CN112487569B - Solving method for working space of mobile robot capable of reaching fixed time length - Google Patents
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Abstract
A solving method for a working space which can be reached by a mobile robot in a fixed time length belongs to the technical field of autonomous object detection, grabbing and man-machine cooperation of mobile robots. The method firstly determines the movement time length of the mobile robot and prepares for the follow-up research on the shortest-time operation of the mobile robot. And then establishing a kinematic model for the six-degree-of-freedom mechanical arm and the mobile chassis respectively. And finally, analyzing the working area of the end effector by adopting a Monte Carlo method based on the movement time of the mobile action robot, the conversion relation between the reachable working space of the mechanical arm end effector and each joint and the kinematic model of the mobile chassis to obtain a point cloud picture of the robot reachable working space at regular time. The method has the advantages of relatively simple solving process and higher accuracy, and can be used in the technical fields of path planning, obstacle avoidance, motion control, man-machine cooperation and the like of the mobile action robot.
Description
Technical Field
The invention belongs to the technical field of autonomous object detection, grabbing and man-machine cooperation of a mobile robot, and relates to a combined motion planning method for a mobile chassis and a mechanical arm, in particular to a method for solving the reachable working space of the mobile robot within a fixed time length.
Background
The mobile robot is a novel intelligent mobile robot system which is formed by additionally arranging a six-degree-of-freedom industrial mechanical arm and an intelligent sensor on a mobile chassis and has active operation capacity, has a series of functions such as environment sensing, autonomous decision making, motion control and the like, and can autonomously move and operate in indoor and outdoor large-range scenes. Compared with a traditional fixed-base mechanical arm, the mobile robot has many advantages. The mechanical arm additionally arranged on the movable chassis has larger working space and can operate in a wider range; the robotic arms may also clear obstacles and provide additional support, enhancing the terrain-passing capability of the mobile chassis. Due to the advantages of the mobile robot, the mobile robot has wide application scenes in the fields of logistics storage, industrial production, earthquake resistance, disaster relief and the like.
In path planning, obstacle avoidance and motion control of the mobile robot, the solution of a working space is always an important problem to be considered, and the solution is an important index for measuring the working capacity of the mobile robot. The working space of a mobile robot refers to the set of location points that the end effector of a robot arm can reach. The working space of each mobile robot is closely related to its own structural form, constraints, etc. The scholars at home and abroad have already carried out a lot of research works on the mechanical arm work space analysis, and certain results are obtained.
The literature (huohui, zheng yuyao, sheep sail, six-degree-of-freedom mechanical arm modeling and working space analysis [ J ] sensor and microsystem 2020,39(01):35-37.) proposes a six-degree-of-freedom mechanical arm working space solving method applied to dangerous environment. According to the method, a coordinate system of each joint of the mechanical arm is analyzed and established, parameters of a connecting rod are determined, and the posture and the position of an end effector are deduced through homogeneous transformation according to a Denavit-Hartenberg multi-body kinematics modeling method. However, this method only considers the complete working space of the robot arm and does not further study the reachable working space based on fixed movement time. In addition, the method is only suitable for solving the working space of the single mechanical arm and is not suitable for the mobile robot with the additional mechanical arm.
The literature (warzara, butcher' S major, mobile robot autonomous grasping work [ J ] computer applications, 2016,36(S1):95-98+102.) proposes a research method for autonomous working of mobile robots. The method establishes a kinematic model for the mechanical arm and the mobile chassis respectively, and can effectively enable the robot to autonomously complete the grabbing operation of the target object in different environments. However, this method does not establish a complete kinematic model for the mobile robot. In addition, this method does not take into account the movement time of the mobile robot, and cannot achieve the shortest time work.
Disclosure of Invention
In order to solve the defects and shortcomings of the existing robot working space solving method, the invention provides a working space solving method for a mobile robot with a fixed time length. The method firstly determines the movement time length of the mobile robot and prepares for the follow-up research on the shortest time operation of the mobile robot. And then establishing a kinematic model for the six-degree-of-freedom mechanical arm and the mobile chassis respectively. And finally, analyzing the working area of the end effector by adopting a Monte Carlo method based on the movement time of the mobile action robot, the conversion relation between the reachable working space of the mechanical arm end effector and each joint and the kinematic model of the mobile chassis to obtain a point cloud picture of the robot reachable working space at regular time.
The technical scheme of the invention is as follows:
a method for solving a working space which can be reached by a mobile robot in a fixed time length comprises the following steps:
(1) six-degree-of-freedom mechanical arm kinematics model establishment
A robotic arm can be thought of as an open kinematic chain formed by a series of rigid bodies (called links) connected in series by revolute joints. One end of the connecting rod is fixed on the base, and the other end of the connecting rod is provided with a tool to complete various operations. The invention adopts a D-H method to establish a mechanical arm joint coordinate system, and the main idea is to describe the spatial relationship of two adjacent connecting rods by using a 4 multiplied by 4 homogeneous transformation matrix. As shown in FIG. 1, z of coordinate system n is selected as the axis of the end joint of the connecting rod n n Z of axis, coordinate system { n-1} n-1 Z of axes and coordinate system n n The common normal direction of the axes is defined as x n Direction of (a), y n The direction of (1) is determined by right manipulations.
Establishing the above robot joint coordinate system, it is also necessary to describe 4 parameters of each link and between two adjacent links: length of connecting rod a n (along x) n From z n-1 To z n The distance therebetween); connecting rod torsion angle alpha n (around x) n From z n-1 To z n The angle therebetween); offset distance d of joint n (along z) n-1 From x n-1 To x n The distance therebetween); angle of rotation theta of joint n (around z) n-1 From x n-1 To x n The angle therebetween).
Along z n-1 The pose transformation of the axis can be described by equation (1):
along x n The pose transformation of the axis can be described by equation (2):
the two pose transformation matrices of formula (1) and formula (2) are superposed to obtain a complete pose coordinate transformation matrix, as shown in formula (3):
solving the pose of the end effector of the mechanical arm based on the kinematic positive solution of the mechanical arm. According to the D-H method and the pose transformation matrix formula (3) between the adjacent joints of the mechanical arm, a pose transformation matrix of the coordinate system of the end effector of the mechanical arm relative to the coordinate system of the base can be obtained, as shown in the formula (4):
wherein the content of the first and second substances,
representing a pose transformation matrix between the base and the link 6,
a pose transformation matrix between the base and the link 1 is shown,
a pose transformation matrix between the connecting rod 1 and the connecting rod 2 is shown,
a pose transformation matrix between the link 2 and the link 3 is shown,
a pose transformation matrix between the link 3 and the link 4 is shown,
a posture transformation matrix between the link 4 and the link 5 is shown,
a pose transformation matrix between the links 5 and 6 is shown,
the first three columns of [ r ] 11 r 21 r 31 ] T ，[r 12 r 22 r 32 ] T ，[r 13 r 23 r 33 ] T Is the attitude vector of the reference point on the end effector relative to the base coordinate system, and the fourth column is the position vector of the reference point on the end effector of the mechanical arm relative to the base coordinate system in three-dimensional space, wherein c x 、c y 、c z Representing the x, y, z coordinates of the end effector in space, respectively.
(2) Mechanical arm fixed-time working space solving method
The invention selects Monte Carlo (Monte Carlo) method to describe the working space of the mechanical arm, and the method is a numerical method for solving approximate solutions of mathematics and engineering technical problems through statistical experiments and random simulation of random variables, and is also called as a simulated statistical method. The Monte Carlo method is simple and easy to implement, the joint type of the mechanical arm is not limited, the error is irrelevant to the degree of freedom, and the calculated amount is proportional to the degree of freedom. The idea of solving the working space by using the Monte Carlo method is as follows: traversing values of all joints in an allowed value range to obtain a set of terminal points, namely a working space, and specifically comprising the following steps:
1) acquiring a position vector of the end effector of the mechanical arm relative to a base coordinate system according to the forward kinematics model of the formula (4);
2) obtaining the value range theta of each joint motion angle of the mechanical arm according to the fixed motion duration T of the mobile motion robot nmin For the lower limit of the value range of the nth joint angle, theta nmax The upper limit of the value range of the nth joint angle is set;
3) generating random step sizes between 0-1 based on a uniformly distributed probability model over (0,1), and then using the random step sizes to generate random values for each joint within the range of motion angles
As shown in equation (5);
4) substituting the joint motion angle random value generated in the step into the obtained position vector to obtain the position coordinate of the end effector in the base coordinate system;
5) circulating the step 1) to the step 5) for N times to obtain spatial three-dimensional coordinate points of N mechanical arm end effectors;
6) the N three-dimensional coordinate points obtained are displayed in a point tracing manner, so that a cloud image of the reachable space of the six-degree-of-freedom mechanical arm end effector relative to the mechanical arm base coordinate system can be obtained, as shown in fig. 2.
(3) Mobile chassis timed long reachable working space solution
The kinematic model of the moving chassis of the moving robot is a two-wheel differential driving model, the motion trail of the moving chassis is a section of circular arc or a section of straight line under ideal conditions, a pair of (v, omega) represents a circular arc trail, wherein v and omega are the linear velocity and the angular velocity of the moving chassis respectively. The coordinates of the moving chassis under the global coordinate system at the time t are represented by x (t) and y (t), and the moving chassis azimuth angle is represented by θ (t), as shown in fig. 3. The triple < x (t), y (t), and theta (t) > represent the pose of the moving chassis at the time t.
The linear velocity of the moving chassis is generated only when the moving chassis moves in the front-rear direction, which is a constraint of the two-wheel differential drive model. With x (t) 0 ) And x (t) n ) Are respectively shown at t 0 And t n X coordinate of the moving chassis at time (y (t) 0 ) And y (t) n ) Similarly, v (t) and ω (t) represent the linear and angular velocities of the moving chassis at time t, respectively, then x (t) n ) And y (t) n ) It can be expressed by equation (6) and equation (7), respectively.
The invention assumes that the initial linear velocity of the mobile chassis is v or-v, and the value range of the initial angular velocity omega is omega min ～ω max The angular velocity and the linear velocity remain constant during the movement time T. Moving the chassis at t 0 The position of the time is set to be at the origin of the global coordinate system, t n ＝t 0 + T, in order to reduce the computing resources, a grid method is adopted to solve the motion track of the mobile chassis in the constant time T, and the specific steps are as follows:
1) dividing the movement time T into m parts in the ith time interval (T) 0 +T/m·(i-1),t 0 + T/m.i) the movement of the mobile chassis can be simplified to first rotation and then translation;
2) the angle deg of the moving chassis rotation during the ith time interval can be represented by equation (8):
deg＝T/m·ω (8)
obtaining a pose transformation matrix T corresponding to the rotation of the mobile chassis according to a formula (9) r ：
3) The distance dis of the moving chassis translation within the ith interval can be represented by equation (10):
dis＝T/m·v (10)
a pose transformation matrix T corresponding to the translation of the moving chassis can be obtained according to the formula (11) t ：
4) Suppose the mobile chassis is at (t) 0 The pose matrix at the moment of + T/m (i-1)) is T old Then move the chassis at (t) 0 Pose matrix T at + T/m.i) time new This can be obtained from equation (12):
T new ＝T t ·T r ·T old (12)
5) assuming that the initial angular velocity ω of the mobile chassis has a value range of ω min ～ω max Each increment has a step size of (ω) max -ω min ) K initial linear velocities v and-v, initial angular velocities ω, t of the moving chassis 0 Substituting the pose matrix of the moment into a formula (12), and obtaining a 2 m.k pose matrix of the mobile chassis in a fixed movement time length T through m iterations;
6) by displaying the three-dimensional coordinate points corresponding to the obtained 2 · m · k attitude matrix in a point drawing manner, a cloud image of reachable space points of the mobile chassis relative to the global coordinate system can be obtained, as shown in fig. 4.
(4) Timing length reachable working space solution for combined motion of movable chassis and mechanical arm
Because the mechanical arm of the mobile robot is fixed on the mobile chassis, the position matrix of the base of the mechanical arm relative to the mobile chassis is kept unchanged when the robot moves and works. In order to simplify the model, assuming that a base coordinate system of the mechanical arm and a mobile chassis coordinate system are the same coordinate system, substituting the position matrix of the mechanical arm end effector relative to the base coordinate system in the formula (4) into the formula (12), and obtaining the position matrix of the mechanical arm end effector relative to the global coordinate system. And displaying the three-dimensional coordinate points corresponding to the obtained pose matrix in a point tracing mode, so that a cloud point diagram of the mobile motion robot, which can reach the working space in a fixed time length, can be obtained.
The invention has the beneficial effects that: the method realizes the solution of the working space which can be reached by the mobile robot in the fixed time length, establishes a kinematic model aiming at the novel intelligent robot with a movable chassis provided with a six-degree-of-freedom mechanical arm, analyzes the working space which can be reached by the robot in the fixed time length by adopting a Monte Carlo method, has relatively simple solution process and higher accuracy, and is beneficial to improving the grabbing efficiency of the mobile robot to a specific object in a large-range scene. The invention can be used in the technical fields of path planning, obstacle avoidance and motion control of the mobile action robot, man-machine cooperation and the like.
Drawings
FIG. 1 is a coordinate relationship diagram between two adjacent links.
Figure 2 is a timed length of the robotic arm to reach the workspace.
FIG. 3 is a diagram of a two-wheel differential driving model.
FIG. 4 is a diagram of a mobile chassis time-length reachable workspace.
Fig. 5 is a time-lapse reachable workspace diagram for a mobile robot.
Detailed Description
The following detailed description of the embodiments of the invention refers to the accompanying drawings and technical solutions.
According to the invention, a Robotics toolkit Robotics Toolbox 10.3 in MATLAB R2018a is selected as a simulation experiment platform, the Robotics toolkit is a toolkit specially used for robot simulation in MATLAB, and the robot tool kit is very convenient to use in the aspects of robot modeling, trajectory planning, control and visualization.
Firstly, determining a D-H parameter, a, required by constructing a six-degree-of-freedom mechanical arm model by using a D-H method 1 Value of 0mm, a 2 Value of 0mm, a 3 Value of 420mm, a 4 Take the value 375mm, a 5 Value of 0mm, a 6 Values of 0mm, theta 1 Taking the value 0rad, theta 2 Taking the value 0rad, theta 3 Taking the value 0rad, theta 4 Taking the value 0rad, theta 5 Taking the value 0rad, theta 6 Taking the value of 0rad, d 1 Values of 0mm, d 2 Value 138mm, d 3 The value of-127 mm, d 4 Values of 114mm, d 5 Values of 114mm, d 6 Value of 90mm, alpha 1 Taking the value 0rad, alpha 2 The value-pi/2 rad, alpha 3 Taking the value 0rad, alpha 4 Taking the value 0rad, alpha 5 The value-pi/2 rad, alpha 6 The value is pi/2 rad. A simulation model of the robot arm was obtained using the Robotics toolkit 10.3 in MATLAB R2018a according to the above parameters.
Secondly, the fixed movement time length T of the mobile robot takes 1s, and accordingly the angle range theta of each joint movement of the mechanical arm can be obtained 1min Is- π rad, θ 1max Is π rad, θ 2min Is- π rad, θ 2max Is 0rad, θ 3min Is-pi/2 rad, theta 3max Is pi/2 rad, theta 4min Is- π rad, θ 4max Is π rad, θ 5min Is- π rad, θ 5max Is π rad, θ 6min Is- π rad, θ 6max Is π rad. And taking the value of the cycle number N as 1000, traversing the value within the range of the value allowed by each joint based on a Monte Carlo method and a formula (5), and substituting the generated joint motion angle random value into a formula (4) to obtain a set of position coordinates of the end effector under a base coordinate system, namely a cloud point diagram of the reachable working space of the mechanical arm.
Thirdly, the initial linear velocity v of the mobile chassis takes a value of 0.5m/s, and the range omega of the initial angular velocity omega is min The value-pi/2 rad, omega max Taking the value of pi/2 rad, the step length (omega) of the initial angular velocity change max -ω min ) K in/k takes the value 100. MiningThe movement time T is divided into m parts by a grid method, and m takes a value of 10. And substituting the parameters into the formula (12) to obtain the reachable working space point cloud picture of the mobile chassis relative to the global coordinate system.
And fourthly, obtaining a cloud point diagram of the working space which can be reached by the mobile robot in the fixed time length according to the fixed time long working space of the mechanical arm, the fixed time long working space of the mobile chassis and the formula (12).
Claims (1)
1. A method for solving a working space which can be reached by a mobile robot in a fixed time length is characterized by comprising the following steps:
(1) six-degree-of-freedom mechanical arm kinematics model establishment
A D-H method is adopted to establish a mechanical arm joint coordinate system, and a 4 multiplied by 4 homogeneous transformation matrix is used for describing the spatial relationship of two adjacent connecting rods; selecting z with the axis of the end joint of the connecting rod n as a coordinate system { n } n Z of axis, coordinate system { n-1} n-1 Z of axes and coordinate system n n The common normal direction of the axes is defined as x n Direction of (a), y n The direction of (2) is determined according to the right technique;
establishing the above robot joint coordinate system, it is also necessary to describe 4 parameters of each link and between two adjacent links: length of connecting rod a n I.e. along x n From z n-1 To z n The distance between them; connecting rod torsion angle alpha n I.e. around x n From z n-1 To z n The angle therebetween; offset distance d of joint n I.e. along z n-1 From x n-1 To x n The distance between them; angle of rotation theta of joint n I.e. around z n-1 From x n-1 To x n The angle therebetween;
along z n-1 The pose change of the axis is described by equation (1):
along x n The pose change of the axis is described by equation (2):
the two pose transformation matrices of formula (1) and formula (2) are superposed to obtain a complete pose coordinate transformation matrix, as shown in formula (3):
solving the pose of the mechanical arm end effector based on the kinematic positive solution of the mechanical arm; obtaining a pose transformation matrix of the coordinate system of the end effector of the mechanical arm relative to the coordinate system of the base according to a D-H method and a pose transformation matrix formula (3) between adjacent joints of the mechanical arm, wherein the pose transformation matrix formula is shown as a formula (4):
wherein the content of the first and second substances,
representing the pose transformation matrix, T, between the base and the connecting rod 6 1 0 Representing a pose transformation matrix between the base and the link 1,
a pose transformation matrix between the connecting rod 1 and the connecting rod 2 is shown,
a posture transformation matrix between the link 2 and the link 3 is shown,
a pose transformation matrix between the link 3 and the link 4 is shown,
a posture transformation matrix between the link 4 and the link 5 is shown,
a pose transformation matrix between the links 5 and 6 is shown,
the first three columns of [ r ] 11 r 21 r 31 ] T ，[r 12 r 22 r 32 ] T ，[r 13 r 23 r 33 ] T Is the attitude vector of the reference point on the end effector relative to the base coordinate system, the fourth column is the position vector of the reference point on the end effector of the mechanical arm relative to the base coordinate system in three-dimensional space, c x 、c y 、c z Respectively representing x, y, z coordinates of the end effector in space;
(2) mechanical arm fixed-time working space solving method
The working space is solved using the monte carlo method: traversing values of all joints in an allowed value range to obtain a set of terminal points, namely a working space, and specifically comprising the following steps:
1) acquiring a position vector of the end effector of the mechanical arm relative to a base coordinate system according to the forward kinematics model of the formula (4);
2) obtaining the value range theta of each joint motion angle of the mechanical arm according to the fixed motion duration T of the mobile motion robot nmin For the lower limit of the value range of the nth joint angle, theta nmax The upper limit of the value range of the nth joint angle is set;
3) generating a random step size between 0 and 1 based on a uniformly distributed probability model over (0,1), and then using the random step size to generate a random value for each joint over a range of angles of motion
As shown in equation (5);
4) substituting the joint motion angle random value generated in the step into the obtained position vector to obtain the position coordinate of the end effector in the base coordinate system;
5) circulating the step 1) to the step 5) for N times to obtain spatial three-dimensional coordinate points of N mechanical arm end effectors;
6) displaying the obtained N three-dimensional coordinate points in a point tracing mode to obtain a cloud picture of the reachable space of the end effector of the six-degree-of-freedom mechanical arm relative to a coordinate system of a mechanical arm base;
(3) mobile chassis timed long reachable working space solution
The kinematic model of the moving chassis of the moving robot is a two-wheel differential driving model, under the ideal condition, the motion trail of the moving chassis is a section of circular arc or straight line, a pair of (v, omega) represents a circular arc trail, wherein v and omega are the linear velocity and the angular velocity of the moving chassis respectively; the coordinates of the moving chassis under the global coordinate system at the time t are represented by x (t) and y (t), and the azimuth angle of the moving chassis is represented by theta (t); the triple < x (t), y (t), theta (t) > represents the pose of the mobile chassis at the time t;
the linear velocity of the moving chassis is generated only when the moving chassis moves along the front-back direction, which is the constraint of the two-wheel differential driving model; with x (t) 0 ) And x (t) n ) Are respectively shown at t 0 And t n X coordinate of the moving chassis at time, y (t) 0 ) And y (t) n ) Similarly, v (t) and ω (t) represent the linear and angular velocities of the moving chassis at time t, respectively, then x (t) n ) And y (t) n ) It can be expressed by equation (6) and equation (7), respectively;
setting the initial linear velocity of the mobile chassis as v or-v and the value range of the initial angular velocity omega as omega min ～ω max The angular velocity and the linear velocity are kept constant within the movement time T; moving chassis at t 0 The position of the time is set to be at the origin of the global coordinate system, t n ＝t 0 + T, in order to reduce the computing resources, a grid method is adopted to solve the motion track of the mobile chassis in the constant time T, and the specific steps are as follows:
1) dividing the movement time T into m parts in the ith time interval (T) 0 +T/m·(i-1),t 0 + T/m.i) the movement of the mobile chassis can be simplified to first rotation and then translation;
2) the angle deg of the moving chassis rotation during the ith time interval can be represented by equation (8):
deg＝T/m·ω (8)
obtaining a pose transformation matrix T corresponding to the rotation of the mobile chassis according to a formula (9) r ：
3) The distance dis of the moving chassis translation within the ith interval can be represented by equation (10):
dis＝T/m·v (10)
a pose transformation matrix T corresponding to the translation of the moving chassis can be obtained according to the formula (11) t ：
4) Setting a movable chassis at (t) 0 The pose matrix at the moment of + T/m (i-1)) is T old Then the moving chassis is at (t) 0 Pose matrix T at + T/m.i) time new This can be obtained from equation (12):
T new ＝T t ·T r ·T old (12)
5) setting the initial angular velocity omega of the mobile chassis to be in the value range omega min ～ω max Each increment has a step size of (ω) max -ω min ) K, initial linear velocities v and-v of the moving chassis, initial angular velocities ω, t 0 Substituting the position matrix of the moment into a formula (12), and obtaining a 2. m.k position matrix of the mobile chassis in a fixed movement time length T through m iterations;
6) displaying the three-dimensional coordinate points corresponding to the obtained 2 m.k attitude matrix in a point tracing mode to obtain a reachable space point cloud picture of the mobile chassis relative to a global coordinate system;
(4) timing length reachable working space solution for combined motion of movable chassis and mechanical arm
Setting a mechanical arm base coordinate system and a mobile chassis coordinate system as the same coordinate system, and substituting the pose matrix of the mechanical arm end effector in the formula (4) relative to the base coordinate system into a formula (12), so as to obtain the pose matrix of the mechanical arm end effector relative to a global coordinate system; and displaying the three-dimensional coordinate points corresponding to the obtained pose matrix in a point tracing mode, so that a cloud point diagram of the mobile motion robot, which can reach the working space in a fixed time length, can be obtained.
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| 六自由度串联机械臂运动学及其工作空间研究;王春等;《组合机床与自动化加工技术》;20200620(第06期);全文 * |
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