is performed. Next, discrete interpolation based on parameter normalization is performed. Then, the discrete interpolation positions are projected and mapped to each subspace. Finally, the interpolation positions are converted into position pulses, which are sent to the servo to control the motor to stop the motion. Based on multiple experiments, this application proposes a high-safety stopping planning method for robots based on generalized space and parameter normalization. By stopping motion planning based on generalized space, the temporal synchronization consistency of the stopping motion of each joint is guaranteed. At the same time, by introducing the maximum acceleration kinematic constraint into the stopping motion planning, the kinematic physical constraints are directly integrated into the planning model, ensuring that the motion parameters of each joint are within a safe range throughout the stopping process. The stopping motion planning only involves simple arithmetic operations, without a large number of complex calculations, and also ensures the continuity of position, velocity, and acceleration. The parameter normalization technology achieves smooth stopping while ensuring that the end-effector trajectory does not deviate from the original motion path, realizing efficient, safe, real-time, and stable stopping control of industrial robots.

[0039] Based on this, the experimental verification of the robot high-safety stopping planning method based on generalized space and parameter normalization disclosed in this embodiment is further elaborated.

[0040] Specifically, in the experiment, a six-DOF robot was given to move in joint space. The initial and final positions of joints 1 to 6 were -150º~150º, -100º~60º, -160º~30º, -200º~200º, -130º~130º, and -140º~140º, respectively. The generalized spatial maximum acceleration A was... gmax1200º•s -2 When the robot moves to position S in generalized space g0 At (300º), a stop command is executed. At this time, the robot control system acquires the velocity V in the generalized space. g0 (450º•s) -1 ) and acceleration A g0 (-600º•s) -2 Immediately initiate a stop plan and halt the movement. For example... Figure 2 The image shows the velocity and acceleration curves during the robot's stopping process. Figure 2 As can be seen from the upper part, in the generalized space, at t=0s, the robot's velocity increases from 450º•s. -1 The deceleration process begins smoothly and continuously, reaching zero at t=0.6375s, at which point the stopping process ends. Simultaneously, it can be seen that projecting the generalized space onto joint spaces 1, 2, and 3 according to the corresponding projection coefficients causes each joint to undergo corresponding stopping and deceleration movements in its respective subspace. Throughout the entire stopping and deceleration process, all joints maintain temporal synchronization, reaching zero velocity simultaneously at t=0.6375s. From... Figure 2 The lower half shows that, in generalized space, at t=0s, the robot's acceleration changes from negative to 600º•s. -2 The acceleration begins to decrease, reaching zero at t=0.12s. Then, the acceleration increases negatively, reaching its maximum absolute value A at t=0.37875s. gmax Then, the acceleration decreases, reaching zero at t=0.6375s. Clearly, throughout the entire stopping process, the acceleration remains continuous and always within the maximum safety limit. Simultaneously, it can be seen that projecting the generalized space onto joint spaces 1, 2, and 3 according to the corresponding projection coefficients ensures that the acceleration changes in each joint space remain time-synchronized, the acceleration remains continuous, and the acceleration always remains within the maximum safety limit.

[0041] Furthermore, such as Figure 3 The image shows the position trajectories of the robot's joints in Cartesian space after forward solving. From... Figure 3 As can be seen from this, the robot is in P s Point P starts moving along the planned path. g0 The motion stops at point P, eventually coming to a stop. gd Point, the movement stops and ends. P gd To P e The curve segment represents the trajectory not traversed in the original planned path. Clearly, the stopping planning method of this application can achieve a smooth stop while ensuring that the final trajectory does not deviate from the original motion path.

[0042] It is worth mentioning that the servo motors and servo drives involved in this invention should be considered as prior art. The specific structure, working principle, control methods, and spatial arrangement of these technical features can be conventionally selected in the field and should not be regarded as the inventive point of this invention. This invention will not be further elaborated in detail.

[0043] For those skilled in the art, modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of this invention should be included within the protection scope of this invention.

Claims

1. A high-safety stopping planning method for robots based on generalized space and parameter normalization, characterized in that, Includes the following steps: Step 1: When the robot is in motion and receives a stop command, immediately acquire the robot's velocity V in generalized space. g0 and acceleration A g0 ; Step 2: Perform stopping motion planning in the generalized space, considering the kinematic constraints of maximum acceleration, to obtain the robot's starting motion from velocity V. g0 The stopping velocity curve when reduced to 0; Step 2 is specifically implemented as follows: First, let's define the acceleration A in the generalized space. g0 Reduce the velocity to 0, and calculate the corresponding velocity V. ga The details are as follows: 　（1） Among them, J g For accelerometer in generalized space, A g0 Time T required to reduce to 0 a = |A g0 / J g |;Then according to V ga The size is used to plan the stopping motion; If V ga If J is less than 0, it indicates that reverse behavior will occur, and J needs to be adjusted. g Revised to J gv ; If V ga = 0, which indicates that the J of the robot system itself in the generalized space is 0. g Just meets V g Reduce to 0, then stop the exercise plan. If V ga If the value is > 0, it means that the robot's speed has not yet decreased to 0, and further stopping motion planning is needed; Step 3: Based on the stopping velocity curve obtained in Step 2, perform discrete interpolation based on parameter normalization in the generalized space to obtain the discrete interpolation position where the robot stops along the original motion path; Step 4: Project the discrete interpolation positions obtained in Step 3 onto each subspace of the generalized space to obtain the interpolation positions of each joint space; Step 5: Convert the interpolation positions of each joint space into position pulses, send them to the servo, and control the motors to stop moving until the robot speed is reduced to 0.

2. The robot high-safety stopping planning method based on generalized space and parameter normalization according to claim 1, characterized in that, In step 1, for a robot with n degrees of freedom, the generalized space is defined as: if the robot moves in the task space, the generalized space is a 2-dimensional space composed of the position space and the attitude space. If a robot moves in joint space, the generalized space is an n-dimensional space composed of n joint spaces.

3. The robot high-safety stopping planning method based on generalized space and parameter normalization according to claim 1, characterized in that, If V ga If J is less than 0, it indicates that reverse behavior will occur, and J needs to be adjusted. g Revised to J gv The details are as follows: 　（2） J after modifying equation (2) gv Substituting into equation (1), it just satisfies V g Reducing it to 0 yields the velocity curve expression for the robot's stopping motion planning, as follows: 　（3） Where the motion time t∈[0, T] av ], after correction A g0 Time T required to reduce to 0 av = |A g0 / J gv | 4. The robot high-safety stopping planning method based on generalized space and parameter normalization according to claim 1, characterized in that, If V ga = 0, which indicates that the J of the robot system itself in the generalized space is 0. g Just meets V g When the value decreases to 0, the motion planning ends, and the velocity curve expression for the robot's stopping motion planning is obtained as follows: 　（4） Where the motion time t∈[0, T] a ].

5. The robot high-safety stopping planning method based on generalized space and parameter normalization according to claim 1, characterized in that, If V ga If the value is > 0, it means that the robot's speed has not yet decreased to 0, and further stopping motion planning is needed, as follows: The velocity curve expression based on a cubic polynomial with time parameters in the generalized space is constructed as follows: 　（5） Wherein, the time parameter x = t / T m T m To from V ga The time to decrease to 0, t∈[0, T] m Taking the derivative of equation (5), we obtain the following expression for the acceleration curve in generalized space: 　（6） From equation (6), it can be seen that when x = 0.5, the acceleration reaches its maximum value, which is the maximum acceleration A in the generalized space. gmax Substituting into equation (6), we can obtain the result under the maximum acceleration constraint from V ga Deceleration time T to 0 m The calculation is as follows: 　（7） Substituting equation (7) into equation (5) and combining it with equation (4), we can obtain the result under the maximum acceleration constraint from V g The velocity curve expression for the motion planning to stop when the velocity decreases to 0 is as follows: 　（8）。 6. The robot high-safety stopping planning method based on generalized space and parameter normalization according to claim 1, characterized in that, In step 3, the velocity curve expression for the stopping motion plan obtained in step 2 is integrated to obtain the corresponding position curve expression as follows: 　（9） Among them, S g0 S represents the robot's position in generalized space when the stop command is received; ga For acceleration A g The robot's position when the value decreases to 0; The path length of motion in the generalized space is defined as the L2 norm of the vector whose elements are the path lengths of motion in each subspace. In the generalized space, motion with any path length can be represented by a parameter-normalized form, as follows: 　（10） Where u is the normalization coefficient, u∈[0,1], S0 is the starting position, S t The target location.

7. The robot high-safety stopping planning method based on generalized space and parameter normalization according to claim 6, characterized in that, Let u be the normalization coefficient corresponding to when the robot receives the stop command. g0 The robot stopped moving in the U-shaped trajectory. g0 Based on this, position interpolation is continued to ensure that the end trajectory does not deviate from the original motion path during the stopping process; During the stopping process, the position increment ΔP(k) in the k-th control cycle is ΔP(k) = S(k) - S(k-1), where k = 1, 2, 3…n are positive integers; thus, the expression for the normalized coefficients during the stopping process is: 　（11） The discrete interpolation position is further obtained as follows: 　（12）。 8. The robot high-safety stopping planning method based on generalized space and parameter normalization according to claim 1, characterized in that, Step 4 is implemented in the following steps: The subspace projection coefficient is defined as the ratio of the subspace motion path length to the generalized space motion path length. If the robot's original planned motion is in the task space, let the projection coefficients for the position space and attitude space be α and α, respectively. c1 and α c2 The discrete interpolation position P(k) in the generalized space is projected onto the position subspace and the attitude subspace as follows: 　（13） Among them, P c1 (k) represents the interpolation position in the location space, P c2 (k) represents the interpolation position in the attitude space; Then, the discrete interpolation positions of the obtained position subspace and attitude subspace are inversely solved into the corresponding joint space interpolation positions.

9. The robot high-safety stopping planning method based on generalized space and parameter normalization according to claim 8, characterized in that, If the robot's original planned motion is in joint space, let the projection coefficients of each joint subspace be α. j1 α j2 …α jn The discrete interpolation position P(k) in the generalized space is projected onto each joint subspace to obtain the interpolation position of each joint subspace, as follows: 　（14）； Among them, P j1 (k), P j2 (k)…P jn (k) represents the interpolation position of the n joint subspaces.

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