Motion control method and device of parallel 3RRS robot, parallel 3RRS robot and medium

Abstract

The present disclosure relates to the technical field of robot control, in particular to a motion control method and device of a parallel 3RRS robot, the parallel 3RRS robot and a medium. The robot comprises a base platform, a moving platform and three RRS chains connecting the base platform and the moving platform. The method comprises: obtaining target attitude information and target position information of the moving platform; based on the structure parameters of the RRS chain in the zero position state and the target attitude information and the target position information, calculating the center coordinates of a first planar figure formed by the center of the spherical hinge joint of the moving platform; calculating the spherical hinge joint center coordinates accordingly; projecting the spherical hinge joint center coordinates into a second planar figure determined by the first connecting rod of the corresponding chain and the Z-axis of the base coordinate system; based on the projected point coordinates, solving the target rotation angle of each first rotation joint; and finally driving each joint to move the moving platform to the target position and attitude. By converting the complex space problem into a planar geometry problem, the calculation is simple, which is conducive to high-precision and high-efficiency real-time control.

Description

Technical Field

[0001] This disclosure relates to the field of robot control technology, specifically to a motion control method, device, parallel 3RRS robot, and medium for a parallel 3RRS robot. Background Technology

[0002] In the field of industrial automation and intelligent manufacturing, parallel robots have been widely used in various work scenarios such as assembly, processing, and material handling due to their significant advantages such as high precision, high rigidity, and high dynamic response. Among them, parallel robots, as a typical parallel mechanism, have shown great application potential in many complex tasks due to their unique structural design and motion characteristics.

[0003] In the motion control of parallel robots, inverse kinematics is a core and crucial step. Inverse kinematics aims to accurately solve for the parameters of each driven joint based on the known target pose of the moving platform, thereby achieving precise control of the moving platform's pose. Accurate and efficient inverse kinematics algorithms are essential for ensuring the robot moves along the expected trajectory and improving operational accuracy and efficiency.

[0004] Currently, numerical iteration is a common method for realizing the inverse kinematics of parallel robots. Based on the idea of ​​iterative approximation, the numerical iteration method first sets initial guesses for the drive joint parameters based on experience, simplified models, or random generation. Then, the initial values ​​are substituted into the forward kinematics model to calculate the actual pose of the moving platform under the current drive parameters. Next, an error function is constructed by comparing the error between the actual pose and the target pose. Then, based on a selected iterative algorithm, such as the Newton-Raphson method or genetic algorithm, the drive joint parameters are corrected, gradually approximating the target pose of the moving platform. This process of forward kinematics calculation, error comparison, and parameter correction is repeated until the error meets the preset accuracy requirements; the corresponding drive joint parameters at this point represent the desired inverse kinematics solution.

[0005] However, numerical iterative methods have revealed several problems in practical applications that urgently need to be addressed. First, convergence is a significant issue. The choice of initial guess values ​​has a decisive impact on convergence. If the initial values ​​deviate significantly from the true solution, the iteration process may fail to converge to the true solution, or even diverge. For example, in complex poses, inappropriate initial values ​​can easily cause the iteration to get stuck in local optima, unable to escape and find the global optimum, leading to inverse kinematics failure. Second, computational efficiency is low. Each iteration requires forward kinematics calculations and error function construction. For complex parallel robots, forward kinematics calculations are inherently complex, and the number of iterations is often large, significantly increasing the overall computation time. This makes it difficult to meet the stringent requirements of real-time control for rapid response, limiting the robot's application in high-speed operation scenarios. Third, accuracy is constrained by various factors. For example, measurement errors generated when sensors measure the pose of the moving platform directly interfere with the iteration direction in the error function; rounding errors during the calculation process also accumulate with the increase of iterations, further reducing the solution accuracy and causing a significant deviation between the final inverse solution and the true solution, affecting the robot's operational accuracy. Fourth, it is extremely sensitive to singular configurations. Near singular configurations, the Jacobian matrix is ​​reduced in rank, and the first derivative information of the error function may be inaccurate or unable to provide an effective iteration direction, leading to instability in the iteration process, or even preventing it from continuing. This not only seriously affects the reliability and accuracy of the inverse solution, but may also cause the robot to be unable to move normally or to exhibit abnormal movement near singular configurations, posing safety hazards to actual production operations.

[0006] In summary, traditional inverse kinematics solutions for parallel robots cannot meet the requirements of high-precision, high-real-time online motion control. Overcoming at least one of the problems existing in traditional inverse kinematics solutions for parallel robots, and providing an inverse kinematics solution that is computationally simple, has clear physical concepts, and can guarantee accurate solutions throughout the entire workspace, in order to achieve high-precision, high-efficiency real-time control of parallel robots in real-time control applications, is an urgent problem to be solved. Summary of the Invention

[0007] To address the problems in the related technologies, this disclosure provides a motion control method, apparatus, parallel 3RRS robot, and medium for a parallel 3RRS robot.

[0008] In a first aspect, this disclosure provides a motion control method for a parallel 3RRS robot. The parallel 3RRS robot includes a base platform and a moving platform, the base platform and the moving platform being connected by three RRS branches. Each RRS branch, starting from the base platform, includes a first rotary joint, a first link, a second rotary joint, a second link, and a ball joint connected in series. The method includes:

[0009] The target attitude information and target position information of the moving platform in the target pose state are obtained. The target attitude information includes: the angle between the rotation axis vector of the moving platform in the XY plane of the base coordinate system and the X-axis and the angle of rotation of the moving platform around the rotation axis. The target position information includes: the displacement of the center point of the moving platform relative to the zero position state along the Z-axis of the base coordinate system.

[0010] Based on the structural parameters of any RRS branch in the zero-position state, the target attitude information, and the target position information, calculate the center coordinates of the first planar figure determined by the center of each ball joint of the three RRS branches in the target attitude state.

[0011] Calculate the coordinates of the center of the ball joint of any RRS branch in the target pose state in the base coordinate system based on the center coordinates of the first planar graphic in the target pose state;

[0012] The coordinates of the projection point of the center of the ball joint of any RRS branch onto the second plane figure determined by the first link of any RRS branch and the Z-axis of the base coordinate system are obtained based on the coordinates of the center of the ball joint of any RRS branch in the base coordinate system.

[0013] The rotation angle of the first rotary joint of any RRS branch in the target pose state is calculated based on the coordinates of the projection point of the center of the ball joint of any RRS branch onto the second planar figure.

[0014] The moving platform is driven to the target pose state based on the rotation angle of the first rotary joint of each RRS branch in the target pose state.

[0015] According to an embodiment of this disclosure, the three RRS branches include: a first RRS branch, a second RRS branch, and a third RRS branch. The first planar shape is a triangle. The center of the ball joint of each RRS branch is distributed on the first circumference by equal circular arcs, and the center of the first rotary joint of each RRS branch is distributed on the second circumference by equal circular arcs. When the moving platform is in the zero position state, the centers of the first and second circumferences overlap with the projection of the origin of the base coordinate system onto the Z-axis of the base coordinate system. The positive X-axis direction of the XY plane of the base coordinate system is the radial direction from the origin of the base coordinate system to the center of the first rotary joint of any RRS branch. The positive Y-axis direction of the XY plane of the base coordinate system is determined by rotating the X-axis counterclockwise by 90 degrees.

[0016] According to an embodiment of this disclosure, calculating the center coordinates of the first planar shape determined by the centers of each ball joint in the target pose state based on the structural parameters of any RRS branch in the zero-position state, the target attitude information, and the target position information includes:

[0017] Based on the structural parameters of any RRS branch in the zero-position state, calculate the height of the center point of the moving platform in the zero-position state;

[0018] Based on the height of the center point of the moving platform in the zero position state, the target posture information, and the target position information, calculate the center coordinates of the first planar graphic in the target posture state;

[0019] The structural parameters of any RRS branch include: the coordinates of the first rotary joint of any RRS branch in the base coordinate system, the length of the first link, the length of the second link, the offset of the ball joint and the moving platform in the Z-axis direction of the base coordinate system, and the radius of the first circumference. The calculation of the height of the center point of the moving platform in the zero-position state based on the structural parameters of any RRS branch in the zero-position state includes:

[0020] The height of the center point of the moving platform in the zero-position state is calculated using the following formula. :

[0021] ;

[0022] The step of calculating the center coordinates of the first planar graphic in the target pose state based on the height of the center point of the moving platform in the zero-position state, the target posture information, and the target position information includes:

[0023] The center coordinates of the first planar figure in the target pose state are calculated using the following formula. :

[0024] ;

[0025] ;

[0026] ;

[0027] ;

[0028] in, The X-coordinate represents the center coordinate. The Y-coordinate represents the center coordinate. The Z-coordinate represents the center coordinate. This represents the angle between the rotation axis vector of the moving platform in the XY plane of the base coordinate system and the X-axis. This represents the angle of rotation of the moving platform about the rotation axis. and The units are all in radians. This represents the displacement of the center point of the moving platform relative to its zero-position state along the Z-axis of the base coordinate system. This represents the offset of the ball joint of any RRS branch relative to the moving platform in the Z-axis direction of the base coordinate system. This indicates the height of the center point of the moving platform in the target pose state. This represents the radius of the first circle. This represents the length of the first link of any of the RRS branches. This represents the length of the second link in any of the RRS branches. This represents the X-coordinate of the first rotary joint of any RRS branch in the base coordinate system. The Z-coordinate of the first rotary joint of any RRS branch in the base coordinate system is represented.

[0029] According to an embodiment of this disclosure, calculating the coordinates of the center of the ball joint of any RRS branch in the target pose state in the base coordinate system based on the center coordinates of the first planar graphic in the target pose state includes:

[0030] Obtaining the attitude rotation matrix of the first planar figure based on the target attitude information includes: obtaining the attitude rotation matrix of the first planar figure using the following formula. :

[0031] , ;

[0032] in, Represents the identity matrix. The unit column vector representing the axis of rotation. express The transpose of the matrix, express antisymmetric matrix, This represents the angle between the rotation axis vector of the moving platform in the XY plane of the base coordinate system and the X-axis. This represents the angle of rotation of the moving platform about the rotation axis. and The units are all in radians;

[0033] Based on the center coordinates of the first planar graphic in the target pose state and the attitude rotation matrix of the first planar graphic, calculate the coordinates of the center of the ball joint of any RRS branch in the target pose state in the base coordinate system, including:

[0034] When any of the RRS branches is the first RRS branch, the coordinates of the center of the ball joint of the first RRS branch in the base coordinate system under the target pose state are calculated by the following formula. :

[0035] ;

[0036] When any of the RRS branches is the second RRS branch, the coordinates of the center of the ball joint of the second RRS branch in the base coordinate system under the target pose state are calculated by the following formula. :

[0037] ;

[0038] When any of the RRS branches is the third RRS branch, the coordinates of the center of the ball joint of the third RRS branch in the base coordinate system under the target pose state are calculated by the following formula. :

[0039] ;

[0040] ;

[0041] ;

[0042] in, This represents the center coordinates of the first planar graphic in the target pose state. The X-coordinate represents the center coordinate. The Y-coordinate represents the center coordinate. The Z-coordinate represents the center coordinate. This represents the radius of the first circle. This represents the rotation matrix of the first RRS branch rotating 120 degrees around the Z-axis of the base coordinate system. This represents the rotation matrix of the first RRS branch rotating 240 degrees around the Z-axis of the base coordinate system.

[0043] According to an embodiment of this disclosure, obtaining the coordinates of the projection point of the center of the ball joint of any RRS branch onto the second plane figure determined by the first link of the any RRS branch and the Z-axis of the base coordinate system based on the coordinates of the center of the ball joint of any RRS branch in the base coordinate system includes:

[0044] The coordinates of the projection point of the center of the ball joint of the first RRS branch onto the second planar figure are obtained by the following formula. :

[0045] ;

[0046] The coordinates of the projection point of the center of the ball joint of the second RRS branch onto the second planar figure are obtained by the following formula. :

[0047] ;

[0048] The coordinates of the projection point of the center of the ball joint of the third RRS branch onto the second planar figure are obtained by the following formula. :

[0049] ;

[0050] in, This represents the X-coordinate of the center of the ball joint of the first RRS branch in the base coordinate system. This represents the Y-coordinate of the center of the ball joint of the first RRS branch in the base coordinate system. This represents the Z-coordinate of the center of the ball joint of the first RRS branch in the base coordinate system. This represents the X-coordinate of the center of the ball joint of the second RRS branch in the base coordinate system. This represents the Y-coordinate of the center of the ball joint of the second RRS branch in the base coordinate system. The Z-coordinate represents the coordinate of the center of the ball joint of the second RRS branch in the base coordinate system. The X-coordinate of the center of the ball joint of the third RRS branch in the base coordinate system. The Y-coordinate of the center of the ball joint of the third RRS branch in the base coordinate system. The Z-coordinate represents the coordinates of the center of the ball joint of the third RRS branch in the base coordinate system.

[0051] According to an embodiment of this disclosure, calculating the rotation angle of the first rotary joint of any RRS branch in the target pose state based on the coordinates of the projection point of the center of the ball joint of any RRS branch onto the second planar graphic includes:

[0052] The joint angle is calculated based on the coordinates of the first rotary joint in any RRS branch in the base coordinate system, the length of the first link, the length of the second link, and the coordinates of the projection point of the center of the ball joint onto the second planar figure. The joint angle refers to the interior angle of the triangle formed by the projection points of the centers of the first rotary joint, the second rotary joint, and the ball joint in any RRS branch onto the second planar figure, with the first rotary joint in any RRS branch as the vertex.

[0053] The azimuth angle of the projection point is calculated based on the coordinates of the first rotary joint in any RRS branch in the base coordinate system and the coordinates of the projection point of the center of the ball joint projected onto the second planar figure. The azimuth angle of the projection point refers to the angle between the vector from the first rotary joint in any RRS branch to the projection point and the preset reference direction in the second planar figure. The preset reference direction in the second planar figure includes: the positive X-axis direction of the base coordinate system, or the projection of the positive X-axis direction of the base coordinate system onto the second planar figure.

[0054] The difference between the azimuth angle of the projection point and the joint angle is used as the rotation angle of the first rotary joint of any RRS branch in the target pose state.

[0055] According to embodiments of this disclosure, the joint angle is calculated using the following formula. :

[0056] , ;

[0057] ;

[0058] ;

[0059] in, This represents the coordinates of the first rotational joint in any of the RRS branches. This represents the X-coordinate of the first rotary joint of any RRS branch in the base coordinate system. This represents the Z-coordinate of the first rotary joint of any RRS branch in the base coordinate system. This represents the coordinates of the projection point of the center of the ball joint of any RRS branch onto the second planar figure. The X-coordinate represents the coordinates of the projection point of the center of the ball joint of any RRS branch onto the second planar figure. The Z-coordinate represents the coordinates of the projection point of the center of the ball joint of any RRS branch onto the second planar figure. This represents the Euclidean distance from the first rotational joint in any of the RRS branches to the projection point. This represents the length of the first link of any of the RRS branches. This indicates the length of the second link of any of the RRS branches;

[0060] The azimuth angle of the projection point is calculated using the following formula. :

[0061] ;

[0062] in, Represents the inverse cosine function. Represents the arctangent function;

[0063] The rotation angle of the first rotational joint of any RRS branch in the target pose state is calculated using the following formula. :

[0064] .

[0065] Secondly, this disclosure provides a motion control device for a parallel 3RRS robot. The parallel 3RRS robot includes a base platform and a moving platform, the base platform and the moving platform being connected by three RRS branches. Each RRS branch, starting from the base platform, includes a first rotary joint, a first link, a second rotary joint, a second link, and a ball joint connected in sequence. The device includes:

[0066] The target pose information acquisition module is configured to: acquire the target pose information and target position information of the moving platform in the target pose state. The target pose information includes: the angle between the rotation axis vector of the moving platform in the XY plane of the base coordinate system and the X-axis and the angle of rotation of the moving platform around the rotation axis. The target position information includes: the displacement of the center point of the moving platform relative to the zero position state along the Z-axis of the base coordinate system.

[0067] The first planar graphic center coordinate calculation module is configured to: calculate the center coordinates of the first planar graphic determined by the center of each ball joint in the target pose state based on the structural parameters of any RRS branch in the zero position state, the target posture information, and the target position information;

[0068] The ball joint center coordinate calculation module is configured to: calculate the coordinates of the center of the ball joint of any RRS branch in the target pose state in the base coordinate system based on the center coordinates of the first planar graphic in the target pose state;

[0069] The ball joint center projection point coordinate calculation module is configured to: obtain the coordinates of the projection point of the center of the ball joint of any RRS branch onto the second plane figure determined by the first link of any RRS branch and the Z-axis of the base coordinate system based on the coordinates of the center of the ball joint of any RRS branch in the base coordinate system.

[0070] The first rotary joint rotation angle calculation module is configured to: calculate the rotation angle of the first rotary joint of any RRS branch in the target pose state based on the coordinates of the projection point of the center of the ball joint of any RRS branch onto the second planar graphic.

[0071] The motion platform drive module is configured to drive the motion platform to the target pose state based on the rotation angle of the first rotary joint of each RRS branch in the target pose state.

[0072] Secondly, this disclosure provides a parallel 3RRS robot, which includes a base platform and a moving platform. The base platform and the moving platform are connected by three RRS branches. Each RRS branch, starting from the base platform, includes a first rotary joint, a first link, a second rotary joint, a second link, and a ball joint connected in series. The parallel 3RRS robot also includes a memory and a processor. The memory stores one or more computer instructions, which are executed by the processor to implement the method described in any of the first aspects.

[0073] Thirdly, this disclosure provides a computer-readable storage medium having computer instructions stored thereon, which, when executed by a processor, implement the method described in any of the first aspects.

[0074] According to the technical solution provided in this disclosure, a motion control method for a parallel 3RRS robot based on the principle of "two-projection dimensionality reduction" is provided. Its core is to decompose the complex spatial kinematics problem into a simple planar geometric solution through two key geometric projections: First, based on the structural parameters of any RRS branch in the zero position state and the target attitude information and target position information of the moving platform in the target pose state (wherein, the target attitude information includes: the angle between the rotation axis vector of the moving platform in the XY plane of the base coordinate system and the X-axis and the angle of rotation of the moving platform around the rotation axis, and the target position information includes: the displacement of the center point of the moving platform relative to the zero position state along the Z-axis direction of the base coordinate system), the center coordinates of the first planar figure determined by the center of each ball joint of the three RRS branches in the target pose state are calculated. Then, based on the center coordinates of the first planar graphic in the target pose state, the coordinates of the center of the ball joint of any RRS branch in the target pose state in the base coordinate system are calculated; then, based on the coordinates of the center of the ball joint of any RRS branch in the base coordinate system in the base coordinate system, the coordinates of the projection point of the center of the ball joint of any RRS branch onto the second planar graphic determined by the first link of any RRS branch and the Z-axis of the base coordinate system are obtained; finally, based on the coordinates of the projection point of the center of the ball joint of any RRS branch onto the second planar graphic in the target pose state, the rotation angle of the first rotary joint of any RRS branch in the target pose state is calculated, and based on the rotation angle of the first rotary joint of each RRS branch in the target pose state in the target pose state, the moving platform is driven to the target pose state.

[0075] The technical solution disclosed herein avoids the traditional complex spatial vector iterative solution, and instead transforms the three-dimensional problem into a two-dimensional plane problem through geometric projection, realizing the closed form of the inverse kinematics solution. The calculation process is simple and efficient, without iterative convergence problems, which is particularly beneficial for the high-precision and high-real-time control of robots.

[0076] It should be understood that the above general description and the following detailed description are exemplary and explanatory only, and are not intended to limit this disclosure. Attached Figure Description

[0077] Other features, objects, and advantages of this disclosure will become more apparent from the following detailed description of non-limiting embodiments, taken in conjunction with the accompanying drawings. In the drawings:

[0078] Figure 1 A structural diagram of a parallel 3RRS robot according to an embodiment of the present disclosure is shown.

[0079] Figure 2A schematic diagram of the structural state of a parallel 3RRS robot in a zero-position state according to an embodiment of the present disclosure is shown.

[0080] Figure 3 A flowchart illustrating a motion control method for a parallel 3RRS robot according to an embodiment of the present disclosure is shown.

[0081] Figure 4 A schematic diagram of a second planar graphic in a target pose state according to an embodiment of the present disclosure is shown;

[0082] Figure 5 A flowchart illustrating a method for calculating the rotation angle of a first rotary joint of any RRS branch in a target pose state, according to an embodiment of the present disclosure;

[0083] Figure 6 A structural block diagram of a motion control device for a parallel 3RRS robot according to an embodiment of the present disclosure is shown.

[0084] Figure 7 A structural block diagram of a parallel 3RRS robot according to an embodiment of the present disclosure is shown. Detailed Implementation

[0085] In the following, exemplary embodiments of the present disclosure will be described in detail with reference to the accompanying drawings to enable those skilled in the art to readily implement them. Furthermore, for clarity, portions unrelated to the description of exemplary embodiments have been omitted from the drawings.

[0086] In this disclosure, it should be understood that terms such as “comprising” or “having” are intended to indicate the presence of features, figures, steps, behaviors, components, parts or combinations thereof disclosed in this specification, and are not intended to exclude the possibility of the presence or addition of one or more other features, figures, steps, behaviors, components, parts or combinations thereof.

[0087] It should also be noted that, unless otherwise specified, the embodiments and features described in this disclosure can be combined with each other. This disclosure will now be described in detail with reference to the accompanying drawings and embodiments.

[0088] In this disclosure, any operation involving the acquisition of user information or user data, or the display of user information or user data to others, is an operation authorized or confirmed by the user, or actively selected by the user.

[0089] As mentioned earlier, traditional parallel 3RRS robot inverse kinematics solution schemes have many problems, such as complex calculation process, low efficiency, and unfavorable to real-time control, which cannot meet the requirements of high-precision and high real-time online motion control.

[0090] In order to achieve high-precision and high-efficiency real-time control of parallel 3RRS robots in real-time control applications and meet the computational requirements for continuous motion of robots along complex Cartesian paths, this disclosure provides an efficient inverse kinematics motion control method for parallel 3RRS robots based on geometric analysis and non-iterative methods. This method can directly calculate the precise rotation angles of the three drive joints (corresponding to the first rotational joint in this disclosure) based only on the two rotational degrees of freedom and one translational degree of freedom of the moving platform.

[0091] Figure 1 A structural diagram of a parallel 3RRS robot according to an embodiment of the present disclosure is shown. Figure 1 As shown, the parallel 3RRS robot includes a base platform and a moving platform. The base platform and the moving platform are connected by three RRS branches. Each RRS branch, starting from the base platform, includes a first rotary joint, a first link, a second rotary joint, a second link, and a ball joint connected in series. In "3RRS", the first "R" represents the active rotary joint located on the base platform, i.e., the drive joint, corresponding to the "first rotary joint" in this disclosure. This is the robot's drive source, directly controlled by a motor. The second "R" represents the passive rotary joint located in the middle of the branch, corresponding to the "second rotary joint" in this disclosure. "S" represents the "ball joint" in this disclosure, and the number "3" indicates that there are three identical RRS branches.

[0092] In one implementation of this disclosure, the base platform and moving platform of the parallel 3RRS robot are both rigid hexagonal flat plates. On the base platform, there are three mounting seats for the first rotary joints arranged in equal arcs (i.e., spaced 120 degrees apart). The moving platform is the robot's end effector, used to mount tools (such as rackets, lenses, machining spindles, etc.), and is the component that directly performs the task. It also has three mounting seats for ball joints arranged in equal arcs. Furthermore, the three RRS branches of the parallel 3RRS robot are completely identical, meaning they have the same structural connections and structural parameters. The three RRS branches include: a first RRS branch, a second RRS branch, and a third RRS branch. Each branch is a power transmission unit from the base platform to the moving platform. The first rotary joint is a driven joint, mounted on a mounting base on the base platform, and directly driven by a servo motor. Its rotational motion is the input for the entire mechanism's motion. The upper end of the first link is connected to the second rotary joint, and the lower end is connected to the first rotary joint, transmitting the rotation of the first rotary joint to the middle of the branch. The second rotary joint is a passive joint, located at the connection between the first and second links, allowing the second link to rotate relative to the first link in one degree of freedom. It does not have a driver; its motion is passively determined by the geometric constraints of the entire mechanism, typically achieved using hinges or bearings. The upper end of the second link is connected to a ball joint, and the lower end is connected to the second rotary joint, transmitting motion from the middle of the branch to the moving platform. The ball joint is also a passive joint, mounted on a mounting base on the moving platform, connecting the second link and the moving platform. It allows the second link to rotate relative to the moving platform in any direction, thus adapting to the complex spatial attitude changes of the moving platform.

[0093] Figure 2 A schematic diagram of the structural state of a parallel 3RRS robot in a zero-position state according to an embodiment of the present disclosure is shown. Figure 2As shown, the coordinate system of the moving platform is the moving platform coordinate system, with its origin at O', which is usually the geometric center of the moving platform. The coordinate system of the base platform is the base coordinate system, with its origin at O, which is usually the geometric center of the base platform. The positive X-axis of the XY plane of the base coordinate system points from the origin O to the radial direction of the center of the first rotary joint of any RRS branch. The positive Y-axis of the XY plane of the base coordinate system is determined by rotating the X-axis counterclockwise by 90 degrees. The center arcs (i.e., spaced 120 degrees apart) of the ball joints of each RRS branch are distributed on the first circumference, with the center of this first circumference being O1. The center arcs of the first rotary joints of each RRS branch are distributed on the second circumference, with the center of this first circumference being O2. When the moving platform is in the zero position, the center O1 of the first circumference and the center O2 of the second circumference overlap with the projection of the origin O of the base coordinate system and the origin O' of the moving platform coordinate system onto the Z-axis of the base coordinate system. The moving platform is in a standard, untilted posture. In the most typical case, the plane of the moving platform is parallel to the plane determined by the first circumference, the plane determined by the second circumference, and the plane of the base platform. The center point of the moving platform is at a known and determined initial height. The Z-axis of the moving platform coordinate system coincides with that of the base coordinate system. After the moving platform tilts, the direction of the Z-axis of the moving platform coordinate system also changes, always remaining perpendicular to the plane of the moving platform.

[0094] Figure 3 A flowchart illustrating a motion control method for a parallel 3RRS robot according to an embodiment of the present disclosure is shown. The motion control method of the present disclosure can be executed by the real-time control system of the parallel 3RRS robot, specifically invoked within each control cycle of each Cartesian space trajectory. It is responsible for converting high-level spatial motion commands into low-level joint angle commands in real time and analytically, and then sending the joint angle commands to the low-level servo drivers. The servo drivers control the motors to rotate to a specified angle, thereby driving the motion platform to actually move to the desired target pose.

[0095] like Figure 3 As shown, the method includes the following steps S310~S360:

[0096] In step S310, the target attitude information and target position information of the moving platform in the target pose state are obtained. The target attitude information includes: the angle between the rotation axis vector of the moving platform in the XY plane of the base coordinate system and the X-axis and the angle of rotation of the moving platform around the rotation axis. The target position information includes: the displacement of the center point of the moving platform relative to the zero position state along the Z-axis direction of the base coordinate system.

[0097] The target pose state refers to the specific position and orientation in space that the system expects the moving platform of the parallel 3RRS robot to ultimately reach at a certain moment. In this disclosure, the target pose state is defined by an intuitive geometric model. Specifically, the orientation of the moving platform is understood as starting from the "zero position state" and rotating by an angle around a specific axis k in the XY plane of the base coordinate system. As a result, this specific axis k is determined by the angle between it and the X-axis or Y-axis of the base coordinate system. The only certainty is that any spatial orientation of the moving platform can be determined by ( , These two parameters precisely describe the position of the moving platform; the position of the moving platform is simplified to the height change of the center point of the moving platform along the Z-axis of the base coordinate system relative to the zero-position state. .

[0098] Because the rotation axis of the moving platform in this disclosure is constrained to lie within the XY plane of the base coordinate system, that is, the center point of the moving platform is constrained to move only in the Z direction within the XY plane, any instantaneous rotation axis that causes the platform to tilt must lie within the XY plane. This means that the parallel 3RRS robot in this disclosure has two rotational degrees of freedom (2R) and one translational degree of freedom (1T) during motion. The center point of the moving platform can move up and down along the Z-axis of the base coordinate system, while translation within the XY plane of the base coordinate system is constrained. It should be noted that when the moving platform tilts ( When (≠0), its center point will also experience a small coupling displacement in the XY plane, but this disclosure uses geometric relationships to connect it with ( , , ) related, therefore It serves as the primary, independent control input.

[0099] When acquiring the target posture information and target position information of the moving platform in the target pose state, one scenario is: if the real-time control system or user interface that calls the motion control method of this disclosure is specifically designed for the method of this disclosure, then it can directly generate or receive (…). , , These three parameters can be set by the operator via a joystick, knob, or direct input, or the motion trajectory can be pre-planned by an advanced planner, where each path point is represented as a series of ( , , (t is time); another case is: in most parallel robot systems, the target pose is usually described by a position vector and an attitude matrix or equivalent quaternions, Euler angles, etc. In this case, a conversion process is needed to transform it into the publicly available ( , , ).

[0100] The transformation process is roughly as follows: After obtaining the coordinates P_target of the moving platform's center point in the base coordinate system and the rotation matrix R_target of the moving platform's coordinate system relative to the base coordinate system, the height z_init of the moving platform's center point in the zero-position state is first obtained from system memory or through calculation. The displacement is then calculated based on the Z-coordinate components in z_init and P_target. Subsequently, since the rotation model disclosed herein is a rotation about a specific axis k in the XY plane, while the general R_target may correspond to a more complex rotation sequence, it is necessary to inversely solve from R_target to obtain the single rotation axis and angle that are most equivalent to it.

[0101] First, calculate the equivalent rotation axis and angle. Since for any rotation matrix R, there exists an equivalent rotation axis u and angle, which can be obtained through the trace or eigenvalue decomposition of the matrix, as shown in the formula:

[0102] ;

[0103] in, Representation matrix The trace is the sum of its main diagonal elements.

[0104] The rotation axis vector u can then be calculated by solving... We obtain the unit rotation axis vector, where, Since this disclosure requires the rotation axis to be in the XY plane of the base coordinate system, the projection of u on the XY plane is taken. After normalizing this projection vector, the atan2 function is used to calculate the angle between this unit vector and the X-axis, i.e. .

[0105] The above conversion process essentially transforms any six-degree-of-freedom pose of the moving platform into the actual achievable pose of the mechanism. The result obtained through this conversion process... and Close to the original .

[0106] According to embodiments of this disclosure, in order to prevent the obtained parameters from being invalid, the range of values ​​in which the parameters are valid can be set according to the actual structural parameters and task requirements, for example: Then, after obtaining the parameters ( , , After that, the obtained (position pose parameter range) is determined according to the preset working position parameter range. , , If the parameter is within the specified range, it is invalid and an error message will be returned; if it is, the following steps will be executed.

[0107] This disclosure uses three input parameters when performing inverse solution calculations. , , Compared to existing technologies that use six degrees of freedom parameters (such as three position coordinates and three Euler angles), this method offers the following advantages:

[0108] 1. When there are six input parameters, solving inverse kinematics often requires dealing with more complex nonlinear equations, involving iterative calculations, matrix inversion, etc., which is computationally burdensome. However, when there are three input parameters in this disclosure, since all subsequent calculations are based on the analytical formulas of these three input parameters, the amount of computation is small, the steps are fixed, and the computational efficiency is significantly improved. This can easily meet the needs of high-frequency real-time control of robots (such as thousands of control cycles per second), making it possible for high-speed and high-dynamic performance operations.

[0109] 2. Parameters and The terms "tilt in which direction" and "tilt by how much" directly correspond to "how much to rise or fall." This description perfectly matches the actual motion pattern of parallel robots, making the physical meaning more intuitive and simplifying trajectory planning.

[0110] 3. The three input parameters ( , , This directly corresponds to the actual physical degrees of freedom, describing all and only the possible poses that the mechanism can reach. Therefore, any valid set of inputs corresponds to a target pose that the mechanism can reach, thus avoiding redundant parameters and unsolvable situations from the outset.

[0111] 4. Since the solution process is based on geometric projection and trigonometry, the calculation of the final driving angle depends on the arccosine and arctangent functions, which are well-state within their domains. This method avoids the numerical computation difficulties commonly encountered in 6-DOF modeling due to the singularity of the Jacobian matrix (such as failure to invert the matrix, joint velocities tending to infinity, etc.), and eliminates the numerical problems caused by singular configurations.

[0112] This solution is particularly suitable for precise motion control of robots within their local workspace. A typical application scenario is achieving the balancing and juggling of a ping-pong ball. This disclosure provides an efficient, precise, and real-time solution to address the most critical and frequent "attitude-height" adjustment problem in this task. Specifically, to maintain the ball's balance on the racket face or achieve rhythmic juggling, the moving platform (racket) needs to continuously adjust its pitch and roll to compensate for the ball's positional shift. This corresponds precisely to... (Direction of rotation axis) and The two posture input parameters are (rotation angle). During the juggling process, the racket needs to move vertically up and down to contact the bottom of the ball at the right time and with the right amount of energy, which corresponds to the dz (height displacement) input parameter. Furthermore, the dynamic changes of the ping-pong ball are extremely rapid, requiring the control system to have extremely low response delay. The inverse kinematics analytical solution provided in this disclosure is fast to calculate and highly deterministic, meeting the stringent requirements of high-frequency real-time control—an advantage that traditional iterative solution methods cannot match. In addition, when implementing the control logic, the output of the upper-level intelligent control algorithm (such as a vision-based PID controller or a reinforcement learning controller) can be directly mapped to the input of the motion control method of this disclosure. For example: the controller calculates that the racket needs to tilt forward by 5 degrees → converts to (…). , For example: the controller calculates that the racket needs to tilt 3 degrees to the right and rise 2cm → converts to ( , , This direct mapping relationship greatly simplifies the architecture of the entire software system.

[0113] In step S320, based on the structural parameters of any RRS branch in the zero-position state, the target posture information, and the target position information, the center coordinates of the first planar figure determined by the centers of the ball joints of the three RRS branches in the target posture state are calculated.

[0114] like Figure 2 As shown, the structural parameters of any RRS branch include: the coordinates of the first rotational joint of any RRS branch in the base coordinate system. Length of the first link The length of the second link The offset between the ball joint and the moving platform in the Z-axis direction of the base coordinate system. and the radius of the first circumference .

[0115] According to embodiments of this disclosure, based on the structural parameters of any RRS branch in the zero-position state, the target attitude information, and the target position information, the center coordinates of the first planar shape determined by the centers of each ball joint in the target pose state are calculated, including:

[0116] Based on the structural parameters of any RRS branch in the zero-position state, calculate the height of the center point of the moving platform in the zero-position state.

[0117] Based on the height of the center point of the moving platform in the zero-position state, the target posture information, and the target position information, the center coordinates of the first planar graphic in the target posture state are calculated.

[0118] The first planar figure is a triangle formed by the centers of three ball hinges. The motion of this figure represents the overall pose (position and attitude) of the moving platform in space.

[0119] Specifically, calculating the height of the center point of the moving platform in the zero-position state based on the structural parameters of any RRS branch in the zero-position state includes:

[0120] Based on the Pythagorean theorem, combined with Figure 2 As shown, the height of the center point of the moving platform in the zero-position state is calculated using the following formula. :

[0121] ;

[0122] The step of calculating the center coordinates of the first planar graphic in the target pose state based on the height of the center point of the moving platform in the zero-position state, the target posture information, and the target position information includes:

[0123] Due to the orientation of the rotary joints, it is obvious that each RRS branch consists of two links (the first link and the second link) and moves in a plane. Therefore, during the movement of the mechanism, the angle between the center of the ball joint and the X-axis of the base coordinate system remains unchanged. Thus, based on the relationship that the centers of the three ball joints on the moving platform remain on the planes defined by their respective branches, the center coordinates of the first planar figure in the target pose state can be calculated using the following formula. :

[0124] ;

[0125] ;

[0126] ;

[0127] ;

[0128] in, The X-coordinate represents the center coordinate. The Y-coordinate represents the center coordinate. The Z-coordinate represents the center coordinate. This represents the angle between the rotation axis vector of the moving platform in the XY plane of the base coordinate system and the X-axis. This represents the angle of rotation of the moving platform about the rotation axis. and The units are all in radians. This represents the displacement of the center point of the moving platform relative to its zero-position state along the Z-axis of the base coordinate system. This represents the offset of the ball joint of any RRS branch relative to the moving platform in the Z-axis direction of the base coordinate system. This indicates the height of the center point of the moving platform in the target pose state. This represents the radius of the first circle. This represents the length of the first link of any of the RRS branches. This represents the length of the second link in any of the RRS branches. This represents the X-coordinate of the first rotary joint of any RRS branch in the base coordinate system. The Z-coordinate of the first rotary joint of any RRS branch in the base coordinate system is represented.

[0129] In step S330, the coordinates of the center of the ball joint of any RRS branch in the target pose state are calculated in the base coordinate system based on the center coordinates of the first planar graphic in the target pose state.

[0130] According to an embodiment of this disclosure, calculating the coordinates of the center of the ball joint of any RRS branch in the target pose state in the base coordinate system based on the center coordinates of the first planar graphic in the target pose state includes:

[0131] First, the attitude rotation matrix of the first planar figure is obtained based on the target attitude information, including: obtaining the attitude rotation matrix of the first planar figure using the following formula. :

[0132] , ;

[0133] in, Represents the identity matrix. The unit column vector representing the axis of rotation. express The transpose of the matrix, express antisymmetric matrix, This represents the angle between the rotation axis vector of the moving platform in the XY plane of the base coordinate system and the X-axis. This represents the angle of rotation of the moving platform about the rotation axis. and The units are all in radians.

[0134] According to the definition of an antisymmetric matrix in mathematical relations, then: .

[0135] Then, based on the center coordinates of the first planar graphic in the target pose state and the attitude rotation matrix of the first planar graphic, the coordinates of the center of the ball joint of any RRS branch in the target pose state in the base coordinate system are calculated, including:

[0136] When any of the RRS branches is the first RRS branch, the coordinates of the center of the ball joint of the first RRS branch in the base coordinate system under the target pose state are calculated by the following formula. :

[0137] ;

[0138] When any of the RRS branches is the second RRS branch, the coordinates of the center of the ball joint of the second RRS branch in the base coordinate system under the target pose state are calculated by the following formula. :

[0139] ;

[0140] When any of the RRS branches is the third RRS branch, the coordinates of the center of the ball joint of the third RRS branch in the base coordinate system under the target pose state are calculated by the following formula. :

[0141] ;

[0142] ;

[0143] ;

[0144] in, This represents the center coordinates of the first planar graphic in the target pose state. The X-coordinate represents the center coordinate. The Y-coordinate represents the center coordinate. The Z-coordinate represents the center coordinate. This represents the radius of the first circle. This represents the rotation matrix of the first RRS branch rotating 120 degrees around the Z-axis of the base coordinate system. This represents the rotation matrix of the first RRS branch rotating 240 degrees around the Z-axis of the base coordinate system.

[0145] In step S340, the coordinates of the projection point of the center of the ball joint of any RRS branch onto the second plane figure determined by the first link of any RRS branch and the Z-axis of the base coordinate system are obtained according to the coordinates of the center of the ball joint of any RRS branch in the base coordinate system.

[0146] When solving the inverse kinematics, the center point of the ball joint in space is vertically projected onto the second planar graph corresponding to its branch. After this projection, the RRS kinematic chain of each branch in space is simplified to the inverse kinematics problem of a planar two-bar linkage within its second planar graph. For each branch, the plane defined by the first link of that branch and the Z-axis of the base coordinate system is the second planar graph. This plane includes the driving joint (first rotary joint) and the main motion plane of that branch. Figure 4 A schematic diagram of a second planar shape in a target pose state according to an embodiment of the present disclosure is shown. In the second planar shape, a triangle is formed by the projection point S of the center of the first rotary joint R1, the first link, the second rotary joint R2, the second link of any RRS branch, and the ball joint of any RRS branch onto the second planar shape. Within the second planar shape, the present disclosure utilizes the law of cosines and inverse trigonometric functions to directly and analytically solve for the rotation angle of the first rotary joint in the target pose state, without iteration, resulting in extremely high computational efficiency. This principle cleverly avoids the difficulty of solving complex spatial nonlinear equations in traditional methods, decomposing the problem through geometric projection, realizing a closed form (analytical solution) of the inverse kinematics solution, and ensuring computational efficiency and determinism.

[0147] According to an embodiment of this disclosure, obtaining the coordinates of the projection point of the center of the ball joint of any RRS branch onto the second plane figure determined by the first link of the any RRS branch and the Z-axis of the base coordinate system based on the coordinates of the center of the ball joint of any RRS branch in the base coordinate system includes:

[0148] The coordinates of the projection point of the center of the ball joint of the first RRS branch onto the second planar figure are obtained by the following formula. :

[0149] ;

[0150] The coordinates of the projection point of the center of the ball joint of the second RRS branch onto the second planar figure are obtained by the following formula. :

[0151] ;

[0152] The coordinates of the projection point of the center of the ball joint of the third RRS branch onto the second planar figure are obtained by the following formula. :

[0153] ;

[0154] in, This represents the X-coordinate of the center of the ball joint of the first RRS branch in the base coordinate system. This represents the Y-coordinate of the center of the ball joint of the first RRS branch in the base coordinate system. This represents the Z-coordinate of the center of the ball joint of the first RRS branch in the base coordinate system. This represents the X-coordinate of the center of the ball joint of the second RRS branch in the base coordinate system. This represents the Y-coordinate of the center of the ball joint of the second RRS branch in the base coordinate system. The Z-coordinate represents the coordinate of the center of the ball joint of the second RRS branch in the base coordinate system. The X-coordinate of the center of the ball joint of the third RRS branch in the base coordinate system. The Y-coordinate of the center of the ball joint of the third RRS branch in the base coordinate system. The Z-coordinate represents the coordinates of the center of the ball joint of the third RRS branch in the base coordinate system.

[0155] In step S350, the rotation angle of the first rotary joint of any RRS branch in the target pose state is calculated based on the coordinates of the projection point of the center of the ball joint of any RRS branch onto the second planar graphic.

[0156] Figure 5 A flowchart illustrating a method for calculating the rotation angle of a first rotary joint of any RRS branch in a target pose state, according to an embodiment of the present disclosure. Figure 5 As shown, the step of calculating the rotation angle of the first rotary joint of any RRS branch in the target pose state based on the coordinates of the projection point of the center of the ball joint of any RRS branch onto the second planar figure includes the following steps S351~S353:

[0157] In step S351, the joint angle is calculated based on the coordinates of the first rotary joint in any RRS branch in the base coordinate system, the length of the first link, the length of the second link, and the coordinates of the projection point of the center of the ball joint onto the second planar figure. The joint angle refers to the interior angle of the triangle formed by the projection points of the centers of the first rotary joint, the second rotary joint, and the ball joint in any RRS branch onto the second planar figure, with the first rotary joint in any RRS branch as the vertex.

[0158] like Figure 4 As shown, the joint angle is... Specifically, the joint angle is calculated using the following formula. :

[0159] , ;

[0160] ;

[0161] ;

[0162] in, This represents the coordinates of the first rotational joint in any of the RRS branches. This represents the X-coordinate of the first rotary joint of any RRS branch in the base coordinate system. This represents the Z-coordinate of the first rotary joint of any RRS branch in the base coordinate system. This represents the coordinates of the projection point of the center of the ball joint of any RRS branch onto the second planar figure. The X-coordinate represents the coordinates of the projection point of the center of the ball joint of any RRS branch onto the second planar figure. The Z-coordinate represents the coordinates of the projection point of the center of the ball joint of any RRS branch onto the second planar figure. This represents the Euclidean distance from the first rotational joint in any of the RRS branches to the projection point. This represents the length of the first link of any of the RRS branches. This indicates the length of the second link of any of the RRS branches.

[0163] when When the absolute value is greater than 1, it indicates that the given parameter ( , , If the error exceeds the working range of the mechanism and there is no solution, you can return an error message or enter safe mode to avoid subsequent calculation errors.

[0164] In step S352, the azimuth angle of the projection point is calculated based on the coordinates of the first rotary joint in any RRS branch in the base coordinate system and the coordinates of the projection point of the center of the ball joint projected onto the second planar figure. The azimuth angle of the projection point refers to the angle between the vector from the first rotary joint in any RRS branch to the projection point and the preset reference direction in the second planar figure. The preset reference direction in the second planar figure includes: the positive X-axis direction of the base coordinate system, or the projection of the positive X-axis direction of the base coordinate system onto the second planar figure.

[0165] like Figure 4 As shown, the azimuth angle of the projection point is the angle between the side formed by points S and R1 in the triangle and the positive direction of the X-axis of the base coordinate system. Specifically, the azimuth angle of the projection point is calculated using the following formula. :

[0166] ;

[0167] in, Represents the inverse cosine function. This represents the arctangent function.

[0168] In step S353, the difference between the azimuth angle of the projection point and the joint angle is used as the rotation angle of the first rotary joint of any RRS branch in the target pose state.

[0169] Specifically, the rotation angle of the first rotary joint of any RRS branch in the target pose state is calculated using the following formula. :

[0170] .

[0171] like Figure 4 As shown, the rotation angle of the first rotary joint of any RRS branch in the target pose state. It is the angle between the side formed by points R1 and R2 in the triangle and the positive direction of the X-axis of the base coordinate system.

[0172] Specifically, the coordinates of the projection point of the center of the ball joint of the first RRS branch onto the second planar figure. The coordinates of the projection point of the center of the ball joint of the second RRS branch onto the second planar figure are as follows: The coordinates of the projection point of the center of the ball joint of the third RRS branch onto the second planar figure are as follows: In the specific solution, it can be based on... , , After obtaining the joint angles and projection point azimuths of the corresponding RRS branches, finally based on The rotation angle of the first rotational joint of each RRS branch in the target pose state is obtained.

[0173] The disclosed technical solution utilizes ingenious geometric projection for dimensionality reduction decomposition, integrating pose parameterization, symmetric structure modeling, coordinate analytical calculation, key geometric projection, and planar trigonometric solving. Its core advantage lies in transforming the complex spatial inverse kinematics problem of parallel mechanisms into a series of direct and efficient analytical calculations, ultimately obtaining a closed-form solution for the driving joint angles. This results in superior computational efficiency and reliability compared to traditional numerical iteration or complex spatial vector methods.

[0174] In step S360, the moving platform is driven to the target pose state based on the rotation angle of the first rotary joint of each RRS branch in the target pose state.

[0175] In one implementation of this disclosure, the central controller generates drive commands based on the rotation angles of the first rotary joints of the three RRS branches in the target pose state, and synchronously sends them to the servo drivers corresponding to each branch via a high-speed real-time communication bus. After receiving the commands, the drivers form closed-loop control based on the position feedback of the built-in encoders, and precisely drive the motors to rotate to the target angle. The rotation of the motors is ultimately converted into the coordinated spatial motion of the three ball joints through the mechanical transmission of the RRS branches, which together constrain and guide the moving platform to accurately reach the target pose state.

[0176] Figure 6 A structural block diagram of a motion control device for a parallel 3RRS robot according to an embodiment of the present disclosure is shown. The parallel 3RRS robot includes a base platform and a moving platform, the base platform and the moving platform being connected by three RRS branches. Each RRS branch, starting from the base platform, includes a first rotary joint, a first link, a second rotary joint, a second link, and a ball joint connected in series. Figure 6As shown, the motion control device 600 of the parallel 3RRS robot includes: a target pose information acquisition module, configured to acquire target pose information and target position information of the moving platform in the target pose state, wherein the target pose information includes: the angle between the rotation axis vector of the moving platform in the XY plane of the base coordinate system and the X-axis and the angle of rotation of the moving platform around the rotation axis, and the target position information includes: the displacement of the center point of the moving platform relative to the zero position state along the Z-axis direction of the base coordinate system; a first planar graphic center coordinate calculation module, configured to calculate the center coordinates of the first planar graphic determined by the centers of each ball joint in the target pose state based on the structural parameters of any RRS branch in the zero position state, the target pose information, and the target position information; and a ball joint center coordinate calculation module, configured to calculate the center coordinates of the first planar graphic in the target pose state based on the center coordinates of the first planar graphic. The system calculates the coordinates of the center of the ball joint of any RRS branch in the base coordinate system under the target pose state; the ball joint center projection point coordinate calculation module is configured to: obtain the coordinates of the projection point of the center of the ball joint of any RRS branch onto the second plane figure determined by the first link of any RRS branch and the Z-axis of the base coordinate system based on the coordinates of the center of the ball joint of any RRS branch in the base coordinate system; the first rotation joint rotation angle calculation module is configured to: calculate the rotation angle of the first rotation joint of any RRS branch in the target pose state based on the coordinates of the projection point of the center of the ball joint of any RRS branch onto the second plane figure; the moving platform driving module is configured to: drive the moving platform to the target pose state based on the rotation angle of the first rotation joint of each RRS branch in the target pose state.

[0177] This disclosure also provides a parallel 3RRS robot. Figure 7 A structural block diagram of a parallel 3RRS robot according to an embodiment of the present disclosure is shown, as follows: Figure 7 As shown, the parallel 3RRS robot includes a base platform and a moving platform. The base platform and the moving platform are connected by three RRS branches. Each RRS branch, starting from the base platform, includes a first rotary joint, a first link, a second rotary joint, a second link, and a ball joint connected in series. The parallel 3RRS robot also includes a memory and a processor. The memory stores one or more computer instructions, which are executed by the processor to implement the method described in any of the above embodiments.

[0178] This disclosure also provides a computer-readable storage medium, which may be a computer-readable storage medium included in the electronic device or computer system described in the above embodiments; or it may be a standalone computer-readable storage medium not assembled into a device. The computer-readable storage medium stores one or more programs, which are used by one or more processors to perform the methods described in this disclosure.

[0179] This disclosure also provides a computer program product, including a computer program that, when executed by a processor, implements any of the methods described in this disclosure.

[0180] The above description is merely a preferred embodiment of this disclosure and an explanation of the technical principles employed. Those skilled in the art should understand that the scope of the invention involved in this disclosure is not limited to technical solutions formed by specific combinations of the above-described technical features, but should also cover other technical solutions formed by arbitrary combinations of the above-described technical features or their equivalents without departing from the inventive concept. For example, technical solutions formed by substituting the above-described features with (but not limited to) technical features disclosed in this disclosure that have similar functions.

Claims

1. A motion control method for a parallel 3RRS robot, characterized in that, The parallel 3RRS robot includes a base platform and a moving platform, the base platform and the moving platform being connected by three RRS branches. Each RRS branch, starting from the base platform, includes a first rotary joint, a first link, a second rotary joint, a second link, and a ball joint connected in series. The method includes: The target attitude information and target position information of the moving platform in the target pose state are obtained. The target attitude information includes: the angle between the rotation axis vector of the moving platform in the XY plane of the base coordinate system and the X-axis and the angle of rotation of the moving platform around the rotation axis. The target position information includes: the displacement of the center point of the moving platform relative to the zero position state along the Z-axis of the base coordinate system. Based on the structural parameters of any RRS branch in the zero-position state, the target attitude information, and the target position information, calculate the center coordinates of the first planar figure determined by the center of each ball joint of the three RRS branches in the target attitude state. Calculate the coordinates of the center of the ball joint of any RRS branch in the target pose state in the base coordinate system based on the center coordinates of the first planar graphic in the target pose state; The coordinates of the projection point of the center of the ball joint of any RRS branch onto the second plane figure determined by the first link of any RRS branch and the Z-axis of the base coordinate system are obtained based on the coordinates of the center of the ball joint of any RRS branch in the base coordinate system. The rotation angle of the first rotary joint of any RRS branch in the target pose state is calculated based on the coordinates of the projection point of the center of the ball joint of any RRS branch onto the second planar figure. The moving platform is driven to the target pose state based on the rotation angle of the first rotary joint of each RRS branch in the target pose state.

2. The method according to claim 1, characterized in that, The three RRS branches include: a first RRS branch, a second RRS branch, and a third RRS branch. The first planar shape is a triangle. The center of the ball joint of each RRS branch is distributed on the first circumference by equal circular arcs, and the center of the first rotary joint of each RRS branch is distributed on the second circumference by equal circular arcs. When the moving platform is in the zero position, the centers of the first and second circumferences overlap with the projection of the origin of the base coordinate system onto the Z-axis of the base coordinate system. The positive X-axis of the XY plane of the base coordinate system is the radial direction from the origin of the base coordinate system to the center of the first rotary joint of any RRS branch. The positive Y-axis of the XY plane of the base coordinate system is determined by rotating the X-axis counterclockwise by 90 degrees.

3. The method according to claim 2, characterized in that, The step of calculating the center coordinates of the first planar shape determined by the centers of each ball joint in the target pose state based on the structural parameters of any RRS branch in the zero-position state, the target attitude information, and the target position information includes: Based on the structural parameters of any RRS branch in the zero-position state, calculate the height of the center point of the moving platform in the zero-position state; Based on the height of the center point of the moving platform in the zero position state, the target posture information, and the target position information, calculate the center coordinates of the first planar graphic in the target posture state; The structural parameters of any RRS branch include: the coordinates of the first rotary joint of any RRS branch in the base coordinate system, the length of the first link, the length of the second link, the offset of the ball joint and the moving platform in the Z-axis direction of the base coordinate system, and the radius of the first circumference. The calculation of the height of the center point of the moving platform in the zero-position state based on the structural parameters of any RRS branch in the zero-position state includes: The height of the center point of the moving platform in the zero-position state is calculated using the following formula. : ； The step of calculating the center coordinates of the first planar graphic in the target pose state based on the height of the center point of the moving platform in the zero-position state, the target posture information, and the target position information includes: The center coordinates of the first planar figure in the target pose state are calculated using the following formula. : ； ； ； ； in, The X-coordinate represents the center coordinate. The Y-coordinate represents the center coordinate. The Z-coordinate represents the center coordinate. This represents the angle between the rotation axis vector of the moving platform in the XY plane of the base coordinate system and the X-axis. This represents the angle of rotation of the moving platform about the rotation axis. and The units are all in radians. This represents the displacement of the center point of the moving platform relative to its zero-position state along the Z-axis of the base coordinate system. This represents the offset of the ball joint of any RRS branch relative to the moving platform in the Z-axis direction of the base coordinate system. This indicates the height of the center point of the moving platform in the target pose state. This represents the radius of the first circle. This represents the length of the first link of any of the RRS branches. This represents the length of the second link in any of the RRS branches. This represents the X-coordinate of the first rotary joint of any RRS branch in the base coordinate system. The Z-coordinate of the first rotary joint of any RRS branch in the base coordinate system is represented.

4. The method according to claim 2, characterized in that, The step of calculating the coordinates of the center of the ball joint of any RRS branch in the target pose state in the base coordinate system based on the center coordinates of the first planar graphic in the target pose state includes: Obtaining the attitude rotation matrix of the first planar figure based on the target attitude information includes: obtaining the attitude rotation matrix of the first planar figure using the following formula. : ， ； in, Represents the identity matrix. The unit column vector representing the axis of rotation. express The transpose of the matrix, express antisymmetric matrix, This represents the angle between the rotation axis vector of the moving platform in the XY plane of the base coordinate system and the X-axis. This represents the angle of rotation of the moving platform about the rotation axis. and The units are all in radians; Based on the center coordinates of the first planar graphic in the target pose state and the attitude rotation matrix of the first planar graphic, calculate the coordinates of the center of the ball joint of any RRS branch in the target pose state in the base coordinate system, including: When any of the RRS branches is the first RRS branch, the coordinates of the center of the ball joint of the first RRS branch in the base coordinate system under the target pose state are calculated by the following formula. : ； When any of the RRS branches is the second RRS branch, the coordinates of the center of the ball joint of the second RRS branch in the base coordinate system under the target pose state are calculated by the following formula. : ； When any of the RRS branches is the third RRS branch, the coordinates of the center of the ball joint of the third RRS branch in the base coordinate system under the target pose state are calculated by the following formula. : ； ； ； in, This represents the center coordinates of the first planar graphic in the target pose state. The X-coordinate represents the center coordinate. The Y-coordinate represents the center coordinate. The Z-coordinate represents the center coordinate. This represents the radius of the first circle. This represents the rotation matrix of the first RRS branch rotating 120 degrees around the Z-axis of the base coordinate system. This represents the rotation matrix of the first RRS branch rotating 240 degrees around the Z-axis of the base coordinate system.

5. The method according to claim 2, characterized in that, The step of obtaining the coordinates of the projection point of the center of the ball joint of any RRS branch onto the second plane figure determined by the first link of the RRS branch and the Z-axis of the base coordinate system based on the coordinates of the center of the ball joint of any RRS branch in the base coordinate system includes: The coordinates of the projection point of the center of the ball joint of the first RRS branch onto the second planar figure are obtained by the following formula. : ； The coordinates of the projection point of the center of the ball joint of the second RRS branch onto the second planar figure are obtained by the following formula. : ； The coordinates of the projection point of the center of the ball joint of the third RRS branch onto the second planar figure are obtained by the following formula. : ； in, This represents the X-coordinate of the center of the ball joint of the first RRS branch in the base coordinate system. This represents the Y-coordinate of the center of the ball joint of the first RRS branch in the base coordinate system. This represents the Z-coordinate of the center of the ball joint of the first RRS branch in the base coordinate system. This represents the X-coordinate of the center of the ball joint of the second RRS branch in the base coordinate system. This represents the Y-coordinate of the center of the ball joint of the second RRS branch in the base coordinate system. The Z-coordinate represents the coordinate of the center of the ball joint of the second RRS branch in the base coordinate system. The X-coordinate of the center of the ball joint of the third RRS branch in the base coordinate system. The Y-coordinate represents the coordinate of the center of the ball joint of the third RRS branch in the base coordinate system. The Z-coordinate represents the coordinates of the center of the ball joint of the third RRS branch in the base coordinate system.

6. The method according to claim 2, characterized in that, The step of calculating the rotation angle of the first rotary joint of any RRS branch in the target pose state based on the coordinates of the projection point of the center of the ball joint of any RRS branch onto the second planar graphic includes: The joint angle is calculated based on the coordinates of the first rotary joint in any RRS branch in the base coordinate system, the length of the first link, the length of the second link, and the coordinates of the projection point of the center of the ball joint onto the second planar figure. The joint angle refers to the interior angle of the triangle formed by the projection points of the centers of the first rotary joint, the second rotary joint, and the ball joint in any RRS branch onto the second planar figure, with the first rotary joint in any RRS branch as the vertex. The azimuth angle of the projection point is calculated based on the coordinates of the first rotary joint in any RRS branch in the base coordinate system and the coordinates of the projection point of the center of the ball joint projected onto the second planar figure. The azimuth angle of the projection point refers to the angle between the vector from the first rotary joint in any RRS branch to the projection point and the preset reference direction in the second planar figure. The preset reference direction in the second planar figure includes: the positive X-axis direction of the base coordinate system, or the projection of the positive X-axis direction of the base coordinate system onto the second planar figure. The difference between the azimuth angle of the projection point and the joint angle is used as the rotation angle of the first rotary joint of any RRS branch in the target pose state.

7. The method according to claim 6, characterized in that, The joint angle is calculated using the following formula. : ， ； ； ； in, This represents the coordinates of the first rotational joint in any of the RRS branches. This represents the X-coordinate of the first rotary joint of any RRS branch in the base coordinate system. This represents the Z-coordinate of the first rotary joint of any RRS branch in the base coordinate system. This represents the coordinates of the projection point of the center of the ball joint of any RRS branch onto the second planar figure. The X-coordinate represents the coordinates of the projection point of the center of the ball joint of any RRS branch onto the second planar figure. The Z-coordinate represents the coordinates of the projection point of the center of the ball joint of any RRS branch onto the second planar figure. This represents the Euclidean distance from the first rotational joint in any of the RRS branches to the projection point. This represents the length of the first link of any of the RRS branches. This indicates the length of the second link of any of the RRS branches; The azimuth angle of the projection point is calculated using the following formula. : ； in, Represents the inverse cosine function. Represents the arctangent function; The rotation angle of the first rotational joint of any RRS branch in the target pose state is calculated using the following formula. : 。 8. A motion control device for a parallel 3RRS robot, characterized in that, The parallel 3RRS robot includes: a base platform and a moving platform, the base platform and the moving platform being connected by three RRS branches, each RRS branch starting from the base platform and comprising, in sequence, a first rotary joint, a first link, a second rotary joint, a second link, and a ball joint; the device includes: The target pose information acquisition module is configured to: acquire the target pose information and target position information of the moving platform in the target pose state. The target pose information includes: the angle between the rotation axis vector of the moving platform in the XY plane of the base coordinate system and the X-axis and the angle of rotation of the moving platform around the rotation axis. The target position information includes: the displacement of the center point of the moving platform relative to the zero position state along the Z-axis of the base coordinate system. The first planar graphic center coordinate calculation module is configured to: calculate the center coordinates of the first planar graphic determined by the center of each ball joint in the target pose state based on the structural parameters of any RRS branch in the zero position state, the target posture information, and the target position information; The ball joint center coordinate calculation module is configured to: calculate the coordinates of the center of the ball joint of any RRS branch in the target pose state in the base coordinate system based on the center coordinates of the first planar graphic in the target pose state; The ball joint center projection point coordinate calculation module is configured to: obtain the coordinates of the projection point of the center of the ball joint of any RRS branch onto the second plane figure determined by the first link of any RRS branch and the Z-axis of the base coordinate system based on the coordinates of the center of the ball joint of any RRS branch in the base coordinate system. The first rotary joint rotation angle calculation module is configured to: calculate the rotation angle of the first rotary joint of any RRS branch in the target pose state based on the coordinates of the projection point of the center of the ball joint of any RRS branch onto the second planar graphic. The motion platform drive module is configured to drive the motion platform to the target pose state based on the rotation angle of the first rotary joint of each RRS branch in the target pose state.

9. A parallel 3RRS robot, characterized in that, The parallel 3RRS robot includes a base platform and a moving platform, the base platform and the moving platform being connected by three RRS branches, each RRS branch starting from the base platform and including a first rotary joint, a first link, a second rotary joint, a second link, and a ball joint connected in series; the parallel 3RRS robot also includes a memory and a processor; wherein the memory is used to store one or more computer instructions, wherein the one or more computer instructions are executed by the processor to implement the method of any one of claims 1 to 7.

10. A computer-readable storage medium storing computer instructions thereon, characterized in that, When the computer instructions are executed by the processor, they implement the method of any one of claims 1 to 7.

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