CN111168684B - On-orbit assembly sequence planning method for large-scale spatial structure - Google Patents
On-orbit assembly sequence planning method for large-scale spatial structure Download PDFInfo
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- CN111168684B CN111168684B CN202010073143.0A CN202010073143A CN111168684B CN 111168684 B CN111168684 B CN 111168684B CN 202010073143 A CN202010073143 A CN 202010073143A CN 111168684 B CN111168684 B CN 111168684B
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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
- B25J9/1664—Programme controls characterised by programming, planning systems for manipulators characterised by motion, path, trajectory planning
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- B—PERFORMING OPERATIONS; TRANSPORTING
- B25—HAND TOOLS; PORTABLE POWER-DRIVEN TOOLS; MANIPULATORS
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- B25J9/00—Programme-controlled manipulators
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Abstract
The invention provides an on-orbit assembly sequence planning method for a large-scale space structure, which comprises the steps of establishing a kinetic equation of an assembly robot, establishing a multi-robot path coordination planning method, analyzing the motion of the robot, calculating energy consumption, establishing an evaluation function and optimizing an assembly sequence by adopting a particle swarm algorithm. In the assembly process, the robots are ensured not to collide with each other and the energy is optimal, and after the assembly sequence planning is finished, the motion planning and control method of the robots can be given, so that the follow-up tasks can be favorably carried out; the constraint indexes ensure the feasibility of assembly, and the optimization indexes consider the shortest moving path and the lowest energy consumption of the robot in the assembly process.
Description
Technical Field
The invention relates to the field of on-orbit assembly of large-scale space structures, in particular to a method for planning an assembly sequence.
Background
With the progress of aerospace technology and the expansion of application requirements, the construction requirements of large space platforms and infrastructures such as space stations, space reflectors, communication antennas, solar power stations, extraterrestrial bases and the like representing the national science and technology strength are increasingly urgent, and the technology and system of on-orbit service and maintenance of the spacecraft are listed in the national significant development plan. The space on-orbit service can expand the space activities of human beings and help the human beings to carry out more extensive, deeper and more innovative space exploration activities.
Large space structures are very different from the satellites, airships, space stations that we are currently familiar with. The large-scale space structure is huge in size, and the current delivery vehicles cannot meet the delivery requirements. Therefore, the large space structure cannot be integrally launched from the ground, and only all parts can be transported to the space for assembly. In the past, space mechanical arms are matched with astronauts to finish assembly in space, but the astronauts have certain dangers when going out of the space. With the increasing volume and complexity of large space structures, the assembly scheme of mechanical arms matched with astronauts is limited, the danger rises continuously, and even tasks cannot be completed.
With the development of robotics, it will become the trend in the future to replace mankind with space robots to perform dangerous space missions. The method for completing the assembly of the large space structure through the coordination operation of the multiple independent space robots becomes a main method for constructing the large space truss structure in the future. However, large space truss structures are large in size and complex, and require multiple robots to work in coordination during assembly.
At present, a plurality of on-orbit assembly sequence planning methods exist. Bonneville uses a genetic algorithm to solve, but has limited capacity of exploring a new space and is easy to fall into local optimization. Hong proposes a three-stage integration method with heuristic work rules to help the planner to generate the best and most efficient assembly sequence, which is finally solved using an inverse neural network method. But when the data is insufficient, the neural network cannot work. Cao uses a new immune algorithm and is applied to assembly sequence optimization, so that the calculation time is shortened, but the shortening time influences the solving precision. Motavall gives an evaluation function for sequence optimization by using a simulated annealing algorithm, but the performance of the algorithm is very sensitive to parameters such as an initial value and the like, and very high requirements are provided for the initial value and parameter setting. Yi proposes that a firefly algorithm is used for sequence planning, but the method has the defects that the inertia weight does not fully utilize target function information, and the moving distance of the firefly cannot be controlled and restrained better. Guo et al adopt a hierarchical programming method and solve with an ant colony algorithm, but pheromones in the ant colony algorithm gradually volatilize with the passage of time, and have the disadvantages of slow convergence speed and easy falling into local optimization.
In order to cope with the situation of robot assembly, Weiwei Wan considers the capturing ability and the assembly direction of the robot, and defines the assemblability. However, the method only considers the constraint of the robot, guarantees the feasibility and does not consider the optimality in the robot assembly process. The Rodrai guez I separates the robot assembly sequence planning problem into two layers, a logical layer and a physical layer. And planning a sequence in a logic layer, detecting and feeding back through a physical layer, improving a logic layer planning result, and improving the robot assembly sequence planning efficiency. However, the method needs real-time feedback of the state, real-time optimization of the assembly sequence is carried out, the calculated amount is large, and high requirements are put forward on an on-board computer.
Disclosure of Invention
In order to overcome the defects of the prior art, the invention provides a method for planning the on-orbit assembly sequence of a large-space structure. The invention redefines the evaluation function of the assembly sequence in consideration of shortest path and minimum energy consumption of the robot in the assembly process. The invention is considered more comprehensive and more practical. And the method has the characteristics of saving energy consumption for rail assembly and planning the motion of the robot while planning an assembly sequence.
The technical scheme adopted by the invention for solving the technical problem comprises the following steps:
firstly, establishing a kinetic equation of an assembly robot;
deducing a dynamic equation of the assembly robot according to a Lagrange function, and obtaining a mechanical arm dynamic equation of the n connecting rods through calculation as follows:
wherein M (q) is an inertia matrix, q is a joint angle,
is a nonlinear term, τ is the joint moment, J is the Jacobian matrix, F e Is the robot end force;
for inverse dynamics problems, according to q and q at each moment
Solving for
Determining q and q at the next time by integral iteration
The following are found by positive kinematic transformation:
q and
the iteration method comprises the following steps:
wherein t represents the time t, and step represents the step length;
the climbing robot adopts a symmetrical design, and when the end effectors are exchanged, only q is required to be ordered 7 ＝q 1 ，q 6 ＝q 2 ，q 5 ＝q 3 ，q 3 ＝q 5 ，q 2 ＝q 6 ，q 1 ＝q 7 And bringing the model into the established model;
step two, establishing a multi-robot path coordination planning method;
firstly, a graph theory method is adopted to establish robot motion path planning into an undirected graph form, an A-algorithm is adopted to plan a single robot motion path, then multi-robot coordinated path planning is carried out, and a coordination method based on the combination of priority and traffic rule constraint is adopted according to the actual assembly task requirement; firstly, determining the priority of each robot according to an assembly task, the capability of the robot, the reliability of the robot and the like, sequencing the robots according to the priority, wherein each robot only needs to consider the robot with the priority in front of the robot when moving; generating a current connected graph according to the current positions of the robots, determining vertexes of the robots capable of moving next step, and planning paths of the robots; if the planned path point passed by the robot at the next moment is in conflict with the path point passed by the robot with higher priority, the robots are in collision; at the moment, a set traffic rule, namely a waiting strategy is introduced, namely, the robot with low priority waits in situ, and after the robot with high priority passes through the conflict point, the robot with low priority continues to move to pass through the conflict point; at the next moment, the positions of the robots are updated, the connected graph is updated, the positions of the robots are updated at each moment repeatedly, and the robots move by one step at each moment, namely the robots are updated by one step each time;
analyzing the robot motion and calculating energy consumption;
dividing the motion of the robot in the assembly process into climbing motion and assembly motion, wherein the climbing motion enables the robot to move on a large-scale space structure, and the assembly motion enables the robot to complete assembly among the assembly units;
after the joint motion is planned, taking the track in the joint space as a nominal track, and controlling the joint angle of the robot so as to achieve the effect of tracking the nominal track; the control objective is to design the feedback controller such that the joint motion q (t) e R n Tracking planned robot joint movements q d (ii) a Adopting inverse dynamics control, taking formula (1) as a dynamics model, and during the trajectory planning, the tail end of the robot has no force and moment, namely F e When the value is 0, the design controller is as follows:
wherein ν is an auxiliary control input:
wherein, tau m In order to control the moment for the joint,
in order to expect the angular acceleration of the joint,
to expect angular velocity of the joint, q d To the desired joint angle, K VT And K PT Is a control gain matrix;
the error kinetics are obtained as follows:
selecting a gain matrix K satisfying a control target VT And K PT The stability of the control system can be ensured;
for the assembly operation, a control method based on force control is adopted to keep the contact force stable, and finally, the energy consumption is calculated according to the control moment, wherein the control method comprises the following steps:
modeling the robot as a rigid body, modeling the environment in which the robot contacts, i.e. the part of the truss structure, as a flexible body, and using K for rigidity p It shows that when the robot end contacts with the environment to generate a tiny displacement deltax, the generated elastic restoring force is:
F＝-K p δx (7)
wherein, F and deltax are both expressed on a task space coordinate system, and a rigidity matrix K p The diagonal matrix represents the stiffness of the part in three directions, and if the elastic restoring force is to be maintained, the robot joint moment should be:
τ＝J T F (8)
wherein J is a robot Jacobian matrix and represents the relationship between the terminal micro displacement and the joint micro displacement of the robot:
δx＝Jδq (9)
when the robot tip is in contact with the environment, the local deformation of the environment caused by the contact is caused by vectors
Represents:
wherein x is the position of the tail end of the robot, x E Is the environmental location;
the position control law of the x-y plane of the robot is designed as follows:
designing a compliance control law of the robot in the z direction as follows:
wherein, tau x-y Control moment in the x-y plane, τ z Control moment in z direction, J (q) is Jacobian matrix, K P And K D Is a control gain matrix;
the energy consumption of the robot is the sum of joint driving energy and electronic equipment energy, and the joint driving energy consumption is far greater than that of the electronic equipment, so that the robot is supposed to consume only the joint driving part;
for robot energy calculation, the absolute value form is adopted:
wherein n is the number of joints of the robot, and T is the total movement time of the robot;
step four: establishing an evaluation function, and optimizing the assembly sequence by adopting a particle swarm algorithm;
as with conventional assembly sequence planning, the relationship between assembly units is first measured:
(1) interference matrix
The interference matrix measures the conflict between the assembly unit to be assembled and the assembled assembly part, and if the assembly has n assembly units, the interference matrix is defined and expressed by IM, then I ijk Showing the assembly unit P j Along direction k with assembly unit P i The interference situation that occurs:
the three-dimensional space defines the assembly direction as three linearly independent vector axes, so that there are six interference matrixes along the three axes, namely IM +x 、IM -x 、IM +y 、IM -y 、IM +z 、IM -z The characteristics of the interference are known I ij(+k) ＝I ji(-k) I.e. assembling the unit P j Along direction k with assembly unit P i Occurring interference with the assembly unit P i Along direction-k with assembly unit P j The interference situation is the same; thus, defining an integrated interference matrix describes whether there is interference between assembled units throughout the assembly process:
the matrix IM describes whether interference occurs during assembly between every two parts;
(2) connection matrix
The assembling method is different among different assembling units, the connection matrix describes the connection relation among different assembling units, and for an assembly body consisting of n assembling units, the connection matrix C is defined as follows:
C＝(c ij ) n×n (15)
wherein, c ij Representing an assembly unit P i And an assembly unit P j The connection condition of (2):
wherein "no connection relation" means that there is no connection structure between the two assembly units; "there is contact connection" means that there is connection relation between two assembling units, but it cannot keep stable state after connection, that is, no external force is applied during connection, and the joint between the assembling units, hinge without fastening are included; "there is a stable connection" means that the assembled units remain stable after connection; the threaded connection, the welding and the like belong to stable connection;
(3) support matrix
For the space truss structure, the working scene is a space or an outer planet; the environment of different scenes is different, the gravity characteristic is also different, the support matrix measures whether stable support relationship exists between the assembly units in the assembly process under different environments and gravity characteristics, and the support matrix S is defined as follows:
S＝(s ij ) n×n (17)
wherein s is ij Representing an assembly unit P j To the assembly unit P i The supporting relationship of (1):
the evaluation indexes of assembly comprise assembly geometric feasibility, assembly stability, assembly weight directionality, assembly polymerization and assembly parallelism, and the following four assembly indexes are provided for a multi-robot assembly space truss task:
(a) assembly geometric feasibility;
the assembly geometric feasibility represents the property that the assembled unit does not interfere with an assembled assembly when assembled; the assembly direction is defined before assembly, the feasible assembly directions of different assembly units are solved, and the assembly geometry means that when the assembly units are assembled according to the assembly sequence, the assembly units in each step have feasible assembly sequences;
assembly geometry is solved by interference matrix, definition G k (P i ) For assembling unit P i The sum of interference values between the assembled body and the assembled body when the assembled body is assembled along the k direction; g k (P i ) Determines the unit P to be assembled i If assembling the unit P i G does not interfere with the assembled assembly in the k direction k (P i ) 0; if the unit P is assembled i Interference with the assembled assembly body in the k direction, G k (P i )≠0，G k (P i ) The specific expression is as follows:
for the assembly sequence { P 1 ,P 2 ,…,P n Is given n g Representing assembly units that cannot be assembled in this sequence, in the calculation of n g Then, it is initially assigned a value of 0, and G is calculated for each assembly unit k (P i ) When G is k (P i ) When equal to 0, n g ＝n g (ii) a When G is k (P i ) When not equal to 0, n g ＝n g + 1; if n is finally calculated g If 0, the assembly sequence is feasible; n is g Not equal to 0, the assembly sequence is not feasible;
(b) stability of assembly
The fitting stability indicates the ability of each fitting unit to maintain the fitting position and the fitting state after the fitting units are fitted; the assembly stability and assembly connection relation is gravity-dependent, so that the solution is obtained by a connection matrix C and a support matrix S, C ij 1 denotes that the assembly unit is connected to the assembly in a contacting manner, c ij 2 denotes that the assembly unit is stably connected to the assembly body, s ij 1 denotes an assembly unit P j To the assembly unit P i Has a supporting function; defining a connection relation n c And n s To n is paired with c And n s Initial assignment of 0, assembly sequence { P 1 ,P 2 ,…,P n In (c), c is calculated for each assembly unit ij And s ij Update n c ＝n c +c ij ，n s ＝n s +s ij ；n c The larger the assembly stability is; n is s The larger the assembly support, the better; and to ensure that the assembly is stable at each step, n is required for each step c > 0 or n s ＞0；
(c) Assembly path
The assembly path represents the sum of the path lengths moved by each robot in the assembly process and is obtained by calculation in the second step; define vertex V and edge E of assembly, for assembly sequence { P } 1 ,P 2 ,…,P n Let n be d Representing the total path of movement of the robot in this assembly sequence, initially an undirected graph G 0 ＝(V 0 ,E 0 ) Calculating the motion path of each robot according to the multi-robot collaborative path planning algorithm
And path length n d0 After the assembly unit is calculated, the next assembly unit is calculated according to the assembly sequence, the undirected graph G is updated to be (V, E), and calculation is carried out
n d ＝n d +n d0 (ii) a After all the assembly units are detected, outputting the path of each robot
And the sum n of the motion paths of the robot d ；
(d) Energy consumption of assembly
Assembly energy consumption represents the sum of the energy consumed by each robot during the assembly process, and is defined as n e Calculated by the formula (12) in the third step; for the assembled sequence { P 1 ,P 2 ,…,P n At least, in the meterCalculating the robot path
Then, according to the energy consumption calculation method of the formula (12), solving the energy consumption fuel of the robot, and enabling n e Outputs each robot motion plan q as full d And a control law τ;
carrying out quantitative calculation on the evaluation indexes, and carrying out normalization processing on different indexes by using an equation (20) to ensure that the evaluation indexes have the same influence on the whole index function; establishing a function model, solving different function values by different assembly sequences, and accurately evaluating the quality of the assembly sequences;
for the sequence { P 1 ,P 2 ,…,P n The evaluation function is:
the constraint conditions that satisfy the feasibility of the assembly sequence are as follows:
wherein n is c Representing the stability of assembly, n s Representing assembly support, n l Representing an assembly path, n e Representing assembly energy consumption. Omega 1 、ω 2 、ω 3 、ω 4 Respectively represent the weight coefficients of each index, and omega 1 +ω 2 +ω 3 +ω 4 1, each weight coefficient can be formulated according to different requirements of different assemblies, and the constraint condition represents a precondition met by an assembly sequence, namely, each step of assembly is required to be stable and each step has an assembly direction, namely, the constraint conditions do not interfere with the assembly;
and under the condition of ensuring that the formula (21) is established, finding the minimum value of the formula (20), namely finding the optimal sequence to obtain the optimal assembly sequence and the action and control sequence of the robot.
The invention has the beneficial effects that:
(1) in the assembly process, the multi-robot coordinated path planning method based on the design priority and the traffic rule is provided in consideration of the path planning of the multi-robot coordinated motion, and the collision among the robots is avoided and the energy is optimal in the assembly process.
(2) The invention analyzes the movement of the robot in the assembling process, and divides the movement in the assembling process into climbing movement based on position control and assembling movement based on force control. Therefore, after the planning of the assembly sequence is finished, the motion planning and control method of the robot can be given, and the follow-up tasks can be performed conveniently.
(3) Evaluation indexes of the assembly sequence are divided into a constraint index and an optimization index, the constraint index ensures the feasibility of assembly, and the optimization index considers the shortest path of the robot movement and the lowest energy consumption in the assembly process.
Drawings
Fig. 1 is a schematic view of a general model of an assembly robot of the present invention.
Fig. 2 is a schematic space structure diagram of the assembly of the present invention, wherein numerals represent assembly unit numbers.
Figure 3 is a diagram of the angular change of the climbing kinematics joint according to the invention.
Figure 4 is a graph of the moment variation of the control of the climbing joint according to the invention.
Fig. 5 is a view showing the angular change of the assembled kinematic joint according to the present invention.
Fig. 6 is a graph showing the variation of the control moment of the articulation joint of the present invention.
FIG. 7 is a graph of the z-axis contact force variation for the assembly of the present invention.
FIG. 8 is a graph of the change of the fit sequence optimization fitness function of the present invention.
Fig. 9 is a diagram of the change of the joint angle of the robot in the whole assembly process of the invention.
Fig. 10 is a diagram of the robot joint control moment variation during the whole assembly process of the present invention.
Fig. 11 is a diagram of the change of the robot energy consumption during the whole assembly process of the present invention.
FIG. 12 is a flow chart of the on-orbit assembly sequence planning of the spatially large structure according to the present invention.
Detailed Description
The invention is further illustrated by the following examples in conjunction with the drawings.
The invention aims to solve the problems in the prior art and provides a brand-new method for planning an on-orbit assembly sequence of a large-scale space structure. And planning an assembly sequence on the premise of ensuring the assembly feasibility, and realizing the optimization of the assembly sequence.
The technical scheme adopted by the invention for solving the technical problem comprises the following steps:
firstly, establishing a dynamic equation of an assembly robot;
deducing a dynamic equation of the assembly robot according to a Lagrange function, and obtaining the dynamic equation of the mechanical arm of the n connecting rod through calculation as follows:
wherein M (q) is an inertia matrix, q is a joint angle,
is a nonlinear term, τ is the joint moment, J is the Jacobian matrix, F e Is the robot end force;
for the inverse dynamics problem, the sum of q and q at each moment is used
Solving for
Determining q and q at the next time by integral iteration
The following were found by positive kinematic transformation:
q and
the iteration method comprises the following steps:
wherein t represents the time t, and step represents the step length;
the climbing robot adopts a symmetrical design, and when the end effectors are exchanged, only q is required to be ordered 7 ＝q 1 ，q 6 ＝q 2 ，q 5 ＝q 3 ，q 3 ＝q 5 ，q 2 ＝q 6 ，q 1 ＝q 7 And then the model is brought into the established model.
Step two, establishing a multi-robot path coordination planning method;
firstly, a graph theory method is adopted to establish robot motion path planning into an undirected graph form, an A-algorithm is adopted to plan a single robot motion path, then multi-robot coordinated path planning is carried out, and a coordination method based on the combination of priority and traffic rule constraint is adopted according to the actual assembly task requirement; firstly, determining the priority of each robot according to an assembly task, the capability of the robot, the reliability of the robot and the like, sequencing the robots according to the priority, wherein each robot only needs to consider the robot with the priority in front of the robot when moving; generating a current connected graph according to the current positions of the robots, determining vertexes of the robots capable of moving next step, and planning paths of the robots; if the planned path point passed by the robot at the next moment is in conflict with the path point passed by the robot with higher priority, the robots are in collision; at the moment, a set traffic rule, namely a waiting strategy, is introduced, namely, the robot with low priority waits in situ, and after the robot with high priority passes through the conflict point, the robot with low priority continues to move to pass through the point; the waiting strategy is beneficial to saving the energy consumption of the robot and is more suitable for space tasks; and at the next moment, updating the positions of the robots, updating the connected graph according to the updated positions, and repeating the updating of the positions of the robots at each moment, wherein the robots move by one step at each moment, namely the robots are updated at each moving step.
Analyzing the robot movement and calculating energy consumption;
dividing the motion of the robot in the assembly process into climbing motion and assembly motion, wherein the climbing motion enables the robot to move on a large space structure, and the assembly motion enables the robot to complete assembly among assembly units;
after the joint motion is planned, taking the track in the joint space as a nominal track, and controlling the joint angle of the robot so as to achieve the effect of tracking the nominal track; the control objective is to design the feedback controller such that the joint motion q (t) e R n Tracking planned robot joint movement q d (ii) a Adopting inverse dynamics control, taking a formula (1) as a dynamic model, and when the trajectory planning is carried out, the tail end of the robot has no force and moment, namely F e 0, so the controller is designed to:
wherein ν is an auxiliary control input:
wherein, tau m In order to control the moment for the joint,
in order to expect the angular acceleration of the joint,
to expect angular velocity of the joint, q d To the desired joint angle, K VT And K PT Is a control gain matrix;
the error dynamics were found to be:
selecting a gain matrix K that satisfies a control target VT And K PT The stability of the control system can be ensured;
for the assembly operation, a control method based on force control is adopted to keep the contact force stable, and finally, the energy consumption is calculated according to the control moment, wherein the control method comprises the following steps:
modeling the robot as a rigid body, modeling the environment in which the robot contacts, i.e. the part of the truss structure, as a flexible body, and using K for rigidity p It shows that when the robot end contacts with the environment to generate a tiny displacement deltax, the generated elastic restoring force is:
F＝-K p δx (7)
wherein, F and deltax are both expressed on a task space coordinate system, and a rigidity matrix K p The diagonal matrix represents the stiffness of the part in three directions, and if the elastic restoring force is to be maintained, the robot joint moment should be:
τ＝J T F (8)
wherein J is a robot Jacobian matrix and represents the relationship between the micro displacement of the tail end of the robot and the micro displacement of the joint:
δx＝Jδq (9)
when the robot tip is in contact with the environment, the local deformation of the environment caused by the contact is caused by vectors
Represents:
Wherein x is the position of the tail end of the robot, x E Is the environmental location;
the position control law of the x-y plane of the robot is designed as follows:
designing a compliance control law of the robot in the z direction as follows:
wherein, tau x-y Control moment in the x-y plane, τ z Control moment in z direction, J (q) jacobian matrix, K P And K D Is a control gain matrix;
the energy consumption of the robot is the sum of joint driving energy and electronic equipment energy, and the joint driving energy consumption is far greater than that of the electronic equipment, so that the robot is supposed to consume only the joint driving part;
for robot energy calculation, the absolute value form is adopted:
wherein n is the number of joints of the robot, and T is the total movement time of the robot;
step four: establishing an evaluation function, and optimizing the assembly sequence by adopting a particle swarm algorithm;
as with conventional assembly sequence planning, the relationship between assembly units is first measured:
(1) interference matrix
Interference matrix measures the conflict between the assembly unit to be assembled and the assembled assembly part, and if the assembly has n assembly units, the interference matrix is defined and expressed by IM, then I ijk Showing the assembly unit P j Along direction k with mounting sheetMeta P i The interference situation that occurs:
the three-dimensional space defines the assembly directions as three linearly independent vector axes, so that there are six interference matrices along the three axes, which are respectively IM +x 、IM -x 、IM +y 、IM -y 、IM +z 、IM -z The characteristics of the interference are known I ij(+k) ＝I ji(-k) I.e. assembling the unit P j Along direction k with assembly unit P i Occurring interference with the assembly unit P i Along direction-k with assembly unit P j The interference condition is the same; thus, defining an integrated interference matrix describes whether there is interference between assembled units throughout the assembly process:
the matrix IM describes whether interference occurs or not when every two parts are assembled;
(2) connection matrix
The assembly method is different among different assembly units, such as: threaded connection, riveting, welding, gluing, pin connection, key connection and molding connection; the connection matrix describes the connection relationship among different assembly units, and for an assembly body consisting of n assembly units, the connection matrix C is defined as follows:
C＝(c ij ) n×n (15)
wherein, c ij Representing an assembly unit P i And assembly unit P j The connection condition of (2):
wherein "no connection relation" means that there is no connection structure between the two assembly units; "there is contact connection" means that there is connection relation between two assembling units, but it cannot keep stable state after connection, that is, no external force is applied during connection, and the joint between the assembling units, hinge without fastening are included; "there is a stable connection" means that the assembled units remain stable after connection; and the threaded connection, the welding and the like belong to stable connection.
(3) Support matrix
For the space truss structure, the working scene is a space or an outer planet; the environment of different scenes is different, the gravity characteristic is also different, the support matrix measures whether stable support relationship exists between the assembly units in the assembly process under different environments and gravity characteristics, and the support matrix S is defined as follows:
S＝(s ij ) n×n (17)
wherein s is ij Representing an assembly unit P j To the assembly unit P i The supporting relationship of (1):
the evaluation indexes of the assembly of the invention comprise assembly geometric feasibility, assembly stability, counterweight directionality, assembly polymerization and assembly parallelism, and aiming at the task of assembling the space truss by multiple robots, the following four assembly indexes are provided:
(a) assembly geometric feasibility;
the assembly geometric feasibility represents the property that the assembled unit does not interfere with an assembled assembly when assembled; the assembly direction is defined before assembly, the feasible assembly directions of different assembly units are solved, and the assembly geometry means that when the assembly units are assembled according to the assembly sequence, the assembly units in each step have feasible assembly sequences;
assembly geometry is solved by interference matrix, definition G k (P i ) For assembling unit P i The sum of the interference values between the assembled body and the assembled body when the assembled body is assembled along the k direction; g k (P i ) Determines the unit P to be assembled i If assembling the unit P i G is not interfered with the assembled assembly body in the k direction k (P i ) 0; if the unit P is assembled i Interference with the assembled assembly body in the k direction, G k (P i )≠0，G k (P i ) The specific expression is as follows:
for the assembled sequence { P 1 ,P 2 ,…,P n Let n be g Representing assembly units that cannot be assembled in this sequence, in the calculation of n g Then, it is initially assigned a value of 0, and G is calculated for each assembly unit k (P i ) When G is k (P i ) When equal to 0, n g ＝n g (ii) a When G is k (P i ) When not equal to 0, n g ＝n g + 1; if n is finally calculated g If 0, the assembly sequence is feasible; n is a radical of an alkyl radical g Not equal to 0, assembly sequence is not feasible;
(b) stability of assembly
The fitting stability indicates the ability of each fitting unit to maintain the fitting position and the fitting state after the fitting units are fitted; the assembly stability and assembly connection relation is gravity-dependent, so that the solution is obtained by a connection matrix C and a support matrix S, C ij 1 denotes that the assembly unit is connected to the assembly in a contacting manner, c ij 2 denotes that the assembly unit is stably connected to the assembly body, s ij 1 denotes an assembly unit P j To the assembly unit P i Has a supporting function; defining a connection relation n c And n s To n is paired c And n s Initial assignment of 0, assembly sequence { P } 1 ,P 2 ,…,P n In (d), c is calculated for each assembly cell ij And s ij Update n c ＝n c +c ij ，n s ＝n s +s ij ；n c The larger the assembly stability is, the better; n is a radical of an alkyl radical s The larger, the assemblyThe better the support; and to ensure that the assembly is stable at each step, n is required at each step c > 0 or n s ＞0；
(c) Assembly path
The assembly path represents the sum of the path lengths of the movement of each robot in the assembly process and is obtained by calculation in the second step; defining vertex V and edge E of assembly, for assembly sequence { P } 1 ,P 2 ,…,P n Is given n d Representing the total path of movement of the robot in this assembly sequence, initially an undirected graph G 0 ＝(V 0 ,E 0 ) Calculating the motion path of each robot according to a multi-robot collaborative path planning algorithm
And path length n d0 After the assembly unit is calculated, the next assembly unit is calculated according to the assembly sequence, the undirected graph G is updated to be (V, E), and calculation is carried out
n d ＝n d +n d0 (ii) a Outputting each robot path after all the assembly units are detected
And the sum n of the motion paths of the robot d (ii) a Obviously, n d The smaller the total path of travel of the robot, the shorter the assembly.
(d) Energy consumption of assembly
Assembly energy consumption represents the sum of the energy consumed by each robot during the assembly process, and is defined as n e Calculated by the formula (12) in the step three; for the assembly sequence { P 1 ,P 2 ,…,P n }, after calculating the robot path
Then, according to the energy consumption calculation method of the formula (12), solving the robot energy consumption fuel, and enabling n e Outputs each robot motion plan q as full d And the control law tau. Obviously, n e The smaller the machineThe smaller the total energy consumed by the robot, the more advantageous the assembly.
The assembly geometric feasibility and the assembly stability are constraint indexes, assembly cannot be completed by assembly sequences which do not meet the first two indexes, and the smaller the assembly path and the assembly energy consumption, the better the assembly sequence.
Carrying out quantitative calculation on the evaluation indexes, and carrying out normalization processing on different indexes by using an equation (20) to ensure that the evaluation indexes have the same influence on the whole index function; and establishing a function model, solving different function values by different assembly sequences, and accurately evaluating the quality of the assembly sequences.
For the sequence { P 1 ,P 2 ,…,P n The evaluation function is:
the constraint conditions that satisfy the feasibility of the assembly sequence are as follows:
wherein n is c Representing the stability of assembly, n s Stands for assembly support, n l Representing an assembly path, n e Representing assembly energy consumption. Omega 1 、ω 2 、ω 3 、ω 4 Respectively represent each index weight coefficient, and ω 1 +ω 2 +ω 3 +ω 4 Each weight coefficient can be formulated according to different requirements of different assemblies, and the constraint condition represents a precondition met by an assembly sequence, namely, each step of assembly needs to be stable, and each step has an assembly direction, namely, the assembly is not interfered with.
And under the condition of ensuring that the formula (21) is established, finding the minimum value of the formula (20), namely finding the optimal sequence to obtain the optimal assembly sequence and the action and control sequence of the robot.
The embodiment comprises the following four steps:
firstly, establishing a kinetic equation of the assembly robot.
Deducing a dynamic equation of the assembly robot according to a Lagrange function, and obtaining a mechanical arm dynamic equation of the n connecting rods through calculation as follows:
wherein tau is the moment at the tail end of the mechanical arm, T is a transformation matrix, n is the number of connecting rods, g is a gravity constant, I ai In the robot, n is 6, which is the equivalent moment of inertia of the transmission device. And since the robot operates in space, g can be regarded as 0, and is simplified as:
in the formula:
writing is in matrix form:
wherein M (theta) is an inertia matrix, theta is a joint angle,
is a nonlinear term, τ is the joint moment, J is the Jacobian matrix, F e Is the robot end force.
For inverse dynamics problems, according to q and q at each moment
Solving for
By iterative integration to find q and q at the next time
The following can be found by a positive kinetic transformation:
q and
the iteration method comprises the following steps:
the climbing robot adopts a symmetrical design, and when the end effectors are exchanged, only theta is required to be adjusted 6 ＝θ 1 ，θ 5 ＝θ 2 ，θ 4 ＝θ 3 ，θ 3 ＝θ 4 ，θ 2 ＝θ 5 ，θ 1 ＝θ 6 And then the model is brought into the established model.
And step two, establishing a multi-robot path coordination planning method.
Firstly, a graph theory method is adopted to establish the motion path planning of the robot into an undirected graph, and an A-star algorithm is adopted to plan the motion path of a single robot. And then performing multi-robot coordinated path planning. And (4) adopting a coordination method combining a priority criterion and a traffic rule according to the actual assembly task requirement. The robot priority is firstly accurately determined according to the assembly task, the robot capability, the robot reliability and the like, the robot priorities are sequenced, and each robot only needs to consider the robot with the priority sequenced in front of the robot when moving. And generating a current connected graph according to the current positions of the robots, determining the vertexes of the robots which can move next, and planning the paths of the robots. If the planned robot paths pass through the same point at the next moment, collisions between the robots will occur. At this time, the established traffic rules, namely waiting strategies, are introduced. The waiting strategy is beneficial to saving the energy consumption of the robot and is more suitable for space tasks. Here, the robot with the higher priority is caused to move first, and the robot with the lower priority keeps the current position and does not move. And at the next moment, updating the position of each robot, updating the connection diagram according to the position, and repeating the process.
Step three, analyzing the robot movement and calculating the energy consumption
The movement of the robot in the assembling process is divided into climbing movement and assembling movement. The climbing motion enables the robot to move on a large space structure, and the assembly motion enables the robot to complete assembly among structures. For climbing movement, three movement modes are analyzed, namely turning gait, creeping gait and sliding gait. And performing motion planning on the three gaits, adopting a position-based control method, and finally selecting a motion mode with the minimum energy consumption according to the analysis of the energy consumption by the control force. The control method comprises the following steps:
after the joint motion is planned, the track in the joint space is used as a nominal track, and the joint angle of the robot is controlled, so that the effect of tracking the nominal track is achieved. The main objective of the control is to design the feedback controller such that the joint motion q (t) e R n Can track the robot joint motion q planned by us d . A simple design method for robot control is to utilize a linear control scheme based on linearization of a system to an operating point, wherein a PD control mode is adopted by a controller, and the specific control law is as follows:
for the assembly operation, a force control based control method is used to keep the contact force stable, and finally the energy consumption is calculated according to the control torque. The control method comprises the following steps:
machine for cuttingThe robot is modeled as a rigid body, the environment contacted by the robot, namely a part of a truss structure, is modeled as a flexible body, and the rigidity of the flexible body is K p And (4) showing. When the robot end contacts with the environment to generate a tiny displacement deltax, the generated elastic restoring force is as follows:
F＝-K p δx (6)
where F and δ x are both represented on the task space coordinate system. Rigidity matrix K p Often chosen as a diagonal matrix representing stiffness in three directions of the part. If the elastic restoring force is to be maintained, the robot joint moment should be:
τ＝J T F (7)
wherein J is a robot Jacobian matrix which can also represent the relationship between the micro displacement of the tail end of the robot and the micro displacement of the joint:
δx＝Jδq (8)
when the robot tip is in contact with the environment, local deformation of the environment caused by the contact may be vectorized
Represents:
In conclusion, the position control law of the x-y plane of the robot is designed as follows:
designing a compliance control law of the robot in the z direction as follows:
step four: and establishing an evaluation function, and optimizing the assembly sequence by adopting a particle swarm algorithm.
The following four evaluation indexes are established:
(1) geometric feasibility: the geometric feasibility of assembly represents the property of the parts assembled without interfering with the already assembled assembly.
(2) Stability: the assembling stability indicates the ability of each part to maintain the assembled position and the assembled state after the parts are assembled.
(3) Assembly path: the assembly path represents the sum of the path lengths traveled by each robot during assembly.
(4) Assembling energy consumption: the assembly energy consumption represents the sum of the energy consumed by each robot during the assembly process.
For the above evaluation index, a quantitative calculation is performed thereon. And different indexes are normalized to ensure the same influence on the whole index function. And establishing a function model, solving different function values by different assembly sequences, and accurately evaluating the quality of the assembly sequences.
For the sequence { P 1 ,P 2 ,…,P n Its merit function is:
the constraint conditions that the assembly sequence is feasible are satisfied as follows:
wherein n is c Representing the stability of assembly, n s Representing assembly support, n l Representing an assembly path, n e Representing assembly energy consumption. Omega 1 、ω 2 、ω 3 、ω 4 Respectively represent the weight coefficients of each index, and omega 1 +ω 2 +ω 3 +ω 4 1. Each weight coefficient can be set according to different requirements of different assemblies. The constraint condition represents a precondition satisfied by the assembly sequence, that is, each step of assembly needs to be stable and each step has an assembly direction, that is, the constraint condition does not interfere with the assembly.
TABLE 1 kinematic and kinetic parameters of an assembly robot
Table 1 shows kinematic and kinetic parameters of the assembly robot system used in the example, and fig. 1 shows a general model of the assembly robot. Fig. 2 is a schematic space structure diagram of the assembly. Fig. 3 and 4 show the change of the joint angle and the joint control moment under the climbing motion, the change of the joint angle is stable, and the tracking error of the controller is small. Fig. 5 and 6 show the joint angle and joint control moment variations under the assembling motion. It can be seen that the joint angle and the joint control moment finally tend to be stable. But the joint control torque is not all zero because this part of the joint torque is used to keep the contact force constant. FIG. 7 is a z-axis contact force variation during assembly, where it can be seen that the contact force is stabilized at 2N, completing the objective of assembly control. Fig. 8 shows the variation of the optimization fitness function of the assembly sequence, in which the fitness function is seen to decrease continuously and finally stabilize at the minimum value, and the optimization process is finished. Fig. 9 to 11 show the joint angle, joint control moment and energy consumption variation throughout the assembly process. One scale on the abscissa represents one motion of the robot, and the dashed brown line represents the end effector switch time. The figure shows that the angular motion curve of the robot joint is smooth, the tracking error of the designed control law is small, and the robot returns to the initial state after moving at each stage. The joint control torque can be used for guiding the selection of each joint steering engine. Robot energy consumption can be used to guide robot energy reserve planning. Fig. 12 is a flowchart of the entire process of sequence planning.
The assembly parts of the embodiment of the invention are space truss structures which are composed of 9 parts, wherein the space truss structures comprise 3 tetrahedral truss units and 6 rods, and the part numbers are shown in figure 2. The assembly robot is a 6 degree-of-freedom robotic arm with a double end-effector, and the kinematic/kinetic parameters of the system are shown in table 1. The method for on-orbit assembly sequence planning of the large-scale space structure is verified by taking a 6-degree-of-freedom robot assembly 9-part space truss as an example. The fuel consumption of three climbing movements of rolling movement, sliding movement and peristaltic movement is compared in a simulation mode, and an optimal climbing movement mode is selected. The control method of the assembly movement is given and the fuel consumption is calculated. And finally, optimizing by adopting a particle swarm optimization algorithm to obtain an optimal assembly sequence of the space structure, wherein the optimal assembly sequence is [1,2,3,6,7,5,4,8 and 9 ]. Simulation results verify that this technique is feasible.
Claims (1)
1. An on-orbit assembly sequence planning method for a large space structure is characterized by comprising the following steps:
firstly, establishing a kinetic equation of an assembly robot;
deducing a dynamic equation of the assembly robot according to a Lagrange function, and obtaining the dynamic equation of the mechanical arm of the n connecting rod through calculation as follows:
wherein M (q) is an inertia matrix, q is a joint angle,
is a nonlinear term, τ is the joint moment, J is the Jacobian matrix, F e Is a robot tip force;
for the inverse dynamics problem, the sum of q and q at each moment is used
Solving for
Determining q and q at the next time by integral iteration
The following are found by positive kinematic transformation:
q and
the iteration method comprises the following steps:
wherein t represents time t, and step represents step length;
the climbing robot adopts a symmetrical design, and when the end effectors are exchanged, only q is required to be ordered 7 ＝q 1 ，q 6 ＝q 2 ，q 5 ＝q 3 ，q 3 ＝q 5 ，q 2 ＝q 6 ，q 1 ＝q 7 And bringing the model into the established model;
step two, establishing a multi-robot path coordination planning method;
firstly, a graph theory method is adopted to establish robot motion path planning into an undirected graph form, an A-algorithm is adopted to plan a single robot motion path, then multi-robot coordinated path planning is carried out, and a coordination method based on the combination of priority and traffic rule constraint is adopted according to the actual assembly task requirement; firstly, determining the priority of each robot according to an assembly task, the capability of the robot and the reliability of the robot, sequencing the robots according to the priority, and only considering the robots with the priority in front of the robots when each robot moves; generating a current connected graph according to the current positions of the robots, determining vertexes of the robots capable of moving next step, and planning paths of the robots; if the planned path point passed by the robot at the next moment conflicts with the path point passed by the robot with higher priority, the robots collide with each other; at the moment, a set traffic rule, namely a waiting strategy is introduced, namely, the robot with low priority waits in situ, and after the robot with high priority passes through the conflict point, the robot with low priority continues to move to pass through the conflict point; at the next moment, the positions of the robots are updated, the connected graph is updated, the positions of the robots are updated at each moment repeatedly, and the robots move by one step at each moment, namely the robots are updated by one step each time;
analyzing the robot movement and calculating energy consumption;
dividing the motion of the robot in the assembly process into climbing motion and assembly motion, wherein the climbing motion enables the robot to move on a large-scale space structure, and the assembly motion enables the robot to complete assembly among the assembly units;
after the joint motion is planned, taking the track in the joint space as a nominal track, and controlling the joint angle of the robot so as to achieve the effect of tracking the nominal track; the control objective is to design the feedback controller such that the joint motion q (t) e R n Tracking planned robot joint movement q d (ii) a Adopting inverse dynamics control, taking formula (1) as a dynamics model, and during the trajectory planning, the tail end of the robot has no force and moment, namely F e When the value is 0, the design controller is as follows:
wherein ν is an auxiliary control input:
wherein, tau m In order to control the moment for the joint,
in order to expect the angular acceleration of the joint,
is due to stage ofAngular velocity of the joints of the eye, q d To desired joint angle, K VT And K PT Is a control gain matrix;
the error kinetics are obtained as follows:
selecting a gain matrix K satisfying a control target VT And K PT The stability of the control system can be ensured;
for the assembly operation, a control method based on force control is adopted to keep the contact force stable, and finally, the energy consumption is calculated according to the control torque, wherein the control method comprises the following steps:
modeling the robot as a rigid body, modeling the environment in which the robot contacts, i.e. the part of the truss structure, as a flexible body, with the stiffness K p It shows that when the robot end contacts with the environment to generate a tiny displacement deltax, the generated elastic restoring force is:
F＝-K p δx (7)
wherein, F and deltax are both expressed on a task space coordinate system, and a rigidity matrix K p The diagonal matrix represents the stiffness of the part in three directions, and if the elastic restoring force is to be maintained, the robot joint moment should be:
τ＝J T F (8)
wherein J is a robot Jacobian matrix and represents the relationship between the terminal micro displacement and the joint micro displacement of the robot:
δx＝Jδq (9)
when the robot tip is in contact with the environment, the local deformation of the environment caused by the contact is vectorially related to the position of the robot tip
Represents:
wherein x is the position of the tail end of the robot, x E Is the environmental location;
the position control law of the x-y plane of the robot is designed as follows:
designing a compliance control law of the robot in the z direction as follows:
wherein, tau x-y Control moment in the x-y plane, τ z Control moment in z direction, J (q) jacobian matrix, K P And K D Is a control gain matrix;
the energy consumption of the robot is the sum of joint driving energy and electronic equipment energy, and the joint driving energy consumption is far larger than that of the electronic equipment, so that the robot is supposed to consume only the joint driving part;
for robot energy calculation, the absolute value form is taken:
wherein n is the number of joints of the robot, and T is the total movement time of the robot;
step four: establishing an evaluation function, and optimizing the assembly sequence by adopting a particle swarm algorithm;
as with conventional assembly sequence planning, the relationship between assembly units is first measured:
(1) interference matrix
Interference matrix measures the conflict between the assembly unit to be assembled and the assembled assembly part, and if the assembly has n assembly units, the interference matrix is defined and expressed by IM, then I ijk Showing the assembly unit P j Along direction k with assembly unit P i The interference situation that occurs:
the three-dimensional space defines the assembly direction as three linearly independent vector axes, so that there are six interference matrixes along the three axes, namely IM +x 、IM -x 、IM +y 、IM -y 、IM +z 、IM -z The characteristics of the interference are known I ij(+k) ＝I ji(-k) I.e. assembly of the unit P j Along direction k with assembly unit P i Occurring interference with the assembly unit P i Along direction-k with assembly unit P j The interference condition is the same; thus, defining an integrated interference matrix describes whether there is interference between assembled units throughout the assembly process:
the matrix IM describes whether interference occurs or not when every two parts are assembled;
(2) connection matrix
The assembling method is different among different assembling units, the connection matrix describes the connection relation among different assembling units, and for an assembly body composed of n assembling units, the connection matrix C is defined as follows:
C＝(c ij ) n×n (15)
wherein, c ij Representing an assembly unit P i And an assembly unit P j The connection condition of (1):
wherein "no connection relation" means that there is no connection structure between the two assembly units; "there is contact connection" means that there is connection relation between two assembling units, but it cannot keep stable state after connection, that is, no external force is applied during connection, and the joint between the assembling units, hinge without fastening are included; "there is a stable connection" means that the assembled units remain stable after connection; the threaded connection and the welding are stable connections;
(3) support matrix
For the space truss structure, the working scene is a space or an outer planet; the environment of different scenes is different, the gravity characteristic is also different, the support matrix measures whether stable support relationship exists between the assembly units in the assembly process under different environments and gravity characteristics, and the support matrix S is defined as follows:
S＝(s ij ) n×n (17)
wherein s is ij Representing an assembly unit P j To the assembly unit P i The supporting relationship of (1):
the evaluation indexes of assembly comprise assembly geometric feasibility, assembly stability, counterweight directionality, assembly polymerization and assembly parallelism, and the following four assembly indexes are provided aiming at a task of assembling the space truss by multiple robots:
(a) assembly geometric feasibility;
the assembly geometric feasibility represents the property of no interference with an assembled assembly body when the assembly unit is assembled; the assembly direction is defined before assembly, the feasible assembly directions of different assembly units are solved, and the assembly geometry means that when the assembly units are assembled according to the assembly sequence, the assembly units in each step have feasible assembly sequences;
assembly geometryBy solving for the interference matrix, defining G k (P i ) For assembling unit P i The sum of the interference values between the assembled body and the assembled body when the assembled body is assembled along the k direction; g k (P i ) Determines the unit P to be assembled i If assembling the unit P i G is not interfered with the assembled assembly body in the k direction k (P i ) 0; if the unit P is assembled i Interference with the assembled assembly body in the k direction, G k (P i )≠0，G k (P i ) The specific expression is as follows:
for the assembly sequence { P 1 ,P 2 ,…,P n Is given n g Representing assembly units that cannot be assembled in the sequence, in calculating n g Then, it is initially assigned a value of 0, and G is calculated for each assembly unit k (P i ) When G is k (P i ) When equal to 0, n g ＝n g (ii) a When G is k (P i ) When not equal to 0, n g ＝n g + 1; if n is finally calculated g If 0, the assembly sequence is feasible; n is a radical of an alkyl radical g Not equal to 0, the assembly sequence is not feasible;
(b) stability of assembly
The fitting stability indicates the ability of each fitting unit to maintain the fitting position and the fitting state after the fitting units are fitted; the relation between the assembly stability and the assembly connection is related to gravity, so that the connection matrix C and the support matrix S are used for solving, C ij 1 denotes that the assembly unit is connected to the assembly in a contacting manner, c ij 2 denotes that the assembly unit is stably connected to the assembly body, s ij 1 denotes an assembly unit P j To the assembly unit P i Has a supporting function; defining a connection relation n c And n s To n is paired c And n s Initial assignment of 0, assembly sequence { P 1 ,P 2 ,…,P n In (d), c is calculated for each assembly cell ij And s ij Update n c ＝n c +c ij ，n s ＝n s +s ij ；n c The larger the assembly stability is, the better; n is a radical of an alkyl radical s The larger the assembly support, the better; and to ensure that the assembly is stable at each step, n is required for each step c >0 or n s >0；
(c) Assembly path
The assembly path represents the sum of the path lengths of the movement of each robot in the assembly process and is obtained by calculation in the second step; defining vertex V and edge E of assembly, for assembly sequence { P } 1 ,P 2 ,…,P n Let n be d Representing the total path of movement of the robot in this assembly sequence, initially an undirected graph G 0 ＝(V 0 ,E 0 ) Calculating the motion path of each robot according to a multi-robot collaborative path planning algorithm
And path length n d0 After the assembly unit is calculated, the next assembly unit is calculated according to the assembly sequence, the undirected graph G is updated to be (V, E), and calculation is carried out
n d ＝n d +n d0 ；
After all the assembly units are detected, outputting the path of each robot
And the sum n of the motion paths of the robot d ；
(d) Energy consumption of assembly
Assembly energy consumption represents the sum of the energy consumed by each robot in the assembly process, and is defined as n e Calculated by the formula (12) in the third step; for the assembled sequence { P 1 ,P 2 ,…,P n After the robot path is calculated
Then, according to the energy consumption calculation method of the formula (12), solving the robot energy consumption fuel, and enabling n e Outputs each robot motion plan q as full d And control law τ;
carrying out quantitative calculation on the evaluation indexes, and carrying out normalization processing on different indexes by using an equation (20) to ensure that the evaluation indexes have the same influence on the whole index function; establishing a function model, solving different function values by different assembly sequences, and accurately evaluating the quality of the assembly sequences;
for the sequence { P 1 ,P 2 ,…,P n }, the evaluation function is:
the constraint conditions that the assembly sequence is feasible are satisfied as follows:
wherein n is c Representing the stability of assembly, n s Representing assembly support, n l Representing an assembly path, n e Representing assembly energy consumption, ω 1 、ω 2 、ω 3 、ω 4 Respectively represent the weight coefficients of each index, and omega 1 +ω 2 +ω 3 +ω 4 1, each weight coefficient can be formulated according to different requirements of different assemblies, and the constraint condition represents a precondition that an assembly sequence meets, namely, each step of the assembly is required to be stable, and each step has an assembly direction, namely, the assembly does not interfere with the assembly;
and under the condition of ensuring that the formula (21) is established, finding the minimum value of the formula (20), namely finding the optimal sequence to obtain the optimal assembly sequence and the action and control sequence of the robot.
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