CN116214516A - Real-time grabbing and track tracking method and system for mobile redundant mechanical arm - Google Patents
Real-time grabbing and track tracking method and system for mobile redundant mechanical arm Download PDFInfo
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Abstract
The invention discloses a real-time grabbing and track tracking method and system for a mobile redundant mechanical arm based on an optimization theory. In the method, the mobile redundant mechanical arm platform carries out real-time distance measurement on the target object based on the camera, and when the distance is smaller than a set threshold value, the grabbing operation is carried out. According to the method, a dynamic model of the mobile redundant mechanical arm platform based on forward kinematics of the robot is built, an optimization model of the mobile redundant mechanical arm platform based on kinetic energy loss is built, a corresponding objective function is designed, and the constraint conditions of the corresponding optimization model are set by combining the physical constraint conditions of the mobile redundant mechanical arm platform. And (3) by sampling time, inputting the current state of the mobile redundant mechanical arm platform, solving the joint angular speed and the mobile platform speed at the next moment, and realizing real-time track tracking of the mobile redundant mechanical arm platform. The invention greatly increases the working range of the mechanical arm, and the established model is simple and easy to solve, can realize accurate track tracking and has wide application prospect.
Description
Technical Field
The invention belongs to the field of intelligent real-time optimal control, and relates to a method and a system for real-time grabbing and track tracking of a mobile redundant mechanical arm based on an optimization theory.
Background
With the continuous development of related technologies such as sensing technology, artificial intelligence technology and the like, autonomous mobile robots with sensing, cognition and self-decision capability are widely applied to military, civil and scientific researches. The mechanical arm is used as the most common and most important actuator in the man-machine co-fusion field, can complete a series of activities such as welding, carrying, throwing and the like, and can also be matched with human beings to complete a plurality of works in complex environments in industry and daily life. As production demands develop and service objects change, the requirements on the sensitivity and operability of the robot arm are also increasing. This presents new challenges for both mathematical theory and engineering practices of robotic arm research. To solve the limitations of the inherent characteristics of typical mechanical arms, to achieve fast trajectory tracking and collaborative work, new mathematical theory and technical methods need to be explored.
Currently, along with the development of industrial production and life demands of people and the change of service objects, the conventional rigid automatic production line has single production product, cannot meet the demands of diversified production, and the flexibility and the intellectualization of the industrial production line become the current mainstream development trend. Therefore, the requirements of sensitivity and operability of the mechanical arm are also increasing. The current industry has the following requirements for mechanical arms: better flexibility, easy-to-operate mechanical property, effective operability, rapid obstacle avoidance capability and the like. The mechanical arm belongs to a redundant robot, the joint space dimension of the mechanical arm is larger than the task space dimension, and the multi-solution property of the mechanical arm can be widely applied to industry and life.
One common approach to mechanical arm research is to conduct mechanical kinetic modeling and analysis. The common mechanical dynamics modeling method comprises Newton-Euler method, lagrange method, kane equation method, virtual work principle method and the like. These methods typically require a large number of mechanical equations to be calculated to solve for intra-articular forces, and the kinetic model format is complex and the computational process is cumbersome. Furthermore, on the basis of mechanical dynamics modeling, the model is required to be subjected to kinematic problem analysis. The kinematic problem refers to solving a functional mapping relation between joint input quantity and terminal output quantity, and mainly comprises analysis of forward kinematics and inverse kinematics. Kinematic analysis is one of the most fundamental and important problems in institutional research, and mainly comprises three aspects of position analysis, velocity analysis and acceleration analysis. Position analysis is the most basic problem of mechanism kinematics analysis and is the basis for solving the problems of speed analysis, acceleration analysis, dynamics modeling, working space analysis, motion control and the like. The position analysis is divided into a position forward solution and a position backward solution, and when the input quantity of each mechanism is known, the pose of the end effector is solved, and the position forward solution is called the position forward solution, and the position backward solution is called the position backward solution. In general, the position of the tandem mechanism is easy to forward, while the position reverse solution is relatively complex and has multiple solutions. The solution method of the position solution mainly comprises an analysis method, a numerical solution and a rotation method. The purpose of the velocity and acceleration analysis is to solve the mapping between the velocity and acceleration of the input joint and the tip velocity and acceleration. The analysis of the kinematic speed and acceleration of the mechanism is carried out by the common methods such as an influence coefficient method, a vector method, a rotation method and the like, and the key is to establish a jacobian matrix and a hessian matrix of the mechanism.
Currently, due to the limitation of the mechanical arm, the operability of a single fixed mechanical arm is very limited and limited in the arm length range, so that the application scene is limited, such as: transporting goods, co-transporting, etc. To overcome this difficulty, adding a movable base to the robotic arm is an effective solution that can greatly increase the working range and flexibility of the robotic arm, enabling it to be used more widely.
Therefore, in order to realize real-time control of the mechanical arm according to the current state and have a wider working range, it is necessary to design a real-time track tracking algorithm of the mobile redundant mechanical arm platform.
Disclosure of Invention
The invention aims to: aiming at the current requirement on real-time control of the mechanical arm, the invention aims to provide a real-time grabbing and track tracking method and system for a mobile redundant mechanical arm based on an optimization theory, which can increase the working range of the mechanical arm and realize accurate track tracking of the track.
The technical scheme is as follows: in order to achieve the above purpose, the invention provides a real-time grabbing and track tracking method for a mobile redundant mechanical arm based on an optimization theory, which is based on real-time track planning of the mobile mechanical arm after an object is identified and grabbed by a camera. Firstly, a dynamic model of a mobile redundant mechanical arm platform based on forward kinematics of a robot is established, then a dynamic energy loss is used as an index to establish an optimized model of the mobile redundant mechanical arm platform, and a corresponding objective function is designed. After relevant constraint conditions of the mobile redundant mechanical arm platform are set up by physical limitation, model solving is carried out, and finally, the real-time speed of the mobile platform and the mechanical arm is obtained, real-time track tracking is achieved, and accurate track tracking of the track is completed. The method comprises the following steps:
(1) A wheeled robot, a redundant mechanical arm and a camera are combined into a movable redundant mechanical arm platform;
(2) Detecting the distance between the platform and the object in real time by utilizing the detection and identification function of the camera on the image, stopping the motion of the platform when the distance between the platform and the object is smaller than a certain threshold value, and grabbing the object by utilizing the mechanical arm;
(3) Based on the forward kinematics theory of the redundant mechanical arm and the kinematics theory of the bottom mobile platform, a mobile redundant mechanical arm platform dynamics model based on the forward kinematics of the robot is established;
(4) Establishing a mobile redundant mechanical arm platform optimization model, wherein the optimization model takes the kinetic energy loss of a mechanical arm joint and a mobile platform as optimization indexes, takes the angular velocity of the mechanical arm joint and the motion velocity of the mobile platform at the bottom as decision variables, takes physical limitations of the mechanical arm and the mobile platform as constraint conditions, takes the maximum angle of the joint of the mechanical arm which allows rotation and the maximum angular velocity of the joint as constraint, and takes the position and the velocity of the bottom mobile platform relative to the tail end of the mechanical arm as constraint;
(5) And converting an objective function and corresponding constraint conditions which are proposed in the mobile redundant mechanical arm platform optimization model into a corresponding secondary optimization problem, taking the global position of the tail end of the mechanical arm, each joint of the mechanical arm and a target track at the current moment as input, and solving the angular velocity of each joint of the mechanical arm and the component velocity of the bottom mobile platform at the next moment in each direction so as to realize real-time tracking of the tail end of the mechanical arm on the target track.
Preferably, in the step (2), the object capturing method based on image recognition is: first, distance threshold dist is set 0 Then, the images captured by the cameras are identified, and the distance movement redundancy of the gripped object at the current moment is measured according to the obtained imagesDistance dist of mechanical arm platform t The method comprises the steps of carrying out a first treatment on the surface of the When dist 0 ≤dist t When the bottom moving platform moves forwards continuously at a set speed; when dist 0 ≥dist t When the robot arm is in use, the bottom moving platform immediately stops moving, and the robot arm starts grabbing objects.
Preferably, in the step (3), a dynamic model of the platform of the mobile redundant manipulator based on forward kinematics of the robot is described as follows:
wherein the method comprises the steps of
For the speed of the robot arm end in the global Cartesian coordinate system at time t, +.>
For the speed of the bottom mobile platform in the global Cartesian coordinate system at time t, +.>
For the Jacobian matrix of the angular velocity of the mechanical arm joint, f (theta) is a given forward transformation function of the mechanical arm, and is related to the physical structure of the mechanical arm, theta is the angle of each joint of the mechanical arm, and>
and the angular velocity of each joint of the mechanical arm at the time t.
Preferably, in the step (4), an objective function of the mobile redundant manipulator platform optimization model is defined as:
wherein [ alpha ] ∈ [0,1] represents the Euclidean norm]Is used for adjusting the kinetic energy of the mechanical arm joint and the moving platform as the weight coefficientThe proportional relationship between the kinetic energy,
for the angular velocity of the joints of the arm, +.>
For the velocity of the bottom mobile platform, Θ, Ω represent the feasible domain of the optimization variables, as determined by their corresponding constraints.
Preferably, in the step (4), the constraint condition of the mobile redundant manipulator platform optimization model is expressed as follows:
wherein, theta,
θ min 、θ max Respectively representing the angle and the angular speed of each joint of the mechanical arm, and the minimum and maximum angles, p and +_of each joint of the mechanical arm which allows rotation>
p min 、p max Respectively representing the position and the speed of the mobile platform, and the minimum and maximum positions, r and +.>
Respectively representing the position and the speed of the tail end of the mechanical arm in a global coordinate system; sigma, gamma are the corresponding scaling factors, respectively, to dynamically update the feasible regions of the corresponding variables.
Preferably, in the step (5), the problem of the second optimization of the transformation is expressed as follows:
subject to Ax＝b,
l≤x≤h,
wherein q=diag { (1- α) I m ,αI n }，
And the synthetic vector representing the joint angular velocity and the moving platform velocity, I and h respectively represent the lower bound and the upper bound of a variable x, A and b are determined by a dynamic model of the moving redundant mechanical arm platform, I is an identity matrix, m is the joint number of the mechanical arm, and n is the dimension of a task space.
Preferably, in the step (5), a fixed-step optimization algorithm is adopted to solve, and the iterative format is as follows:
wherein Proj (·) is a projection operator, and the upper and lower bounds thereof are h, l, y t For the dual variable, λ is the iteration step, k is the iteration number,
for gradient, eig represents matrix eigenvalues.
Based on the same inventive concept, the invention provides a real-time grabbing and track tracking system of a mobile redundant mechanical arm based on an optimization theory, wherein the system adopts a wheeled robot, a redundant mechanical arm and a camera to be combined into a mobile redundant mechanical arm platform; the system comprises a grabbing module and a track tracking module, wherein the grabbing module detects the distance between a platform and an object in real time by utilizing the detection and identification function of a camera on an image, and stops moving when the distance between the platform and the object is smaller than a certain threshold value, and grabs the object by utilizing a mechanical arm; the track tracking module is used for constructing a dynamic model of the mobile redundant mechanical arm platform based on the forward kinematics theory of the redundant mechanical arm and the kinematics theory of the bottom mobile platform; the method comprises the steps of constructing a mobile redundant mechanical arm platform optimization model, wherein the optimization model takes kinetic energy loss of a mechanical arm joint and a mobile platform as optimization indexes, takes the angular speed of the mechanical arm joint and the motion speed of the mobile platform at the bottom as decision variables, takes physical limitation of the mechanical arm and the mobile platform as constraint conditions, takes the maximum angle of the joint of the mechanical arm and the maximum angular speed of the joint as constraint, and takes the position and the speed of the mechanical arm relative to the tail end of the mechanical arm as constraint for the mobile platform at the bottom; and the system is used for converting the objective function and the corresponding constraint condition which are put forward in the mobile redundant mechanical arm platform optimization model into a corresponding secondary optimization problem, taking the global position of the tail end of the mechanical arm, each joint of the mechanical arm and the target track at the current moment as input, and solving the angular velocity of each joint of the mechanical arm and the component velocity of the bottom mobile platform at the next moment in each direction so as to realize real-time tracking of the tail end of the mechanical arm on the target track.
The beneficial effects are that: compared with the prior art, the invention has the following advantages:
1) Compared with the condition that most mechanical arm track control methods are only suitable for independent mechanical arms, the operating range is limited to the arm length, and the mobile redundant mechanical arm track control method based on the optimization theory overcomes the defect. The movable base is introduced into the mechanical arm, so that the working range of the mechanical arm is greatly increased, and the system can better execute industrial activities such as transporting goods, cooperatively transporting and the like, so that the system can be widely applied;
2) Compared with the modeling method for solving the intra-articular force by adopting the mechanical equation based on Newton-Euler method, lagrangian method, kane equation method, virtual work principle method and the like in most mechanical arm track control methods, the method has the defects of complex dynamic model format, complex calculation process and the like, and the mobile redundant mechanical arm track control method based on the optimization theory provided by the invention directly models based on the forward kinematics of the mechanical arm, has the characteristics of simplicity and easiness in solving, and greatly reduces the space resources and time resources consumed in the solving process;
3) According to the invention, the kinetic energy loss is taken as an optimization target, the constraint optimization algorithm with fixed step length is utilized to solve the joint angular speed of the mechanical arm and the speed of the mobile platform, the real-time performance is ensured due to the low time complexity of the algorithm while the accurate track tracking is realized, and the optimal speed at the next moment can be calculated according to the current real-time state.
Drawings
FIG. 1 is a flow chart of an embodiment of the present invention;
FIG. 2 is a schematic diagram of an apparatus employed in the present invention;
FIG. 3 is a schematic view of the position of the device prior to a gripping operation according to the present invention;
FIG. 4 is a schematic diagram of a grabbing operation using AR code to identify objects in accordance with the present invention;
FIG. 5 is a time-error plot of a single algorithm performed in a physical experiment of the present invention;
FIG. 6 is a graph of the velocity change of the mobile platform in the physical experiment of the present invention;
FIG. 7 is a graph showing the change of the angular velocity of a mechanical arm joint in a physical experiment of the invention;
fig. 8 is a diagram of the actual trajectory of the end of the robot arm in the physical experiment of the present invention.
Detailed Description
The objects, technical solutions and advantages of the present invention will be described in further detail with reference to the accompanying drawings and specific examples.
Most mechanical arm track control methods are only suitable for the condition of independent mechanical arms, the operational range is limited to the arm length, and meanwhile, modeling of most mechanical arm track control methods is complex, so that quick solving of an algorithm is not facilitated. This obviously does not meet the real-time control requirements in real-time trajectory control of the robotic arm. As shown in fig. 1, the invention provides a real-time grabbing and track tracking method for a mobile redundant mechanical arm based on an optimization theory by using the equipment shown in fig. 2, and the method adopts a wheeled robot, a redundant mechanical arm and a camera to be combined into a mobile redundant mechanical arm platform, and specifically comprises the following steps:
1. object grabbing based on AR image recognition
First, distance threshold dist is set 0 Then, the AR image captured by the camera is identified, and according to the obtained AR imageThe distance dist of the gripped object from the movable redundant mechanical arm platform at each moment is measured by the image of (a) t ：
When dist 0 ≤dist t At the same time, the mobile platform continues to move forward at a certain speed, as shown in fig. 3;
when dist 0 ≥dist t When the moving platform immediately stops moving, the mechanical arm starts to grab objects, as shown in fig. 4.
2. Dynamic model of mobile redundant mechanical arm platform based on forward kinematics of robot is established
The model describes the change process of the tail end position of the mechanical arm under a global Cartesian coordinate system based on the forward kinematics theory of the redundant mechanical arm and combined with the relative motion relation of the mechanical arm and the bottom moving platform; and then describing the change process of the speed of the mobile platform under a global Cartesian coordinate system by combining the kinematic relation between displacement and time, and combining the dynamic model and the dynamic model to obtain the dynamic model of the mobile redundant mechanical arm platform based on the forward kinematics of the robot so as to realize the tracking of the tail end of the mechanical arm to a specific track. The specific process is as follows:
determining a mapping relation f (-) from a Joint Space (Joint Space) of the mechanical arm to a Task Space (Task Space) of the mechanical arm by parameters of the mechanical arm and forward kinematics of the mechanical arm, wherein the mapping relation f (-) comprises the following steps:
p'(t)=f(θ(t))
wherein p' (t) ∈R n Representing three-dimensional coordinates of the end of the mechanical arm based on the base of the mechanical arm, and theta (t) epsilon R m The angle of each joint of the mechanical arm at the time t is represented, f represents a coordinate transformation matrix of the mechanical arm, m represents the joint number of the mechanical arm, and n represents the task space dimension.
Based on the movement law of the mobile platform, the real-time position p (t) is obtained, and finally, the three-dimensional coordinate r (t) of the tail end of the mechanical arm in the global coordinate system is obtained:
r(t)=p(t)+f(θ(t))
obtaining the speed relation among the three after deriving the equation, namely, a dynamic model of the movable redundant mechanical arm platform:
wherein the method comprises the steps of
For the speed of the robot arm end in the global coordinate system at time t, < >>
For the speed of the bottom mobile platform in the global coordinate system at time t, +>
Is Jacobian matrix about the angular velocity of the mechanical arm joint +.>
And the angular velocity of each joint of the mechanical arm at the time t.
3. Establishing mobile redundant mechanical arm platform optimization model based on kinetic energy loss
The model is based on the fact that the kinetic energy loss of the mechanical arm joint and the mobile platform is used as an optimization index, the angular velocity of the mechanical arm joint and the motion velocity of the mobile platform at the bottom are used as decision variables to establish a corresponding optimization model, and the optimal angular velocity of the mechanical arm joint and the optimal motion velocity of the mobile platform at the bottom at each moment are solved based on the model, so that the kinetic energy loss of the system is minimum. The specific description is as follows:
taking the energy loss of the system as an optimization index, establishing an objective function about the kinetic energy loss of the mechanical arm joint and the mobile platform, and defining as follows:
wherein ||·| represents the euclidean norm is used to determine, alpha epsilon [0,1] is a weight coefficient, the mechanical arm is used for adjusting the proportional relation between the kinetic energy of the mechanical arm joint and the kinetic energy of the moving platform.
4. Providing constraint conditions for constructing mobile redundant mechanical arm platform based on physical limitation
The constraint condition considers the physical limitation of the hardware of the mechanical arm and the mobile platform on the formation of the mechanical arm, wherein the mechanical arm takes the maximum angle of the joint which allows rotation and the maximum angular velocity of the joint as constraints, and the bottom mobile platform takes the position and the velocity of the mechanical arm relative to the tail end of the mechanical arm as constraints.
First, the relation between the end speed of the mechanical arm and the joint angular speed needs to be satisfied:
wherein the method comprises the steps of
And the preset speed of the tail end of the mechanical arm under the global coordinate system at the moment t is set.
Relevant constraints caused by physical hardware are:
θ min ≤θ≤θ max ,
p min ≤p-r≤p max ,
wherein θ is min ,θ max Respectively represents the minimum and maximum angles of each joint of the mechanical arm which is allowed to rotate, p min ,p max Representing the minimum and maximum positions the mobile platform is allowed to reach, respectively. In particular, depending on the specific physical meaning of the variable, it may be updated for the last four constraints as:
where σ, γ are the corresponding scaling factors, respectively, to dynamically update the feasible domains of the corresponding variables.
Further, the above formula can be converted into:
wherein θ - The i-th element of (2) is expressed as
θ + The i-th element of (2) is expressed as +.>
p - The j-th element is expressed as
The j-th element is expressed as
In addition, considering that the degree of freedom of the moving platform is 2, there is no velocity component in the z direction thereof, the constraint is expressed as follows:
wherein the matrix
As a constraint matrix in the z-direction.
5. Model solving by adopting constraint optimization algorithm based on fixed step length
The objective function and the constraint conditions proposed in the three and four steps are synthesized, and the optimization problem can be written as a quadratic programming problem as follows:
subject to Ax＝b,
l≤x≤h,
wherein q=diag { (1- α) I m ,αI n }，
Synthetic vector representing joint angular velocity and moving platform velocity, +.>
l＝((p - ) T ,(θ - ) T ) T ，h＝((p + ) T ,(θ + ) T ) T 。
Finally, solving by adopting a constraint optimization algorithm with fixed step length, wherein the iteration format is as follows:
wherein Proj (&) is a projection operation, and the upper and lower bounds thereof are h, l and y t As a dual variable, λ is the iteration step.
Solving by using a constraint optimization algorithm with a fixed step length to obtain the joint angular velocity of the mechanical arm at the moment t+1 and the velocity x of the moving platform t+1 And then inputting a speed value into the mobile mechanical arm system and executing, and reading the real-time position r (t+1) of the tail end of the mechanical arm after the execution is finished.
And after all the time points are sampled, moving the redundant mechanical arm platform to reach the designated position, and stopping the system from moving.
The following is a real-time tracking method of the mobile redundant mechanical arm platform track based on the optimization theory. The test adopts a TurtleBot3 Waffle_Pi incomplete constraint wheeled robot, an OpenManipulator-X redundant mechanical arm and a Raspberry Camera V2 camera to form a mobile redundant mechanical arm platform. The mechanical arm joint speed vector dimension m and the tail end position vector dimension n are respectively n=3 and m=4. Weight coefficient alpha=0.8, maximum and minimum speed of mobile platform
The maximum and minimum angular velocity of the mechanical arm joint is +.>
The preset trajectory equation is:
the experimental results are shown in FIGS. 5-8. Fig. 5 shows the variation of error convergence during execution of an algorithm, as seen at t=10 -4 s, the error converges to a preset value of 1×10 -3 m, the figure verifies the accuracy and instantaneity of the constraint optimization algorithm with fixed step length in real-time track planning. Fig. 6 shows the change of the speed of the mobile platform in the whole real-time track planning process, fig. 7 shows the change of the angular speed of the mechanical arm joint in the whole real-time track planning process, and fig. 6 and fig. 7 verify that the mechanical arm joint speed and the speed of the mobile platform are continuous and meet the set constraint conditions, and can quickly respond according to the real-time state of the system. Drawing of the figureAnd 8, displaying the real-time position of the tail end of the mechanical arm, wherein the track of the tail end of the mechanical arm is consistent with the preset track, and verifying the accuracy of the method.
The real-time track tracking method of the mobile redundant mechanical arm platform based on the optimization theory has the characteristics of accuracy and rapidness, can effectively realize real-time accurate tracking of the preset track, and has a satisfactory result in the actual object carrying application scene.
Based on the same inventive concept, the mobile redundant mechanical arm real-time grabbing and track tracking system based on the optimization theory provided by the embodiment of the invention adopts a wheeled robot, a redundant mechanical arm and a camera to be combined into a mobile redundant mechanical arm platform; the system comprises a grabbing module and a track tracking module, wherein the grabbing module detects the distance between the platform and the object in real time by utilizing the detection and identification function of the camera on the image, and stops moving when the distance between the platform and the object is smaller than a certain threshold value, and grabs the object by utilizing the mechanical arm; the track tracking module is used for constructing a dynamic model of the mobile redundant mechanical arm platform based on the forward kinematics of the robot based on the forward kinematics theory of the redundant mechanical arm and the kinematics theory of the bottom mobile platform; the method comprises the steps of constructing a mobile redundant mechanical arm platform optimization model, wherein the optimization model takes kinetic energy loss of a mechanical arm joint and a mobile platform as optimization indexes, takes the angular speed of the mechanical arm joint and the motion speed of the mobile platform at the bottom as decision variables, takes physical limitation of the mechanical arm and the mobile platform as constraint conditions, takes the maximum angle of the joint of the mechanical arm and the maximum angular speed of the joint as constraint, and takes the position and the speed of the mechanical arm relative to the tail end of the mechanical arm as constraint for the mobile platform at the bottom; and the system is used for converting the objective function and the corresponding constraint condition which are put forward in the mobile redundant mechanical arm platform optimization model into a corresponding secondary optimization problem, taking the global position of the tail end of the mechanical arm, each joint of the mechanical arm and the target track at the current moment as input, and solving the angular velocity of each joint of the mechanical arm and the component velocity of the bottom mobile platform at the next moment in each direction so as to realize real-time tracking of the tail end of the mechanical arm on the target track. Specific implementation details refer to the above method embodiments, and are not repeated.
Claims (10)
1. The method for capturing and tracking the track of the mobile redundant mechanical arm in real time is characterized by comprising the following steps of:
(1) A wheeled robot, a redundant mechanical arm and a camera are combined into a movable redundant mechanical arm platform;
(2) Detecting the distance between the platform and the object in real time by utilizing the detection and identification function of the camera on the image, stopping the motion of the platform when the distance between the platform and the object is smaller than a certain threshold value, and grabbing the object by utilizing the mechanical arm;
(3) Based on the forward kinematics theory of the redundant mechanical arm and the kinematics theory of the bottom mobile platform, a mobile redundant mechanical arm platform dynamics model based on the forward kinematics of the robot is established;
(4) Establishing a mobile redundant mechanical arm platform optimization model, wherein the optimization model takes the kinetic energy loss of a mechanical arm joint and a mobile platform as optimization indexes, takes the angular velocity of the mechanical arm joint and the motion velocity of the mobile platform at the bottom as decision variables, takes physical limitations of the mechanical arm and the mobile platform as constraint conditions, takes the maximum angle of the joint of the mechanical arm which allows rotation and the maximum angular velocity of the joint as constraint, and takes the position and the velocity of the bottom mobile platform relative to the tail end of the mechanical arm as constraint;
(5) And converting an objective function and corresponding constraint conditions which are proposed in the mobile redundant mechanical arm platform optimization model into a corresponding secondary optimization problem, taking the global position of the tail end of the mechanical arm, each joint of the mechanical arm and a target track at the current moment as input, and solving the angular velocity of each joint of the mechanical arm and the component velocity of the bottom mobile platform at the next moment in each direction so as to realize real-time tracking of the tail end of the mechanical arm on the target track.
2. The method for capturing and tracking the track of the mobile redundant manipulator in real time according to claim 1, wherein in the step (2), the method for capturing the object based on the image recognition is as follows: first, distance threshold dist is set 0 Then, the image captured by the camera is identified, and the captured image at the current time is measured according to the obtained imageDistance dist of object taking distance moving redundant mechanical arm platform t The method comprises the steps of carrying out a first treatment on the surface of the When dist 0 ≤dist t When the bottom moving platform moves forwards continuously at a set speed; when dist 0 ≥dist t When the robot arm is in use, the bottom moving platform immediately stops moving, and the robot arm starts grabbing objects.
3. The method for real-time grasping and tracking of a mobile redundant manipulator according to claim 1, wherein in the step (3), a dynamic model of a platform of the mobile redundant manipulator based on forward kinematics of the robot is described as follows:
wherein the method comprises the steps of
For the speed of the robot arm end in the global Cartesian coordinate system at time t, +.>
For the speed of the bottom mobile platform in the global Cartesian coordinate system at time t, +.>
For the Jacobian matrix of the angular velocity of the mechanical arm joint, f (theta) is a given forward transformation function of the mechanical arm, and is related to the physical structure of the mechanical arm, theta is the angle of each joint of the mechanical arm, and>
and the angular velocity of each joint of the mechanical arm at the time t.
4. The method for real-time capturing and tracking a track of a mobile redundant manipulator according to claim 1, wherein in the step (4), an objective function of a mobile redundant manipulator platform optimization model is defined as:
wherein [ alpha ] ∈ [0,1] represents the Euclidean norm]Is used for adjusting the proportional relation between the kinetic energy of the mechanical arm joint and the kinetic energy of the moving platform as the weight coefficient,
for the angular velocity of the joints of the arm, +.>
For the velocity of the bottom mobile platform, Θ, Ω represent the feasible region of the optimization variables.
5. The method for real-time grasping and tracking of a mobile redundant manipulator according to claim 1, wherein in the step (4), constraints of the mobile redundant manipulator platform optimization model are expressed as follows:
wherein, theta,
θ min 、θ max Respectively representing the angle and the angular speed of each joint of the mechanical arm, and the minimum and maximum angles of each joint of the mechanical arm which is allowed to rotate; p, & gt>
p min 、p max Respectively representMobile platform position, speed, minimum and maximum positions the mobile platform is allowed to reach, r, or #>
Respectively representing the position and the speed of the tail end of the mechanical arm in a global coordinate system; sigma, gamma are the corresponding scaling factors, respectively, to dynamically update the feasible regions of the corresponding variables.
6. The method for real-time grasping and tracking of a mobile redundant manipulator according to claim 1, wherein in the step (5), the transformed quadratic optimization problem is expressed as follows:
subject to Ax＝b,
l≤x≤h,
wherein q=diag { (1- α) I m ,αI n }，
Indicating angular velocity +.>
Speed of mobile platform
The synthetic vectors of the variable X are respectively represented by the lower bound and the upper bound of the variable X, A and b are determined by a dynamic model of the mobile redundant mechanical arm platform, I is a unit matrix, m is the joint number of the mechanical arm, n is the space dimension of a task, and alpha E [0,1]]Is a weight coefficient.
7. The method for real-time capturing and tracking the track of the mobile redundant manipulator according to claim 6, wherein in the step (5), a fixed-step optimization algorithm is adopted for solving, and the iterative format is as follows:
wherein Proj (·) is a projection operator, and the upper and lower bounds thereof are h, l, y t For the dual variable, λ is the iteration step, k is the iteration number,
for gradient, eig represents matrix eigenvalues.
8. The real-time grabbing and track tracking system of the mobile redundant mechanical arm is characterized in that the system adopts a wheeled robot, the redundant mechanical arm and a camera to form a mobile redundant mechanical arm platform; the system comprises a grabbing module and a track tracking module, wherein the grabbing module detects the distance between a platform and an object in real time by utilizing the detection and identification function of a camera on an image, and stops moving when the distance between the platform and the object is smaller than a certain threshold value, and grabs the object by utilizing a mechanical arm; the track tracking module is used for establishing a dynamic model of the mobile redundant mechanical arm platform based on the forward kinematics theory of the redundant mechanical arm and the kinematics theory of the bottom mobile platform; the method comprises the steps of establishing a mobile redundant mechanical arm platform optimization model, wherein the optimization model takes kinetic energy loss of a mechanical arm joint and a mobile platform as optimization indexes, takes the angular speed of the mechanical arm joint and the motion speed of the mobile platform at the bottom as decision variables, takes physical limitation of the mechanical arm and the mobile platform as constraint conditions, takes the maximum angle of the joint of the mechanical arm and the maximum angular speed of the joint as constraint, and takes the position and the speed of the mechanical arm relative to the tail end of the mechanical arm as constraint for the mobile platform at the bottom; and the system is used for converting the objective function and the corresponding constraint condition which are put forward in the mobile redundant mechanical arm platform optimization model into a corresponding secondary optimization problem, taking the global position of the tail end of the mechanical arm, each joint of the mechanical arm and the target track at the current moment as input, and solving the angular velocity of each joint of the mechanical arm and the component velocity of the bottom mobile platform at the next moment in each direction so as to realize real-time tracking of the tail end of the mechanical arm on the target track.
9. The mobile redundant manipulator real-time grasping and trajectory tracking system according to claim 8, wherein in the trajectory tracking module, a dynamic model of a mobile redundant manipulator platform based on forward kinematics of a robot is described as follows:
wherein the method comprises the steps of
For the speed of the robot arm end in the global Cartesian coordinate system at time t, +.>
For the speed of the bottom mobile platform in the global Cartesian coordinate system at time t, +.>
For the Jacobian matrix of the angular velocity of the mechanical arm joint, f (theta) is a given forward transformation function of the mechanical arm, and is related to the physical structure of the mechanical arm, theta is the angle of each joint of the mechanical arm, and>
and the angular velocity of each joint of the mechanical arm at the time t.
10. The method for capturing and tracking the track of the mobile redundant manipulator in real time according to claim 8, wherein in the track tracking module, an objective function of the mobile redundant manipulator platform optimization model is defined as:
wherein [ alpha ] ∈ [0,1] represents the Euclidean norm]Is used for adjusting the proportional relation between the kinetic energy of the mechanical arm joint and the kinetic energy of the moving platform as the weight coefficient,
for the angular velocity of the joints of the arm, +.>
For the velocity of the bottom mobile platform, Θ, Ω represent the feasible region of the optimization variables;
constraint conditions of the mobile redundant manipulator platform optimization model are expressed as follows:
wherein, theta,
θ min 、θ max Respectively representing the angle and the angular speed of each joint of the mechanical arm, and the minimum and maximum angles, p and +_of each joint of the mechanical arm which allows rotation>
p min 、p max Respectively representing the position and the speed of the mobile platform, and the minimum and maximum positions, r and +.>
Respectively representing the position and the speed of the tail end of the mechanical arm in a global coordinate system; sigma, gamma are the corresponding scaling factors, respectively, to dynamically update the feasible regions of the corresponding variables. />
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