CN115507858A - Single-robot and multi-robot driving path navigation method - Google Patents

Single-robot and multi-robot driving path navigation method Download PDF

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CN115507858A
CN115507858A CN202211478448.5A CN202211478448A CN115507858A CN 115507858 A CN115507858 A CN 115507858A CN 202211478448 A CN202211478448 A CN 202211478448A CN 115507858 A CN115507858 A CN 115507858A
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node
robot
time
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subsequent
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CN115507858B (en
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房殿军
蒋济州
向佳豪
蒋红琰
罗尔夫·施密特
王平
任晓霞
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Qingdao Sino German Intelligent Technology Research Institute
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01C—MEASURING DISTANCES, LEVELS OR BEARINGS; SURVEYING; NAVIGATION; GYROSCOPIC INSTRUMENTS; PHOTOGRAMMETRY OR VIDEOGRAMMETRY
    • G01C21/00—Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00
    • G01C21/20—Instruments for performing navigational calculations
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02P—CLIMATE CHANGE MITIGATION TECHNOLOGIES IN THE PRODUCTION OR PROCESSING OF GOODS
    • Y02P90/00—Enabling technologies with a potential contribution to greenhouse gas [GHG] emissions mitigation
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Abstract

The invention discloses a single robot and a multi-robot running path navigation method, which belong to the technical field of navigation and are used for path navigation of multiple robotsPWill bePLeading the data into a module to be processed, and calling and fusing a heuristic method to detect a path setPWhether a conflict exists in (1); if no conflict exists, the path set is outputPAnd finishing, if the conflict exists, calling a single robot driving path navigation method to formAAnd will beALeading the data into a module to be processed, and repeatedly executing the dataPAnd (4) importing the data into a module to be processed until no conflict exists.

Description

Single-robot and multi-robot driving path navigation method
Technical Field
The invention discloses a single-robot and multi-robot driving path navigation method, and belongs to the technical field of navigation.
Background
With the continuous development of logistics technology, the intelligent technology represented by artificial intelligence and robots is deeply integrated with a warehouse logistics system, a warehouse system combined with an intelligent sorting robot is developed, and the key for improving the navigation capability of a multi-robot system in the warehouse logistics system is to improve the logistics efficiency. In multi-robot system navigation, the algorithm of the multi-robot path planning problem mostly assumes that the motions of the robots have uniform duration, and the time is dispersed into time steps, and each time step of the robots occupies one node and moves to an adjacent node in a unit time step. However, in a real scene, the motion of the robot is continuous and uneven, and meanwhile, the influences of the geometric dimension, the motion direction and the like of the robot need to be considered. Therefore, the multi-robot path planning problem algorithm under discrete time has certain limitation in the practical environment.
The conventional multi-robot path planning related algorithm described above strongly constrains the graph and the robot, including but not limited to the following points: the time discretization is carried out as unit step length; the time overhead spent for each move is one unit step; the robot just occupies an independent position in each time step, and the positions correspond to nodes on the graph; robot edgex、yThe coordinate axis moves in four directions, and focusing and multidirectional movement are not considered; each robot moves at a constant speed without considering the geometric size, and the influence of inertia effect is ignored. The above conditions define that the motion of multiple robots is synchronous, the cost of moving to adjacent nodes is a unit time step, and the multi-robot path planning problem under the strong constraint is defined as a unit cost multi-robot path planning problem. However, in the actual movement of the robots in the real warehousing environment, because the movement of each robot is continuous and non-uniform, the movement of each robot is difficult to achieve complete synchronization, and the movement duration is the sameAnd the time expenditure and the waiting cost of the multi-robot path planning problem are increased due to the constraints that the waiting time can only be multiples of the time step length and the like. In addition, the problem of unit overhead multi-robot path planning limits that only node conflicts and edge conflicts exist among multiple robots, and node occupation conflicts caused by the size of the robots are not fully considered.
Disclosure of Invention
The invention provides a single-robot and multi-robot driving path navigation method, which solves the problem that navigation paths of a multi-robot system in the prior art are easy to conflict.
The single robot driving path navigation method comprises the following steps:
s1, inputting a grid map G, a starting node S and a final node into a processing system of the robot
Figure 370678DEST_PATH_IMAGE001
Representing a subsequent node;
s2, the processing system comprises a module to be processed, a processed module and a subsequent module, wherein the processed node is led into the processed module, and the unprocessed node is led into the unprocessed module;
s3, importing the starting node into a module to be processed, and initializing an unprocessed module;
s4, if the nodes exist in the module to be processed, executing S5, if the nodes do not exist, outputting the robot path, and then ending;
s5, selecting the minimum node in the total cost of the initial node from the module to be processed as the current node, outputting the robot path if the current node reaches the target state of the initial node, and ending the robot path, otherwise, putting the current node into the processed module, and calling a state expansion method to generate a subsequent module;
s6, judging whether the subsequent nodes in the subsequent module are expanded or not, and if the subsequent nodes are expanded, setting the total cost and the actual cost of the subsequent nodes as the total cost and the actual cost of the subsequent nodes
Figure 959922DEST_PATH_IMAGE002
Then executing S7, if the expansion is not carried out, directly executing S7;
s7, judging whether the actual cost of the subsequent node is larger than the actual cost of the initial node and the actual cost from S to S
Figure 270818DEST_PATH_IMAGE001
If yes, the actual cost of the subsequent node is equal to the actual cost of the initial node and the sum of the costs from s to s
Figure 666027DEST_PATH_IMAGE001
Then executing S8, if not, directly executing S8;
s8, updating the time variable of the subsequent node, enabling the total cost of the subsequent node to be equal to the sum of the actual cost of the subsequent node and the estimated cost of the subsequent node, and then importing the subsequent node into the module to be processed;
and S9, repeatedly executing the steps from S4 to S8 until the module to be processed has no node.
The state expansion method comprises the following steps:
z1, inputting a starting node, initializing a subsequent module, and setting a function M(s) to return to the action executed by the starting node;
z2, for each action in M(s)mLet s perform action m with a starting safety interval time equal to the sum of the time spent performing action m and the time of s, and let s perform action m with an ending safety interval time equal to the sum of the time spent performing action m and the interval ending time;
z3, outputting a subsequent module and ending if each configuration parameter in the configuration of the state s after the action m is executed meets the judgment condition; if the judgment condition is not satisfied, lettEqual to safety intervaliInternal earliest arrival to post-execution action m state
Figure 152503DEST_PATH_IMAGE003
And then determines the time of the configurationtIf yes, outputting the subsequent module and ending, if not, making the subsequent state equal toiAndtand configuring the state, and importing the subsequent state into the subsequent module.
The judgment conditions in Z3 include:iis greater than the end safety interval time when state s performs action m, oriIs less than the starting safety interval time when state s performs action m.
The multi-robot driving path navigation method comprises the following steps:
b1, inputting a grid map G, an initial node s and a final node t into a path processing system of the robot;
b2, planning an optimal path for each robot by using a single robot driving path navigation method, and calculating path cost;
b3, merging the optimal paths of the robots into a path setPWill bePLeading the path to a module to be processed, and calling and fusing a heuristic method to detect a path setPWhether a conflict exists in (1);
b4, if no conflict exists, outputting the path setPEnding, if conflict exists, executing B5;
b5, defining quadruplets
Figure 381491DEST_PATH_IMAGE004
To show the robotr i In a time period oft i Execute actions at the timea i Will interact with the robotr j In a time period oft j Execute actions at the same timea j The sound-making conflict is generated,t i 、t j are all time periods of time,r i is a new path ofP i A plurality ofP i Composing a set of new pathsAAnd a single robot driving path navigation method is called to formAAnd will beAAnd (4) importing the data into a module to be processed, and repeatedly executing B3 until no conflict exists.
Compared with the prior art, the invention has the beneficial effects that: the CCBS algorithm is optimal, complete and efficient. Under the condition that the number of the robots is the same, compared with a CBS algorithm, the operation speed of the CCBS is greatly improved, and when the number of the robots is 30, the calculation speed of the CCBS is only 99% of that of the CBS. The high-level and low-level search extension of the CCBS is less, the improved SIPP algorithm as a low-level search algorithm has smaller search space by a method of calculating a position-time interval pair to replace an original position-time step pair, and the algorithm operation efficiency is improved; the improved ECCBS and hybrid-ECCBS algorithm improves the operation efficiency, and meanwhile, the conflict detection and solution performance is better, and the operation time is relatively less. The hybrid-ECCBS can offset the accumulated overhead loss caused by the suboptimal boundary, and the solution time is still acceptable when the number of robots reaches 70 in the simulation environment.
Drawings
FIG. 1 is a graph comparing the MAPF problem with the MAPFR problem;
FIG. 2 is
Figure 445262DEST_PATH_IMAGE005
Motion models of the neighborhood weighted graph at d =2,3,4,5;
FIG. 3 is an example of collision detection for robots of different geometries;
fig. 4 is a robot 1 motion timeline;
FIG. 5 is an example of a high level constraint tree resolving a conflict;
FIG. 6 is a CCBS high level restriction tree extension;
fig. 7 is a schematic view of the principle of focus search.
Detailed Description
The following description will further illustrate embodiments of the present invention with reference to specific examples:
the single robot driving path navigation method comprises the following steps:
s1, inputting a grid map G, a starting node S and a final node into a processing system of the robot
Figure 644162DEST_PATH_IMAGE001
Representing a subsequent node;
s2, the processing system comprises a module to be processed, a processed module and a subsequent module, wherein the processed node is led into the processed module, and the unprocessed node is led into the unprocessed module;
s3, importing the starting node into a module to be processed, and initializing an unprocessed module;
s4, if the nodes exist in the module to be processed, executing S5, if the nodes do not exist, outputting the robot path, and then ending;
s5, selecting the minimum node in the total cost of the initial node from the module to be processed as a current node, outputting a robot path if the current node reaches the target state of the initial node, and ending, otherwise, putting the current node into the processed module, and calling a state expansion method to generate a subsequent module;
s6, judging whether the subsequent nodes in the subsequent module are expanded or not, and if the subsequent nodes are expanded, setting the total cost and the actual cost of the subsequent nodes as the total cost and the actual cost of the subsequent nodes
Figure 719565DEST_PATH_IMAGE002
Then executing S7, if the expansion is not carried out, directly executing S7;
s7, judging whether the actual cost of the subsequent node is larger than the actual cost of the initial node and the actual cost from S to S
Figure 385033DEST_PATH_IMAGE001
If yes, the actual cost of the subsequent node is equal to the actual cost of the initial node and the sum of the costs from s to s
Figure 139362DEST_PATH_IMAGE001
Then executing S8, if not, directly executing S8;
s8, updating the time variable of the subsequent node, enabling the total cost of the subsequent node to be equal to the sum of the actual cost of the subsequent node and the estimated cost of the subsequent node, and then importing the subsequent node into the module to be processed;
and S9, repeatedly executing the steps from S4 to S8 until the module to be processed does not have a node.
The state expansion method comprises the following steps:
z1, inputting a starting node, initializing a subsequent module, and setting a function M(s) to return to the action executed by the starting node;
z2, for each action in M(s)mLet s equal the time it takes to perform action m to sThe sum of time, the end safety interval time when s executes the action m is equal to the sum of the time consumed by executing the action m and the interval end time;
z3, outputting a subsequent module and ending if each configuration parameter in the configuration of the state s after the action m is executed meets the judgment condition; if the judgment condition is not satisfied, lettEqual to safety intervaliInternal earliest arrival to post-execution action m state
Figure 673112DEST_PATH_IMAGE003
And then determines the time of the configurationtIf yes, outputting the subsequent module and ending, if not, making the subsequent state equal toiAndtand configuring the state, and importing the subsequent state into the subsequent module.
The judgment conditions in Z3 include:iis greater than the ending safety interval time when state s performs action m, oriIs less than the starting safety interval time when state s executes action m.
The navigation method for the driving path of the multiple robots comprises the following steps:
b1, inputting a grid map G, an initial node s and a final node t into a path processing system of the robot;
b2, planning an optimal path for each robot by using a single robot driving path navigation method, and calculating path cost;
b3, merging the optimal paths of the robots into a path setPWill bePLeading the data into a module to be processed, and calling and fusing a heuristic method to detect a path setPWhether a conflict exists in (1);
b4, if no conflict exists, outputting the path setPAnd ending, if the conflict exists, executing B5;
b5, defining quadruplets
Figure 603022DEST_PATH_IMAGE004
To show the robotr i In a time period oft i Execute actions at the timea i Will interact with the robotr j In a time period oft j Execute actions at the timea j The sound-making conflict is generated,t i 、t j are all time periods of time,r i the new path of (A) isP i A plurality ofP i Composing a set of new pathsAAnd a single robot driving path navigation method is called to formAAnd will beAAnd (4) importing the data into a module to be processed, and repeatedly executing B3 until no conflict exists.
In order to enable the multi-robot path planning algorithm to be better adapted to the real warehousing environment, a non-unit overhead multi-robot path planning problem corresponding to the multi-robot path planning algorithm is provided. Undirected connected graph of non-unit overhead multi-robot path planning problem
Figure 32866DEST_PATH_IMAGE006
On the basis of the weight, add the weight to form an undirected weighted graph
Figure 946595DEST_PATH_IMAGE007
In which each node is definedvNon-uniform positive value weight of
Figure 752877DEST_PATH_IMAGE008
The weight of the edge reflects the duration of the robot motion. Representing a non-unit overhead multi-robot path planning problem MAPF closer to a real motion scene as MAPF R MAPF and MAPF as in FIG. 1 R Comparison of (4). For the four-way connectivity map, MAPF R The robots under the problem can freely start and stop, do not need to wait for the next time step to start moving, and can avoid collision only by keeping each robot in a safe interval, so that the accumulated overhead of the system is reduced.
For a multi-degree-of-freedom motion model, MAPF, of a mobile robot in an intelligent machine picking system R Is not limited to a four-way communication diagram, but is expanded to
Figure 68452DEST_PATH_IMAGE009
A neighborhood grid multidirectional connectivity graph, thisThe computation of the time-cost is no longer based on the manhattan distance but on the euclidean distance. For example, for the case of d =3, the robot may be allowed to move diagonally along the four hypotenuses in the eight-way connectivity graph, with the overhead of diagonal movement being along the coordinate axis
Figure 403618DEST_PATH_IMAGE010
In comparison of four-direction movement and eight-direction movement of multiple robots at the same initial target position, the degree of freedom of the robot movement is higher, but the collision detection model should be changed accordingly. A schematic diagram in the case of d =2,3,4,5, etc. is shown in fig. 2. MAPF, a variant of the multi-robot path planning problem MAPF under continuous-time constraints R More storage environment practical factors are considered.
For solving the non-unit overhead multi-robot path planning problem MAPF R The invention provides an improved CCBS double-layer search algorithm based on continuous time constraint. The lower-layer algorithm part is an improved safe time interval SIPP algorithm, so that a single-robot continuous time path planning algorithm is introduced firstly.
First, the present invention proposes a continuous time Path Planning algorithm for a single robot, i.e. a Safe time Interval (SIPP) algorithm.
The Safe Time interval (Safe Time Internal) means that the robot can stay at the nodevThe longest period of time during which there is no conflict with other robots, but during which there is a conflict one time step before and one time step after the period. In contrast, a collision Time interval (conflicttime Internal) represents a continuous Time period, in which Time steps Conflict with the dynamic obstacle, but the former Time step and the latter Time step are safe Time intervals. Defining a State Space (State Space) as a Set of all possible configurations of the system (Set of Configuration), replacing a plurality of states in the past (expressed as Configuration and Time step pair State = (Configuration, time interval)) with a single State (expressed as Configuration and Time interval pair State = (Configuration)) on the State Space descriptionTime step)), where Configuration is an independent variable independent of time, defined as a set of robot poses
Figure 663698DEST_PATH_IMAGE011
And contains multidimensional information such as position coordinates, orientation angles, and joint angles.
The safe time interval algorithm SIPP is improved on the basis of the A-algorithm, and the main improvement is that an extended state node is generated and a time variable is updated for a subsequent node. SIPP algorithm uses evaluation function of A-algorithm
Figure 414617DEST_PATH_IMAGE012
In which
Figure 912594DEST_PATH_IMAGE013
Which represents the total overhead of the system,
Figure 90766DEST_PATH_IMAGE014
representing the actual cost, representing the distance from the initial node to the current location node,
Figure 838142DEST_PATH_IMAGE015
in order to estimate the cost, the distance from the current node to the target node is expressed as a heuristic operator. The SIPP algorithm establishes a time axis for each spatial configuration at initialization for predicting the trajectory of dynamic obstacles.
In the SIPP algorithm, the input quantities are a grid map G, a start node s and a final node t. In the algorithm flow, if s is used to represent the current state,
Figure 392751DEST_PATH_IMAGE001
indicating its subsequent state, from s to
Figure 745235DEST_PATH_IMAGE001
Can be expressed as
Figure 94308DEST_PATH_IMAGE016
. First of all, when a user wants to use the apparatus,defining two lists, namely openlist and closed list, storing nodes which are already traversed in the closed list and storing nodes which are not yet traversed in the openlist. Will be in the initial state
Figure 328980DEST_PATH_IMAGE017
Put into openlist, initialize closelist to empty set. When the openlist is not an empty set, the following loop is executed: firstly, selecting from openlist
Figure 156122DEST_PATH_IMAGE018
The minimum node is used as currentnode (current node), if currentnode has reached the target state, path is output, otherwise currentnode is put into closelist, and state expansion method is adopted
Figure 628692DEST_PATH_IMAGE019
Generating a list of subsequent nodes for state s
Figure 414245DEST_PATH_IMAGE020
. For each one
Figure 870634DEST_PATH_IMAGE021
In (1)
Figure 94942DEST_PATH_IMAGE001
If not previously expanded
Figure 828543DEST_PATH_IMAGE001
Then it will
Figure 644052DEST_PATH_IMAGE022
And
Figure 722823DEST_PATH_IMAGE023
are all provided with
Figure 750822DEST_PATH_IMAGE024
。
If it is not
Figure 604509DEST_PATH_IMAGE025
To make an order
Figure 325340DEST_PATH_IMAGE026
. Then updated
Figure 897267DEST_PATH_IMAGE001
And time variable of
Figure 463377DEST_PATH_IMAGE027
At the same time will
Figure 171570DEST_PATH_IMAGE001
Inserted into openlist. The above cycle is repeated until openlist is empty.
State expansion method
Figure 328882DEST_PATH_IMAGE028
The action executed by the function M(s) to return to the state s includes both the wait and move actions. Firstly, a successor state node list is listed
Figure 716001DEST_PATH_IMAGE029
Set as the empty set. For each action M in M(s), let config be the configuration of state s after execution of action M, including information such as coordinates, angles, etc. of the robot.
Figure 492327DEST_PATH_IMAGE030
For each action's execution time, to assist in confirming which safe time intervals are available in the generated configuration.
Figure 55027DEST_PATH_IMAGE031
And
Figure 648819DEST_PATH_IMAGE032
indicating the start and end safety intervals when state s performs action m. For each configuration parameter in configi，
Figure 257655DEST_PATH_IMAGE033
And
Figure 837672DEST_PATH_IMAGE034
indicating the corresponding start and end times. If it is not
Figure 520457DEST_PATH_IMAGE035
Or
Figure 19572DEST_PATH_IMAGE036
This configuration iteration is skipped, with the start and end times not being within the safe interval. This iteration is also skipped if there is no time within the safe interval at which the configuration config can be reached earliest. If the configuration iteration is not skipped after the two determinations, the method is implemented
Figure 787808DEST_PATH_IMAGE037
Namely the nodes of the subsequent state, and the nodes of the subsequent state have the objective function of minimizing the cumulative cost
Figure 499412DEST_PATH_IMAGE037
To arrive at the configured time as early as possible. Will be provided with
Figure 895758DEST_PATH_IMAGE037
Is added to
Figure 706719DEST_PATH_IMAGE029
In the list. Repeating the iteration action m until the iteration is finished, and returning a successor state node list
Figure 696672DEST_PATH_IMAGE029
。
Based on the robot Continuous multi-degree-of-freedom motion model considering the safety interval and the strong constraint of the CBS algorithm under the multi-robot path planning problem, the invention provides a CCBS (Continuous-time Conflict-Based Search) algorithm Based on Continuous time constraint, and can solve the multi-robot path planning problem under Continuous time. As a complete, robust and optimal double-layer search algorithm, the CCBS follows the high-layer constraint tree of the CBS algorithm at the high layer for solving the robot conflict. The low-level algorithm searches for a path satisfying the constraint condition for each robot based on the improved SIPP algorithm. The main differences from CBS are: on the high level search, different conflict detection and conflict resolution models are adopted. Due to the discrete and continuous time differences, CCBS employs a collision detection and collision resolution mechanism that computes time intervals. CBS adds position-time pair as constraint on constraint tree, and CCBS adds action-time pair as constraint; on the low-level search, the improved SIPP algorithm is adopted as the path search algorithm of the single robot.
The CCBS employs different collision detection and collision resolution models in the higher layer search. Under the continuous time constraint, the robot can have any geometric dimension, so the time overhead of each action can be any, the position-time step-based conflict detection model in the CBS is not applicable any more, the actions are adopted in the CCBS to describe conflicts, and quadruples are defined
Figure 946388DEST_PATH_IMAGE038
To show the robotr i In a time period oft i Execute actions at the timea i Will interact with the robotr j In a time period oft j Execute actions at the same timea j The sound-making conflict is generated,t i 、t j are all time periods.
The method adopts a closed-loop accurate detection method based on collective computation to carry out conflict detection, and has the core that the time of possible conflicts in the future of the dynamic barrier is predicted, whether time overlapping exists when a plurality of robots with specific shapes execute actions is detected, and a safe time interval is computed for the possible conflicts among the actions so as to avoid the collisions. The robot model is abstracted into disc processing, the condition that geometric conflict occurs is that the connecting line of the circle centers of the two robots is smaller than the sum of the radiuses of the robots, the time period of the geometric conflict is a conflict time interval, and the safety time interval is the complement of the conflict interval on the total movement time interval. As shown in FIG. 3, 3 robots are providedMove from the initial position to the target position along the respective tracks in case of slight conflict, and have a radius relation
Figure 728399DEST_PATH_IMAGE039
All robots move at uniform speed and the speed isvThe length of the grid side islWhen detecting that there is a possible conflict between the robot 1 and the robots 2 and 3, the condition for ensuring that there is no geometric conflict between the robots is
Figure 710261DEST_PATH_IMAGE040
In the above formula, the first reaction mixture is,
Figure 187510DEST_PATH_IMAGE041
the distance from the center of the robot 1 to the center of the robot 2,
Figure 37655DEST_PATH_IMAGE042
the same is true. For time interval conflicts, the movement time of the robot 3 is
Figure 283959DEST_PATH_IMAGE043
At time intervals
Figure 764619DEST_PATH_IMAGE044
According to
Figure 729164DEST_PATH_IMAGE045
The condition can be calculated by the time when the robot 3 and the robot 1 start to overlap geometrically
Figure 117420DEST_PATH_IMAGE046
And end time
Figure 483811DEST_PATH_IMAGE047
，
Figure 666530DEST_PATH_IMAGE048
Then the conflict time interval is
Figure 711847DEST_PATH_IMAGE049
Safe time intervalIs that
Figure 773300DEST_PATH_IMAGE050
. In a similar way, a safe time interval of robot 1 can be obtained as
Figure 994197DEST_PATH_IMAGE051
Safe time intervals for the robot 2
Figure 613397DEST_PATH_IMAGE052
Fig. 4 shows a motion time axis of the robot 1 as an example.
In the aspect of conflict resolution mechanism, the high-level constraint tree is also expanded by adopting the optimal priority search and is selectedopenlistAnd taking the node N with the minimum repeated iteration accumulated cost as a root node of the constraint tree, firstly judging whether the node N is a target node, and if the node N is the target node, terminating iteration. Secondly, a conflict detection mechanism verifies whether a conflict exists in the path planning under the condition that the N is used as the root node, and if the conflict exists, the conflict exists
Figure 552535DEST_PATH_IMAGE053
Then N is expanded into two constraint child nodes, respectively
Figure 751435DEST_PATH_IMAGE054
And
Figure 561259DEST_PATH_IMAGE055
since each action completion time is arbitrary and continuous and needs to be described by a time interval, adding a constraint to each child node requires calculating a conflict time interval existing between each action, and for a conflict, calculating a time interval of a conflict existing between each action
Figure 616940DEST_PATH_IMAGE053
Act ina i And actionsa j The maximum collision time interval of (d) is expressed as: fromt i Start to perform motiona i Robot (2)r i Will be in timet j Begin to perform an actiona j Robot (2)r j A collision occurs. Left sub-tree of constraint tree
Figure 371269DEST_PATH_IMAGE056
Presentation robotr i In the time domain
Figure 514806DEST_PATH_IMAGE057
Inability to perform actions thereina i Similar constraint tree right subtree
Figure 710295DEST_PATH_IMAGE058
Presentation robotr j In the time domain
Figure 140139DEST_PATH_IMAGE059
Inability to perform actions thereina j The time period is calculated by the collision detection model. In conflict time interval
Figure 912923DEST_PATH_IMAGE057
And
Figure 860150DEST_PATH_IMAGE059
the calculation of (the safe time interval is opposite) needs to consider the kinematics and the geometric dimension of the robot, but only the uniform motion is considered by neglecting the inertia effect of starting and stopping the robot, and the dimensions of the robots are arbitrary and the same. By using multiple time samples, the sampling time interval is a very small time increment
Figure 503621DEST_PATH_IMAGE060
From the start time point of the collision time intervalt i Starting to increment until the end of the collision interval, so
Figure 510892DEST_PATH_IMAGE061
Wherein n is a positive integer. FIG. 5 is an example of the high level constraint tree resolution conflict described above.
As the CCBS conflict detection model needs to calculate the safety time interval considering the volume size of the robot, compared with the situation that the CBS only needs to calculate the conflict position node and the time without considering the volume size, along with the increase of the scale number of the robot, especially for a picking system of an intensive warehouse, the conflict detection occupies a large part of the operation time of an algorithm, and in order to accelerate the conflict detection and simplify a conflict detection mechanism model, only action conflicts with time overlapping and geometric shape overlapping are detected. In addition, the following two heuristic methods are adopted to accelerate the collision detection process.
A history conflict Heuristic method (Past-conflicts Heuristic) is used for tracking and recording each pair of robots
Figure 770972DEST_PATH_IMAGE062
And the number of times of conflict occurrence is determined, the robot pairs with the larger number of times of conflict occurrence in the past are considered preferentially when the conflict is detected, the search is stopped immediately when the conflict search is detected, and the conflict is added into the constraint tree to generate child nodes for conflict resolution. The principle adopted by the robot is that the robots with a large number of conflicts in the past may conflict with each other in the future, so that the robot takes priority in detection. Although the heuristic can accelerate the collision detection, there is a limitation that what type of collision is preferentially solved when the constraint tree nodes are expanded has a great influence on the size and the overall running time of the constraint tree, so that the collision type is considered to be classified. Conflicts are divided here into basic conflicts (Cardinal conflicts) and Semi-basic conflicts (Semi-Cardinal conflicts). Basic conflict means that any constraint added when resolving a conflict raises the system cumulative Cost (Sum of Cost, SOC), while semi-basic conflict means that one constraint added when resolving a conflict raises the SOC, but the other constraint added does not change the SOC, i.e. there is a sub-tree in the constraint tree to increase the system SOC. There is also a Non-fundamental conflict (Non-fundamental conflict) associated with it, meaning that any constraint added does not change the SOC. The basic conflict is solved firstly, and then the semi-basic conflict is solved to accelerate the algorithm speed, because the basic conflict is the main conflict type which causes the system SOC to be improved, and after two sub-constraint trees are addedThere is no more expensive path between the two robots to choose from, and resolving such conflicts first reduces the likelihood of semi-basic conflicts occurring. Although the historical conflict elicitation needs to detect all conflict types for resolution, the method can terminate the search once a conflict is detected, and does not need to wait until all conflict types are detected.
A fusion Heuristic method (Hybrid Heuristic) is used for fusing acceleration of conflict detection of a history conflict Heuristic method and a method for preferentially solving basic conflict acceleration. All conflict types are detected at the beginning and only basic conflicts are selected for resolution, if all the nodes are non-basic conflicts (no basic conflicts or semi-basic conflicts), the heuristic method of selecting historical conflicts for subtrees containing the nodes in all constraint tree nodes is replaced. The fusion heuristic is primarily directed to nodes that contain only non-fundamental conflicts.
For the lower search part of the CCBS, the aforementioned SIPP algorithm is employed. The SIPP only considers the path search of a single robot for avoiding the dynamic obstacle, and for better high-level constraint suitable for the CCBS algorithm, a consistent solution meeting the constraint condition is searched, and the SIPP is required to be limited from executing actions in a conflict time interval. For robotr i Is restricted by
Figure 521890DEST_PATH_IMAGE063
The classified discussion is made for the case where the action is waiting and moving.
The first kind isa i When the movement action is executed. Let initial and target positions be vAND
Figure 19867DEST_PATH_IMAGE064
If it is an actiona i For a robotr i Step of time
Figure 57094DEST_PATH_IMAGE065
When the initial position v is reached, the action is removed and a new action is added
Figure 945415DEST_PATH_IMAGE066
Denotes waiting at v until the moment
Figure 234445DEST_PATH_IMAGE067
Then move to
Figure 586929DEST_PATH_IMAGE068
. The constraint is added to avoid
Figure 326215DEST_PATH_IMAGE069
In-process conflict occurs, waiting for conflict interval
Figure 436253DEST_PATH_IMAGE070
And after the collision is finished, the mobile terminal moves to avoid the generation of the collision.
The second kind isa i When a wait action is performed. If it is moveda i Is composed ofr i At time intervals
Figure 263395DEST_PATH_IMAGE071
Wait at internal node v, then generate a new action
Figure 735965DEST_PATH_IMAGE066
By disabling the time interval in sectionsr i Waiting for, limiting during, the periodr i Only at time intervals
Figure 380573DEST_PATH_IMAGE072
And
Figure 712328DEST_PATH_IMAGE073
and (4) internally waiting. This constraint is added to prevent conflicts from occurring while node v waits.
In an embodiment, d =3 allows diagonal motion, three disc robot radii
Figure 608740DEST_PATH_IMAGE074
The side length of the grid is 2m, the grid moves at a constant speed and the speeds are all
Figure 935816DEST_PATH_IMAGE075
The start (filled circle) and target position (dashed circle) are in the figure. After inputting grid map G, initial node list s and target node list T, firstly neglecting conflict calling function
Figure 751325DEST_PATH_IMAGE076
Planning an optimal path for each robot and calculating the path cost of each robot to obtainr 1 Of (2) a
Figure 835956DEST_PATH_IMAGE077
，r 2 Of (2) a
Figure 598376DEST_PATH_IMAGE078
，r 3 Of (2) a
Figure 311117DEST_PATH_IMAGE079
Set of paths
Figure 432613DEST_PATH_IMAGE080
And the total cost for calculating the three paths is 22.828, and the conflict exists at the position E
Figure 4540DEST_PATH_IMAGE081
At this time, the root node is not the target node, two child nodes need to be generated to solve the conflict, and the constraint is added to the left node on the constraint tree
Figure 570651DEST_PATH_IMAGE082
Right node adding constraints
Figure 137898DEST_PATH_IMAGE083
Calling the bottom layer
Figure 436155DEST_PATH_IMAGE076
Calculate a new path that satisfies the left node constraint, at this pointr 1 It is necessary to wait for 2s at Dr 2 By conflicting nodesE, moving the movable table after the step E,r 1 new path of (2)
Figure 229799DEST_PATH_IMAGE084
，r 2 Is kept constant
Figure 334021DEST_PATH_IMAGE085
，r 3 At this point, there is no conflicting edge
Figure 286934DEST_PATH_IMAGE086
The vehicle is continuously driven, and the vehicle is driven,
Figure 490513DEST_PATH_IMAGE087
the total cost of computation is 24.828, and Openlist is updated with A, howeverr 2 Stay inr 3 The hard magnet generates new conflict at the H position, further branch expansion solution is needed, the condition of adding the right node is considered firstly at the momentr 2 It is necessary to wait 2s at Br 1 The node E passes through the collision node and then moves,r 1 new path of (2)
Figure 99349DEST_PATH_IMAGE088
，r 2 The path remains unchanged
Figure 944945DEST_PATH_IMAGE089
，r 3 At the moment, no protruding edge exists
Figure 752364DEST_PATH_IMAGE090
The vehicle is continuously driven, and the vehicle is driven,
Figure 720320DEST_PATH_IMAGE091
the total calculation cost is also 24.828, and when no conflict exists, a consistent solution, namely paths of all robots, is output. The constraint tree corresponding to resolving conflicts is shown in FIG. 6.
Meanwhile, in order to improve the calculation speed and the scale of the CCBS algorithm, the CCBS is subjected to boundary suboptimal expansionAnd (4) performing optimization, namely improving a low-level SIPP search algorithm and a high-level search tree of the CCBS by adopting a focus search method. The ECCBS algorithm with the suboptimal expanded boundary can also improve the calculation scale and the operation speed of the CCBS, and is convenient to compare with the performance of the ECBS algorithm under the same environment variable. In the aspect of low-level algorithm, SIPP is based on
Figure 222977DEST_PATH_IMAGE092
Improved algorithm of, therefore, CBS
Figure 341106DEST_PATH_IMAGE093
The focus search of the algorithm is equally applicable.
Focus search may utilize a free-spread cumulative cost function
Figure 3031DEST_PATH_IMAGE094
The value of (a) widens the selection range of the optimal solution to an interval, thereby shortening the time taken to find the optimal solution. Given configurable sub-optimal factors
Figure 141888DEST_PATH_IMAGE095
Specifying a search path total cost equal to or less than a boundary value
Figure 397420DEST_PATH_IMAGE096
Wherein
Figure 178295DEST_PATH_IMAGE097
Is the total cost of the optimal path. The focus search defines Openlist for storing traversed nodes and Focallist, which is a subset of Openlist and defines two arbitrary functions
Figure 163568DEST_PATH_IMAGE098
And
Figure 145431DEST_PATH_IMAGE099
，
Figure 622680DEST_PATH_IMAGE100
determines which nodes are in the Focallist
Figure 676086DEST_PATH_IMAGE101
Representing minimum on Openlist
Figure 312604DEST_PATH_IMAGE098
Value of,
Figure 465368DEST_PATH_IMAGE102
is a node in Openlist, then
Figure 164333DEST_PATH_IMAGE103
For all nodes n
Figure 818169DEST_PATH_IMAGE104
The latter minimum value can be expressed as
Figure 512455DEST_PATH_IMAGE105
Sub-optimum factor for a given boundary
Figure 570541DEST_PATH_IMAGE106
Focallist contains a minimum overhead
Figure 287961DEST_PATH_IMAGE103
To the boundary value
Figure 214329DEST_PATH_IMAGE107
Figure 763122DEST_PATH_IMAGE108
As shown in fig. 7,
Figure 523268DEST_PATH_IMAGE109
，
Figure 321459DEST_PATH_IMAGE110
for selecting which nodes of the Focallist to expand,
Figure 254780DEST_PATH_IMAGE111
can be selected as
Figure 613341DEST_PATH_IMAGE112
Or
Figure 544388DEST_PATH_IMAGE113
Other parameters may be considered depending on the constraints. By using
Figure 564297DEST_PATH_IMAGE114
And
Figure 238991DEST_PATH_IMAGE111
the focus search for an arbitrary function is represented as
Figure 762377DEST_PATH_IMAGE115
Accumulating the cost function in the optimization of the boundary suboptimal extension of CCBS
Figure 333166DEST_PATH_IMAGE116
The nodes used for selecting and storing the Focallist are set with different suboptimal factors to meet the requirements
Figure 371530DEST_PATH_IMAGE117
The node(s) is stored in the Focallist from the Openlist. Conflict elicitor
Figure 318757DEST_PATH_IMAGE118
An extension node is decided. The high level focus search is also based on
Figure 696649DEST_PATH_IMAGE119
The node stored in the Focallist is selected,
Figure 969498DEST_PATH_IMAGE120
the node extended in Focallist is selected.
The method carries out experimental simulation in the warehouse multi-robot environment based on the CCBS algorithm under continuous time, considers the motion direction, the geometric dimension and the motion model under continuous time for being closer to the real scene, and carries out test calculationMethod for solving MAPF R And (4) performing various indexes of path quality and algorithm performance in case of problems. The CCBS algorithm under continuous time is mainly designed according to the following three aspects:
(1) Solving MAPF in structured standard warehouse map by CCBS algorithm R And comparing the performance of each index of the problem path quality and the algorithm performance with the experimental result of the discrete-time CBS algorithm under the same calculation example.
(2) ECCBS improved through boundary suboptimal thought is compared with an ECBS algorithm experimental result of discrete time, and a hybird-ECCBS algorithm after conflict detection is accelerated by fusing a heuristic method R And (4) optimizing each algorithm index on the problem.
(3) Testing MAPF R In the problem of
Figure 229578DEST_PATH_IMAGE121
In the neighborhood connected graph, the influence of different motion direction d values on path results and various indexes of algorithm performance.
In order to verify the performance of the algorithm of the invention, a multi-robot warehousing environment is adopted for simulation. The simulation map is a 161m × 63m standardized warehouse map, which comprises 5699 goods shelves, each grid node is 1m × 1m in size, and the simulation map is in the shape of a disc and is in the size of
Figure 980497DEST_PATH_IMAGE122
The reason for setting this particular size is that multiple robots can safely follow the previous robot movement without collision when moving diagonally and furthermore do not geometrically conflict with the robot located in the center of the grid when the cross-diagonal movement occurs, the robot speed being 1m/s.
CBS is a multi-robot path planning algorithm that is widely used. The invention provides an improved CCBS algorithm on the basis of CBS, a conflict detection and conflict solution mechanism for calculating time intervals is adopted in high-level search, and a low-level algorithm is designed on the basis of a safe time interval SIPP algorithm, so that the CCBS can better solve the problem of multi-robot path planning in continuous time and is verified through a simulation experiment; performing boundary suboptimal expansion on CCBSDeveloping optimization to form an improved ECCBS algorithm, introducing a fusion heuristic method to accelerate the formation of a hybrid-ECCBS algorithm, and accelerating the solution of the multi-robot path planning problem in continuous time; provides a multi-degree-of-freedom motion model of a mobile robot and uses
Figure 150578DEST_PATH_IMAGE123
The neighborhood weighted graph ensures that the motion direction of the robot in the multi-robot path planning problem is not limited to four directions any more, thereby improving the motion diversity of the robot; the system accumulated cost can be reduced by properly increasing the value d of the movable direction of the robot, but the operation time of the algorithm is prolonged due to the fact that the value d is too large. In general, the value of d can be set to 2,3 or 4 according to the actual robot operation condition, and if the value of d is set to 5, an acceptable path solution cannot be obtained when the number of robots is too large.
It is to be understood that the above description is not intended to limit the present invention, and the present invention is not limited to the above examples, and those skilled in the art may make modifications, alterations, additions or substitutions within the spirit and scope of the present invention.

Claims (4)

1. The single robot driving path navigation method is characterized by comprising the following steps:
s1, inputting a grid map G, a starting node S and a final node into a processing system of the robot
Figure 462142DEST_PATH_IMAGE001
Representing a subsequent node;
s2, the processing system comprises a module to be processed, a processed module and a subsequent module, wherein the processed node is led into the processed module, and the unprocessed node is led into the unprocessed module;
s3, importing the starting node into a module to be processed, and initializing an unprocessed module;
s4, if the nodes exist in the module to be processed, executing S5, if the nodes do not exist, outputting the robot path, and then ending;
s5, selecting the minimum node in the total cost of the initial node from the module to be processed as a current node, outputting a robot path if the current node reaches the target state of the initial node, and ending, otherwise, putting the current node into the processed module, and calling a state expansion method to generate a subsequent module;
s6, judging whether the subsequent nodes in the subsequent module are expanded or not, and if the subsequent nodes are expanded, setting the total cost and the actual cost of the subsequent nodes as the total cost and the actual cost of the subsequent nodes
Figure 678360DEST_PATH_IMAGE002
Then executing S7, if the expansion is not carried out, directly executing S7;
s7, judging whether the actual cost of the subsequent node is larger than the actual cost of the initial node and the actual cost from S to S
Figure 92023DEST_PATH_IMAGE001
If yes, the actual cost of the subsequent node is equal to the actual cost of the initial node and the sum of the costs from s to s
Figure 116611DEST_PATH_IMAGE001
Then executing S8, if not, directly executing S8;
s8, updating the time variable of the subsequent node, enabling the total cost of the subsequent node to be equal to the sum of the actual cost of the subsequent node and the estimated cost of the subsequent node, and then importing the subsequent node to a module to be processed;
and S9, repeatedly executing the steps from S4 to S8 until the module to be processed has no node.
2. The single robot travel path navigation method as set forth in claim 1, wherein the state extension method includes:
z1, inputting a starting node, initializing a subsequent module, and setting a function M(s) to return to the action executed by the starting node;
z2, for each action in M(s)mLet s perform action m with a starting safe interval time equal to the sum of the time spent performing action m and the time of sMaking s an end safety interval time when executing action m equal to the sum of time consumed by executing action m and an interval end time;
z3, outputting a subsequent module and ending if each configuration parameter in the configuration of the state s after the action m is executed meets the judgment condition; if the judgment condition is not satisfied, lettEqual to safety intervaliInternal earliest arrival to post-execution action m state
Figure 200105DEST_PATH_IMAGE001
And then determines the time of the configurationtIf yes, outputting the subsequent module and ending, if no, making the subsequent state equal toiAndtand configuring the state, and importing the subsequent state into the subsequent module.
3. The single-robot travel path guidance method according to claim 2, wherein the judgment condition in Z3 includes:iis greater than the end safety interval time when state s performs action m, oriIs less than the starting safety interval time when state s performs action m.
4. A multi-robot travel path navigation method using the single-robot travel path navigation method of any one of claims 1 to 3, comprising:
b1, inputting a grid map G, an initial node s and a final node t into a path processing system of the robot;
b2, planning an optimal path for each robot by using a single robot driving path navigation method, and calculating path cost;
b3, merging the optimal paths of the robots into a path setPWill bePLeading the data into a module to be processed, and calling and fusing a heuristic method to detect a path setPWhether a conflict exists in (1);
b4, if no conflict exists, outputting the path setPAnd ending, if the conflict exists, executing B5;
b5, defining quadruplets
Figure 434777DEST_PATH_IMAGE003
To show the robotr i In a time period oft i Execute actions at the timea i Will communicate with the robotr j In a time period oft j Execute actions at the timea j The sound-making conflict is generated,t i 、t j are all time periods of time,r i the new path of (A) isP i A plurality ofP i Composing a set of new pathsAAnd a single robot driving path navigation method is called to formAAnd will beAAnd (4) importing the data into a module to be processed, and repeatedly executing B3 until no conflict exists.
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