CN110561440A - multi-objective planning method for acceleration layer of redundant manipulator - Google Patents
multi-objective planning method for acceleration layer of redundant manipulator Download PDFInfo
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- B—PERFORMING OPERATIONS; TRANSPORTING
- B25—HAND TOOLS; PORTABLE POWER-DRIVEN TOOLS; MANIPULATORS
- B25J—MANIPULATORS; CHAMBERS PROVIDED WITH MANIPULATION DEVICES
- B25J9/00—Programme-controlled manipulators
- B25J9/16—Programme controls
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- B—PERFORMING OPERATIONS; TRANSPORTING
- B25—HAND TOOLS; PORTABLE POWER-DRIVEN TOOLS; MANIPULATORS
- B25J—MANIPULATORS; CHAMBERS PROVIDED WITH MANIPULATION DEVICES
- B25J9/00—Programme-controlled manipulators
- B25J9/16—Programme controls
- B25J9/1602—Programme controls characterised by the control system, structure, architecture
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- B—PERFORMING OPERATIONS; TRANSPORTING
- B25—HAND TOOLS; PORTABLE POWER-DRIVEN TOOLS; MANIPULATORS
- B25J—MANIPULATORS; CHAMBERS PROVIDED WITH MANIPULATION DEVICES
- B25J9/00—Programme-controlled manipulators
- B25J9/16—Programme controls
- B25J9/1656—Programme controls characterised by programming, planning systems for manipulators
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Abstract
A multi-objective planning method for an acceleration layer of a redundant manipulator is characterized in that optimization performance indexes and inequality criteria of the acceleration layer are respectively designed; establishing an acceleration layer multi-target planning scheme by combining a planning task at the tail end of the mechanical arm and the physical limit of the mechanical arm joint, wherein the scheme is restricted by an acceleration layer Jacobian matrix equation, a mechanical arm dynamic equation, an obstacle avoidance inequality, a joint angle limit, a joint speed limit, a joint acceleration limit and a joint torque limit; converting the multi-target planning scheme into a standard quadratic optimization problem, and solving the quadratic optimization problem by adopting a numerical algorithm; and the lower computer controller drives each joint of the mechanical arm to complete a given terminal planning task according to the solving result of the algorithm. The acceleration layer multi-target planning scheme designed by the invention can enable the mechanical arm to still complete a given terminal planning task under the condition that the joint is limited and has an obstacle, and the aim of repeated motion is fulfilled.
Description
Technical Field
The invention relates to the field of motion planning and control of a redundant manipulator, in particular to a multi-target planning method for an acceleration layer of the redundant manipulator.
Background
redundant robots play an increasingly important role in industrial automation production activities, such as welding, assembly, painting, etc. Two hotspots in the application study of redundant manipulators are repetitive motion planning and obstacle avoidance: this is related to whether a robotic arm can successfully complete repetitive end-planning tasks in a complex industrial environment.
at present, various repeated movement planning schemes and obstacle avoidance planning schemes are proposed and effectively applied to the mechanical arm. However, most planning schemes achieve only a single goal (i.e., repetitive motion or obstacle avoidance), and only a few planning schemes can achieve both repetitive motion and obstacle avoidance. For these planning schemes, which achieve multiple objectives, they were both designed on the velocity layer and studied ignoring the mechanical arm dynamics. Obviously, they cannot handle the joint acceleration limit and the joint torque limit of the robot arm, and cannot be directly applied to the robot arm related to acceleration or torque control, so the application range of the solution is greatly limited. More importantly, due to lack of consideration of the dynamics of the robotic arm, these solutions tend to fail in industrial application practice, thereby resulting in the inability of the robotic arm to perform a given end planning task.
Disclosure of Invention
The invention mainly aims to overcome the defects in the prior art, and provides a multi-target planning method for an acceleration layer of a redundant manipulator, which can enable the manipulator to complete a given terminal planning task under the condition that joints are limited and have obstacles, and achieves the purpose of repeated motion.
The invention adopts the following technical scheme:
A multi-objective planning method for an acceleration layer of a redundant manipulator is characterized by comprising the following steps:
1) Designing an optimized performance index and an obstacle avoidance inequality of an acceleration layer;
2) establishing an acceleration layer multi-target planning scheme by combining a planning task at the tail end of the mechanical arm, the physical limit of a mechanical arm joint and the optimization performance index of an acceleration layer, wherein the acceleration layer multi-target planning scheme is restricted by an acceleration layer Jacobian matrix equation, a mechanical arm dynamic equation, an obstacle avoidance inequality, a joint angle limit, a joint speed limit, a joint acceleration limit and a joint torque limit;
3) Converting the multi-target planning scheme of the acceleration layer into a standard quadratic optimization problem, and solving the quadratic optimization problem by adopting a numerical algorithm;
4) And the lower computer controller drives each joint of the mechanical arm to act according to the solving result to complete the given terminal planning task.
preferably, the optimized performance index of the acceleration layer is as follows:
Wherein | · | purple2Which represents the two-norm of the vector,The acceleration of the joints of the mechanical arm is represented,The method comprises the steps of representing the speed of a mechanical arm joint, representing a mechanical arm joint angle theta, and representing an initial state of the mechanical arm joint theta (0); the design parameter lambda is more than 0 and is used for adjusting the performance index so as to enable the mechanical arm to achieve the purpose of repeated motion planning.
preferably, the obstacle avoidance inequality is as follows:
Wherein the coefficient matrices M and N are respectively defined as M ═ xC-xO,yC-yO,zC-zO]TJCandUpper labelTRepresenting transpositions of matrices or vectors, (x)C,yC,zC) Spatial coordinates representing robot arm patch, (x)O,yO,zO) Spatial coordinates representing points of environmental obstacles, JCA jacobian matrix representing the robot arm criterion points,denotes JCThe time derivative of (a).
preferably, the multi-objective programming scheme of the acceleration layer is designed as follows:
Minimization
Is constrained to
Wherein the equality is constrainedCorresponding to the motion planning task of the tail end of the mechanical arm on an acceleration layer, alpha and beta represent design parameters and the numerical values of alpha > 0 and beta > 0, J represents a Jacobian matrix of the mechanical arm,denotes the time derivative of J, and e denotes the positional error of the end of the robot arm and is defined as e ═ f (θ) -rdF (-) denotes a non-linear mapping function, rdRepresents the desired trajectory of the motion of the end of the robot arm, and epsilon represents the velocity error of the end of the robot arm and is defined asIs represented by rdThe time derivative of (a) of (b),To representThe time derivative of (a); constraint of equalityexpressing a kinetic equation of the mechanical arm, H expressing an inertia matrix of the mechanical arm, c expressing a centrifugal force variable, g expressing a gravity variable, and tau expressing a joint moment of the mechanical arm; constraint of inequalityThe device is used for avoiding environmental obstacles by the mechanical arm;and τ±Respectively representing joint angle limit, joint velocity limit, joint acceleration limit and joint moment limit.
Preferably, the multi-objective programming scheme of the acceleration layer is converted into a standard quadratic optimization problem, and the performance index of the problem is xTx/2+pTx, the constraint conditions are Cx ═ d, Ax ≦ b, η-≤x≤η+Wherein η±Representing the joint angle theta and joint velocityand joint accelerationRear upper and lower polesThe process is limited in that, and, k1> 0 and k2the joint limit conversion parameter is represented by > 0, and the joint limit conversion margin is represented by delta > 0.
Preferably, a numerical algorithm is adopted to solve the quadratic optimization problem, specifically: and converting the solution of the quadratic optimization problem into equivalent solution of a piecewise linear projection equation, and calculating by adopting a corresponding numerical algorithm to obtain the solution of the piecewise linear projection equation and the optimal solution of the quadratic optimization problem.
As can be seen from the above description of the present invention, compared with the prior art, the present invention has the following advantages:
The invention can effectively overcome the defects of the existing method, provides the acceleration layer multi-target planning method which can enable the redundant manipulator to still complete the given terminal planning task under the condition that the joints are limited and have obstacles and achieve the purpose of repeated motion, and has important significance and value for the application practice of the manipulator in the complex industrial environment.
Drawings
FIG. 1 is a flow chart of the present invention.
The invention is described in further detail below with reference to the figures and specific examples.
Detailed Description
The invention is further described below by means of specific embodiments.
The multi-target planning method for the acceleration layer of the redundant manipulator shown in fig. 1 mainly comprises six parts, namely designing performance indexes and inequality criteria capable of realizing repeated motion and obstacle avoidance, establishing a multi-target planning scheme for the acceleration layer, converting the multi-target planning scheme into a standard quadratic optimization problem, a numerical algorithm solver, a lower computer controller and the redundant manipulator. Specifically, the method comprises the following steps:
1) firstly, in order to realize the purposes of repeated movement of the mechanical arm and obstacle avoidance, an optimization performance index and an obstacle avoidance inequality of an acceleration layer are respectively designed.
the performance indexes of the acceleration layer capable of realizing repeated motion are designed as follows:
Wherein | · | purple2Which represents the two-norm of the vector,The acceleration of the joints of the mechanical arm is represented,the method comprises the steps of representing the speed of a mechanical arm joint, representing a mechanical arm joint angle theta, and representing an initial state of the mechanical arm joint theta (0); the design parameter lambda is more than 0 and is used for adjusting the performance index so as to enable the mechanical arm to achieve the purpose of repeated movement.
The inequality criterion for avoiding obstacles is designed as
Wherein the coefficient matrices M and N are respectively defined as M ═ xC-xO,yC-yO,zC-zO]TJCandupper labelTRepresenting transpositions of matrices or vectors, (x)C,yC,zC) Spatial coordinates representing robot arm patch, (x)O,yO,zO) Spatial coordinates representing points of environmental obstacles, JCa jacobian matrix representing the robot arm criterion points,denotes JCThe time derivative of (a).
2) And then, establishing a scheme capable of realizing multiple planning targets simultaneously, namely an acceleration layer multi-target planning scheme, by combining the planning task at the tail end of the mechanical arm and the physical limit of the mechanical arm joint.
Based on the performance index (1) and the inequality criterion (2), the following acceleration layer multi-target planning scheme can be established by combining the planning task at the tail end of the mechanical arm and the physical limit of the mechanical arm joint:
minimization
Constraint conditions are as follows:
θ-≤θ≤θ+ (7)
τ-≤τ≤τ+ (10)
wherein the equality is constrainedcorresponding to the motion planning task of the tail end of the mechanical arm on an acceleration layer, J represents a Jacobian matrix of the mechanical arm,denotes the time derivative of J, and e denotes the positional error of the end of the robot arm and is defined as e ═ f (θ) -rdf (-) denotes a non-linear mapping function, rdRepresents the desired trajectory of the motion of the end of the robot arm, and epsilon represents the velocity error of the end of the robot arm and is defined asIs represented by rdThe time derivative of (a) of (b),To representThe time derivative of (a); constraint of equalityExpressing a kinetic equation of the mechanical arm, H expressing an inertia matrix of the mechanical arm, c expressing a centrifugal force variable, g expressing a gravity variable, and tau expressing a joint moment of the mechanical arm; constraint of inequalityThe device is used for avoiding environmental obstacles by the mechanical arm; theta±、And τ±Respectively representing joint angle limit, joint velocity limit, joint acceleration limit and joint moment limit.
3) Further, the planning scheme is converted into a standard quadratic optimization problem, and a numerical algorithm is adopted to solve the problem, specifically as follows:
for the above acceleration layer multi-objective planning schemes (3) - (10), it can be converted into a quadratic optimization problem of the following criteria:
minimizing xTx/2+pTx (11)
constraint conditions are as follows: cx ═ d (12)
Ax≤b (13)
η-≤x≤η+ (14)
Wherein,A＝[MT -HT HT]T，η±Representing the joint angle theta and joint velocityAnd joint accelerationthe upper and lower limits of the rear, and,k1> 0 and k2The joint limit conversion parameter is represented by > 0, and the joint limit conversion margin is represented by delta > 0.
the solution of the quadratic optimization problem (11) - (14) described above can be converted into the solution of the following piecewise linear projection equation:
u-PΩ(u-(Mu+q))＝0 (15)
Wherein, PΩ(. cndot.) represents a piecewise linear projection operator. The primal-dual decision vector u, coefficient matrix M and vector q in the piecewise linear projection equation (15) are respectively defined as follows:
where I denotes an identity matrix, and the dual variables w and v correspond to the equality constraint (12) and the inequality constraint (13), respectively. To solve the above piecewise-linear projection equation (15) and the corresponding quadratic optimization problems (11) - (14), the following numerical algorithm may be employed:
σ(uk)＝uk-PΩ(uk-(Muk+q))
where the superscript k denotes the number of iterations and k is 0,1,2, …. Given an initial value u0through continuous iterative calculation of the numerical algorithm, a theoretical solution of the piecewise linear projection equation (15) can be obtained, so that optimal solutions of quadratic optimization problems (11) - (14), namely the optimal solutions of the acceleration layer multi-target planning schemes (3) - (10) are obtained.
4) finally, the solution result is used for driving each joint of the mechanical arm so that the mechanical arm can still complete a given terminal planning task under the condition that the joints are limited and have obstacles, and the purpose of repetitive motion is achieved, and the method specifically comprises the following steps:
After the optimal solution of the acceleration layer multi-target planning schemes (3) - (10) is obtained through calculation by adopting the numerical algorithm solver, the corresponding solution result is transmitted to the lower computer controller to drive the motion of each joint of the mechanical arm, so that the given terminal planning task can be still completed under the condition that the joints are limited and have obstacles, and the aim of repeated motion is fulfilled.
The above description is only an embodiment of the present invention, but the design concept of the present invention is not limited thereto, and any insubstantial modifications made by using the design concept should fall within the scope of infringing the present invention.
Claims (6)
1. A multi-objective planning method for an acceleration layer of a redundant manipulator is characterized by comprising the following steps:
1) designing an optimized performance index and an obstacle avoidance inequality of an acceleration layer;
2) establishing an acceleration layer multi-target planning scheme by combining a planning task at the tail end of the mechanical arm, the physical limit of a mechanical arm joint and the optimization performance index of an acceleration layer, wherein the acceleration layer multi-target planning scheme is restricted by an acceleration layer Jacobian matrix equation, a mechanical arm dynamic equation, an obstacle avoidance inequality, a joint angle limit, a joint speed limit, a joint acceleration limit and a joint torque limit;
3) Converting the multi-target planning scheme of the acceleration layer into a standard quadratic optimization problem, and solving the quadratic optimization problem by adopting a numerical algorithm;
4) and the lower computer controller drives each joint of the mechanical arm to act according to the solving result to complete the given terminal planning task.
2. the multi-objective programming method for the acceleration layer of the redundant manipulator according to claim 1, wherein the optimized performance indexes of the acceleration layer are as follows:
Wherein | · | purple2which represents the two-norm of the vector,the acceleration of the joints of the mechanical arm is represented,The method comprises the steps of representing the speed of a mechanical arm joint, representing a mechanical arm joint angle theta, and representing an initial state of the mechanical arm joint theta (0); the design parameter lambda is more than 0 and is used for adjusting the performance index so as to enable the mechanical arm to achieve the purpose of repeated motion planning.
3. The multi-objective programming method for the acceleration layer of the redundant manipulator according to claim 2, wherein the obstacle avoidance inequality is as follows:
wherein the coefficient matrices M and N are respectively defined as M ═ xC-xO,yC-yO,zC-zO]TJCAndUpper labelTrepresenting transpositions of matrices or vectors, (x)C,yC,zC) Spatial coordinates representing robot arm patch, (x)O,yO,zO) Spatial coordinates representing points of environmental obstacles, JCA jacobian matrix representing the robot arm criterion points,Denotes JCthe time derivative of (a).
4. The multi-objective programming method for the acceleration layer of the redundant manipulator according to claim 3, wherein the multi-objective programming scheme for the acceleration layer is designed as follows:
Minimization
Is constrained toθ-≤θ≤θ+，τ-≤τ≤τ+；
Wherein the equality is constrainedcorresponding to the motion planning task of the tail end of the mechanical arm on an acceleration layer, alpha and beta represent design parameters and the numerical values of alpha > 0 and beta > 0, J represents a Jacobian matrix of the mechanical arm,Denotes the time derivative of J, and e denotes the positional error of the end of the robot arm and is defined as e ═ f (θ) -rdAnd f (-) represents oneA non-linear mapping function, rdRepresents the desired trajectory of the motion of the end of the robot arm, and epsilon represents the velocity error of the end of the robot arm and is defined as is represented by rdThe time derivative of (a) of (b),To representThe time derivative of (a); constraint of equalityExpressing a kinetic equation of the mechanical arm, H expressing an inertia matrix of the mechanical arm, c expressing a centrifugal force variable, g expressing a gravity variable, and tau expressing a joint moment of the mechanical arm; constraint of inequalitythe device is used for avoiding environmental obstacles by the mechanical arm; theta±、And τ±respectively representing joint angle limit, joint velocity limit, joint acceleration limit and joint moment limit.
5. The method as claimed in claim 4, wherein the acceleration layer multi-objective programming scheme is converted into a standard quadratic optimization problem with performance index xTx/2+pTx, the constraint conditions are Cx ═ d, Ax ≦ b, η-≤x≤η+Wherein C＝J，A＝[MT-HT HT]T，η±Representing the joint angle theta and joint velocityAnd joint accelerationThe upper and lower limits of the rear, and, k1> 0 and k2the joint limit conversion parameter is represented by > 0, and the joint limit conversion margin is represented by delta > 0.
6. The multi-objective programming method for the acceleration layer of the redundant manipulator according to claim 1,2, 3, 4 or 5, wherein a numerical algorithm is used for solving a quadratic optimization problem, and specifically comprises the following steps: and converting the solution of the quadratic optimization problem into equivalent solution of a piecewise linear projection equation, and calculating by adopting a corresponding numerical algorithm to obtain the solution of the piecewise linear projection equation and the optimal solution of the quadratic optimization problem.
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| CN112605992A (en) * | 2020-12-09 | 2021-04-06 | 中山大学 | Method and device for controlling cyclic motion of double-arm robot |
| CN112847323A (en) * | 2021-01-06 | 2021-05-28 | 中国铁建重工集团股份有限公司 | Robot model parameter error compensation method, device, electronic device and medium |
| CN113084803A (en) * | 2021-03-31 | 2021-07-09 | 信阳师范学院 | Multi-task control method for redundant manipulator based on multilayer structure |
| CN113232016A (en) * | 2021-04-13 | 2021-08-10 | 哈尔滨工业大学（威海） | Mechanical arm path planning method integrating reinforcement learning and fuzzy obstacle avoidance |
| CN113618742A (en) * | 2021-08-24 | 2021-11-09 | 深圳市优必选科技股份有限公司 | Robot obstacle avoidance method and device and robot |
| CN114571448A (en) * | 2021-12-30 | 2022-06-03 | 广州铁路职业技术学院（广州铁路机械学校） | Joint-limited pseudo-inverse repetitive motion planning method for redundant manipulator |
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| CN111958598A (en) * | 2020-08-17 | 2020-11-20 | 北方工业大学 | Multi-target fusion redundant drive parallel robot internal force optimization method and system |
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| CN113232016A (en) * | 2021-04-13 | 2021-08-10 | 哈尔滨工业大学（威海） | Mechanical arm path planning method integrating reinforcement learning and fuzzy obstacle avoidance |
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| CN113618742A (en) * | 2021-08-24 | 2021-11-09 | 深圳市优必选科技股份有限公司 | Robot obstacle avoidance method and device and robot |
| US20230101489A1 (en) * | 2021-09-27 | 2023-03-30 | Ubtech Robotics Corp Ltd | Redundant robot joint acceleration planning method, redundant robot using the same, and computer readable storage medium |
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| CN114571448A (en) * | 2021-12-30 | 2022-06-03 | 广州铁路职业技术学院（广州铁路机械学校） | Joint-limited pseudo-inverse repetitive motion planning method for redundant manipulator |
| CN115107027A (en) * | 2022-07-06 | 2022-09-27 | 海南大学 | Wheel type mobile mechanical arm repetitive motion planning method with anti-noise characteristic |
| CN115107028A (en) * | 2022-07-06 | 2022-09-27 | 海南大学 | Noise-tolerant three-wheel omnidirectional mobile mechanical arm repetitive motion planning method |
| CN115157262A (en) * | 2022-07-29 | 2022-10-11 | 中山大学 | Obstacle avoidance and optimization control method and system for joint-limited redundant mechanical arm and robot |
| CN115157262B (en) * | 2022-07-29 | 2023-07-11 | 中山大学 | Obstacle avoidance and optimal control method and system for joint-limited redundant mechanical arm and robot |
| CN116968016A (en) * | 2022-11-16 | 2023-10-31 | 重庆大学 | Construction method of hydraulic arm tail end speed feasible space and visual interaction system |
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