CN105116902A - Mobile robot obstacle avoidance navigation method and system - Google Patents

Mobile robot obstacle avoidance navigation method and system Download PDF

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Publication number
CN105116902A
CN105116902A CN201510571370.5A CN201510571370A CN105116902A CN 105116902 A CN105116902 A CN 105116902A CN 201510571370 A CN201510571370 A CN 201510571370A CN 105116902 A CN105116902 A CN 105116902A
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robot
value
node
obstacle
executing
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王玉亮
王晓刚
王巍
薛林
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Beijing Science And Technology Ltd Of Evolution Person Robot
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Beijing Science And Technology Ltd Of Evolution Person Robot
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Priority to CN201510571370.5A priority Critical patent/CN105116902A/en
Publication of CN105116902A publication Critical patent/CN105116902A/en
Priority to PCT/CN2016/098460 priority patent/WO2017041730A1/en
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    • GPHYSICS
    • G05CONTROLLING; REGULATING
    • G05DSYSTEMS FOR CONTROLLING OR REGULATING NON-ELECTRIC VARIABLES
    • G05D1/00Control of position, course, altitude or attitude of land, water, air or space vehicles, e.g. using automatic pilots
    • G05D1/02Control of position or course in two dimensions

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  • Engineering & Computer Science (AREA)
  • Aviation & Aerospace Engineering (AREA)
  • Radar, Positioning & Navigation (AREA)
  • Remote Sensing (AREA)
  • Physics & Mathematics (AREA)
  • General Physics & Mathematics (AREA)
  • Automation & Control Theory (AREA)
  • Control Of Position, Course, Altitude, Or Attitude Of Moving Bodies (AREA)

Abstract

The invention discloses a mobile robot obstacle avoidance navigation method and system. The method includes the following steps that: a global map of a home environment is established; the starting point and destination of the movement of a robot are set; the movement path of the robot is planned according to the A* algorithm; the position of a obstacle is marked in the global map; the movement path of the robot is re-planned according to the A* algorithm; the robot is controlled to move according to the planned path; and the robot arrives at the destination and stops moving. With the mobile robot obstacle avoidance navigation method and system of the invention adopted, unknown environment can be detected, so that the information of unknown obstacles can be obtained, and the estimation function is adopted to plan the shortest and most economical path, and therefore, the equipment cost of the obstacle avoidance navigation of the robot can be decreased; the position and movement attitude of the robot can be monitored in real time, and the walking attitude of the robot can be adjusted and controlled in real time, and the accuracy and effectiveness of the obstacle avoidance navigation of the robot can be ensured.

Description

Mobile robot obstacle avoidance navigation method and system
Technical Field
The invention relates to the technical field of automation, in particular to a method and a system for obstacle avoidance navigation of a mobile robot.
Background
The development of robotics is a common crystal for the comprehensive development of science and technology. Robots can be classified by use into military robots, industrial robots, service robots, etc., wherein there is a great demand for mobile robots among these types of robots.
The research range of the mobile robot covers: the system comprises a plurality of aspects such as architecture, a control mechanism, an information system, a sensing technology, a planning strategy and a driving system, and relates to a plurality of subject fields such as mechanical kinematics, artificial intelligence, intelligent control, mode recognition, image processing, a vision technology, a sensing technology, computer network and communication, and even a biological information technology. The mobile robot is widely applied to industries such as industry, agriculture, medical treatment, service and the like, and is well applied to harmful and dangerous occasions such as the fields of urban safety, national defense, space detection and the like. The research level of the mobile robot is an important mark for measuring the scientific and technological development level and the comprehensive national strength of a country. The 'robot revolution' is expected to become an entry point and an important growth point of the 'third industrial revolution', and will influence the global manufacturing pattern. International Association of robots (IFR) prediction: the robot revolution creates a market of billions of dollars, thereby driving the rapid development of key technologies and markets such as new material function modules related to robots, perception acquisition and recognition, intelligent control and navigation, and the like.
Intelligent robots, such as floor sweeping robots and home service robots, are increasingly widely used in industrial production and home life, and the robots need to be flexibly, efficiently and intelligently moved and have autonomous navigation capability. The autonomous obstacle avoidance technology is a key index for evaluating the intelligent degree of the robot, embodies the processing capacity of unknown obstacles, and is also one of key technologies for the intelligent robot to complete preset tasks in a position environment. The mobile robot is in an unknown, complex and dynamic unstructured environment, and under the condition of no manual intervention, the mobile robot should have the capability of sensing the environment information of the mobile robot by using a sensor carried by the mobile robot, model the environment, avoid obstacles autonomously and reduce the consumption of time and energy as much as possible.
In the technical field of robot obstacle avoidance navigation, scholars at home and abroad propose effective solutions. The ultrasonic sensor is used for detecting the obstacles, compass positioning is utilized, and a Bayesian probability algorithm is used for calculating the probability of the obstacles, so that environmental information monitoring and path planning are realized. The optimal control technology solves the obstacle avoidance problem of the robot by using visual feedback, controls the robot by using an image-based target image minimum scheme related to the expected behavior of the robot, and achieves the minimization of a target function by using a dynamic quasi-Newton method to perform dynamic recursive least square Jacobian estimation. The method comprises the steps of acquiring approximate three-dimensional information of an obstacle by using a monocular camera, acquiring accurate information of the obstacle by using an ultrasonic sensor, and jointly detecting the obstacle information by using monocular vision and ultrasonic waves. An intelligent mobile robot platform developed by Chinese academy of sciences, namely Am, has comprehensive functions of visual tracking, voice conversation, autonomous obstacle avoidance and the like, and is provided with 16 ultrasonic sensors and 16 infrared sensors for detecting obstacles.
The existing robot autonomous obstacle avoidance navigation technology has the defects of complex structure, expensive hardware cost and high maintenance cost, and is not suitable for the rapidly-increased robot development requirement.
Disclosure of Invention
The invention provides a method and a system for obstacle avoidance navigation of a mobile robot, which can detect an unknown environment, acquire information of an unknown obstacle, and introduce an estimation function to plan a shortest and most economical path, thereby saving equipment cost of the obstacle avoidance navigation of the robot. The scheme can also monitor the position and the moving posture of the robot in real time, dynamically adjust and control the walking state of the robot in real time according to the deviation of the robot and the planned path, and ensure the accuracy and effectiveness of the obstacle avoidance navigation of the robot.
The technical scheme of the invention provides an obstacle avoidance navigation method for a mobile robot, which comprises the following steps:
establishing a global map of a home environment;
setting a starting point and an end point of the movement of the robot;
planning the moving path of the robot according to the A-algorithm;
marking a location of an obstacle in the global map;
re-planning the moving path of the robot according to the A-algorithm;
controlling the robot to move according to the planned path;
and when the robot reaches the terminal, the robot stops moving.
Further, the a-algorithm includes the following steps:
A. putting the starting point s into an open table;
B. traversing the sub-nodes in 8 directions around the s node;
C. judging whether the 8 child nodes are in an open table or a close table;
if the child node is in the open table, executing D;
if the child node is in the close table, executing F;
if the child node is not in the open table or the close table, executing H;
D. recalculating the value of the node h (n) + g (n) in the open table, and judging whether the value is reduced;
if so, executing E;
if no reduction occurs, executing I;
E. updating the h (n) + g (n) value of the node in the open table, and turning to I;
F. recalculating the h (n) + g (n) value of the node in the close table, and judging whether the h (n) + g (n) value is reduced or not;
if the number is reduced, executing G;
if no reduction occurs, executing I;
G. the child node is removed from the close table and put into the open table, turning to I;
H. calculating the h (n) + g (n) value of the child node and adding the h (n) + g (n) value into an open table;
I. sorting according to the values of h (n) + g (n), and selecting the node with the minimum value to be put into a close table;
J. judging whether h (n) is 0;
if the value is 0, executing K;
if not, executing B;
K. and finding an end point.
Wherein, the open table is used for storing the nodes which are generated but not examined;
the closed table is used to record the nodes that have been visited.
Further, the f (n) value is calculated by:
the adjacent nodes of the node n have eight search directions which are respectively upper, lower, left, right, left upper, left lower, right upper and right lower;
for each search direction, an estimation function is used to calculate an estimation value from the current point to the next point, and the direction with the smallest estimation value is set as the next motion direction.
Further, the estimation function is
f(n)=g(n)+h(n)
Wherein,
f (n) is an estimate of the current point to the next point,
g (n) is the actual value from the starting point s to the node n, representing the preferential trend of the search breadth,
h (n) is an estimate of the best path from node n to target point D, including heuristic information in the search.
Further, detecting an obstacle by using ultrasonic waves, and converting the position of the obstacle in a robot coordinate system into a position in a global map;
and setting an obstacle detection threshold value to be 1500mm, not processing when the obstacle detection threshold value exceeds 1500mm, and marking the obstacle in the global map when the obstacle detection threshold value is less than 1500 mm.
Furthermore, the planned path is represented by a two-dimensional array;
the number of rows of the two-dimensional array represents the number of straight line segments in a path, and the number of columns represents the grid position in each straight line segment;
and points in the path defined by the two-dimensional array are local target points.
Further, the controlling the robot to move according to the planned path further includes:
updating the position and the posture of the robot in real time in the motion process;
and calculating the deviation between the current position of the robot and the local target point, and correcting the deviation in real time in the walking process to realize the real-time control of the robot.
The technical scheme of the invention also provides a system for obstacle avoidance and navigation of the mobile robot, which comprises the following steps: a control unit, a milemeter, an ultrasonic sensor and an attitude sensor, wherein,
the control unit is used for storing and adjusting the map, calculating an A-algorithm, controlling the robot to move and correcting the deviation of the robot movement;
the odometer is used for measuring the walking distance of the robot indoors;
the ultrasonic sensor is used for detecting the obstacle information around the robot;
the attitude sensor is used for detecting the attitude and the moving direction of the robot.
Further, the control unit receives the measurement data from the odometer and calculates the position of the robot;
and the control unit calculates the deviation from the local target point in the planned path according to the position of the robot.
Further, the control unit receives the measurement data of the attitude sensor to obtain the attitude and the moving direction of the robot;
and the control unit controls the motion of the robot in real time according to the calculated deviation and the posture of the robot.
The technical scheme of the invention provides a method and a system for obstacle avoidance navigation of a mobile robot, which can detect an unknown environment, acquire the information of an unknown obstacle, plan the shortest and most economical path by adopting an estimation function and save the equipment cost of an obstacle avoidance navigation system of the robot. The scheme can also monitor the position and the moving posture of the robot in real time, dynamically adjust and control the walking state of the robot in real time according to the deviation of the robot and the planned path, and ensure the accuracy and effectiveness of the obstacle avoidance navigation of the robot.
Additional features and advantages of the invention will be set forth in the description which follows, and in part will be obvious from the description, or may be learned by practice of the invention. The objectives and other advantages of the invention will be realized and attained by the structure particularly pointed out in the written description and claims hereof as well as the appended drawings.
The technical solution of the present invention is further described in detail by the accompanying drawings and embodiments.
Drawings
The accompanying drawings, which are included to provide a further understanding of the invention and are incorporated in and constitute a part of this specification, illustrate embodiments of the invention and together with the description serve to explain the principles of the invention and not to limit the invention. In the drawings:
fig. 1 is a flowchart of a method for obstacle avoidance navigation of a mobile robot according to an embodiment of the present invention;
FIG. 2 is a schematic diagram illustrating the calculation of an estimation function f (n) according to an embodiment of the present invention;
fig. 3 is a schematic diagram illustrating 8 search directions adjacent to a node a according to an embodiment of the present invention;
fig. 4 is a flowchart of a method for planning a moving path of a robot according to the a-x algorithm according to a second embodiment of the present invention;
fig. 5 is a structural diagram of an obstacle avoidance navigation system of a mobile robot according to one embodiment to two embodiments of the present invention.
Detailed Description
The preferred embodiments of the present invention will be described in conjunction with the accompanying drawings, and it will be understood that they are described herein for the purpose of illustration and explanation and not limitation.
The first embodiment is as follows: provided is a method for obstacle avoidance and navigation of a mobile robot.
Fig. 1 is a flowchart of a method for obstacle avoidance navigation of a mobile robot according to an embodiment of the present invention. As shown in fig. 1, the process includes the following steps:
step 101, establishing a global map of a home environment.
The global map is a moving range where the robot is located, and information such as a coordinate origin, an obstacle, a moving range and the like is marked;
the global map is a grid map, is a mesh graph consisting of a series of square grids and marks the information of the indoor environment;
the grid map records the positions of the grids in abscissa (X-coordinate) and ordinate (Y-coordinate), and records the probability of each grid being occupied by an obstacle in CV values.
And 102, setting a starting point and an end point of the robot movement.
The method comprises the steps of manually inputting a moving starting point and an end point of the robot, or setting the starting point and the end point for a fixed task of the robot, or setting the starting point and the end point for the robot through voice recognition;
the robot starts the task, i.e. moves from the starting point to the end point.
And 103, planning the moving path of the robot according to the A-x algorithm.
The algorithm comprises the following steps:
A. putting the starting point s into an open table;
B. traversing the sub-nodes in 8 directions around the s node;
C. judging whether the 8 child nodes are in an open table or a close table;
if the child node is in the open table, executing D;
if the child node is in the close table, executing F;
if the child node is not in the open table or the close table, executing H;
D. recalculating h (n) + g (n) and judging whether to reduce;
if so, executing E;
if no reduction occurs, executing I;
E. updating the h (n) + g (n) value of the node in the open table, and turning to I;
F. recalculating the h (n) + g (n) value of the node in the close table, and judging whether the h (n) + g (n) value is reduced or not;
if the number is reduced, executing G;
if no reduction occurs, executing I;
G. the child node is removed from the close table and put into the open table, turning to I;
H. calculating the h (n) + g (n) value of the child node and adding the h (n) + g (n) value into an open table;
I. sorting according to the values of h (n) + g (n), and selecting the node with the minimum value to be put into a close table;
J. judging whether h (n) is 0;
if the value is 0, executing K;
if not, executing B;
K. and finding an end point.
Wherein, the open table is used for storing the nodes which are generated but not examined;
the closed table is used to record the nodes that have been visited.
The calculation method of the value of the estimation function f (n) comprises the following steps:
the adjacent nodes of the node n have eight search directions which are respectively upper, lower, left, right, left upper, left lower, right upper and right lower;
for each search direction, calculating an estimation value from a current point to a next point by using an estimation function, and setting the direction with the minimum estimation value as a next motion direction;
the estimated value of node n is
f(n)=g(n)+h(n)
Wherein,
f (n) is an estimate of the current point to the next point,
g (n) is the actual value from the starting point s to the node n, representing the preferential trend of the search breadth,
h (n) is an estimate of the best path from node n to target point D, including heuristic information in the search.
The planned path is represented by a two-dimensional array;
the number of rows of the two-dimensional array represents the number of straight line segments in a path, and the number of columns represents the grid position in each straight line segment;
and points in the path defined by the two-dimensional array are local target points.
Step 104, detecting and marking the position of the obstacle during the movement.
In the moving process of the robot, detecting information of an obstacle by using ultrasonic waves, and converting the position of the obstacle in a robot coordinate into a position in a global map;
and setting an obstacle detection threshold value to be 1500mm, not processing when the obstacle detection threshold value exceeds 1500mm, and marking the obstacle in the global map when the obstacle detection threshold value is less than 1500 mm.
And 105, re-planning the moving path of the robot according to the A-x algorithm.
Planning the moving path of the robot according to the A-x algorithm again according to the global map added with the obstacle information;
the robot retrieves the adjusted two-dimensional array to represent the new path.
And 106, controlling the robot to move according to the planned path.
Updating the position and posture information of the robot in real time in the motion process through a stroke meter and a posture sensor;
and calculating the deviation between the current position of the robot and the local target point, and correcting the deviation in real time in the walking process to realize the real-time control of the robot.
And step 107, judging whether the robot reaches the end point.
Judging whether the position and the end point of the robot coincide or not
And step 108, stopping the robot.
The robot reaches the end point, i.e. stops moving.
Example two: a method for planning a movement path of a robot according to an A-algorithm.
Fig. 4 is a flowchart of a method for planning a moving path of a robot according to the a-x algorithm in the second embodiment of the present invention. As shown in fig. 4, the method flow includes the following steps:
step 201, putting a starting point s into an open table;
step 202, traversing child nodes in 8 directions around the s node;
step 203, judging whether the 8 child nodes are in an open table or a close table;
if the child node is in the open table, go to step 204;
if the child node is in the close table, go to step 206;
if the child node is not in the open table or close table, go to step 208;
step 204, recalculating the values of h (n) + g (n) of the nodes in the open table, and judging whether the values are reduced or not;
if so, go to step 205;
if no decrease occurs, go to step 209;
step 205, updating the h (n) + g (n) value of the node in the open table, and turning to step 209;
step 206, recalculating the h (n) + g (n) values of the nodes in the close table, and judging whether to decrease;
if so, go to step 207;
if no decrease occurs, go to step 209;
step 207, the child node is removed from the close table and put into the open table, and the process goes to step 209;
step 208, calculating the h (n) + g (n) value of the child node, and adding the h (n) + g (n) value into an open table;
step 209, sorting according to the values of h (n) + g (n), and selecting the node with the minimum value to be put into a close table;
step 210, judging whether h (n) is 0;
if yes, go to step 211;
if not, go to step 202;
and step 211, finding an end point.
Wherein, the open table is used for storing the nodes which are generated but not examined;
the closed table is used to record the nodes that have been visited.
Fig. 5 is a structural diagram of an obstacle avoidance navigation system of a mobile robot according to one embodiment to two embodiments of the present invention. The system comprises: a control unit 301, an odometer 302, an ultrasonic sensor 303, an attitude sensor 304, wherein,
the control unit is used for storing and adjusting the map, calculating an A-algorithm, controlling the robot to move and correcting the deviation of the robot movement;
the odometer is used for measuring the walking distance of the robot indoors;
the ultrasonic sensor is used for detecting the obstacle information around the robot;
the attitude sensor is used for detecting the attitude and the moving direction of the robot.
Further, the control unit receives the measurement data from the odometer and calculates the position of the robot;
and the control unit calculates the deviation from the local target point in the planned path according to the position of the robot.
Further, the control unit receives the measurement data of the attitude sensor to obtain the attitude and the moving direction of the robot;
and the control unit controls the motion of the robot in real time according to the calculated deviation and the posture of the robot.
The technical scheme of the invention provides a method and a system for obstacle avoidance navigation of a mobile robot, which can detect an unknown environment, acquire the information of an unknown obstacle, and introduce an estimation function to plan the shortest and most economical path, thereby saving the equipment cost of the obstacle avoidance navigation of the robot. The scheme can also monitor the position and the moving posture of the robot in real time, dynamically adjust and control the walking state of the robot in real time according to the deviation of the robot and the planned path, and ensure the accuracy and effectiveness of the obstacle avoidance navigation of the robot.
As will be appreciated by one skilled in the art, embodiments of the present invention may be provided as a method, system, or computer program product. Accordingly, the present invention may take the form of an entirely hardware embodiment, an entirely software embodiment or an embodiment combining software and hardware aspects. Furthermore, the present invention may take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, optical storage, and the like) having computer-usable program code embodied therein.
The present invention is described with reference to flowchart illustrations and/or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the invention. It will be understood that each flow and/or block of the flow diagrams and/or block diagrams, and combinations of flows and/or blocks in the flow diagrams and/or block diagrams, can be implemented by computer program instructions. These computer program instructions may be provided to a processor of a general purpose computer, special purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, create means for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be stored in a computer-readable memory that can direct a computer or other programmable data processing apparatus to function in a particular manner, such that the instructions stored in the computer-readable memory produce an article of manufacture including instruction means which implement the function specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer implemented process such that the instructions which execute on the computer or other programmable apparatus provide steps for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
It will be apparent to those skilled in the art that various changes and modifications may be made in the present invention without departing from the spirit and scope of the invention. Thus, if such modifications and variations of the present invention fall within the scope of the claims of the present invention and their equivalents, the present invention is also intended to include such modifications and variations.

Claims (10)

1. A method for obstacle avoidance navigation of a mobile robot is characterized by comprising the following steps:
establishing a global map of a home environment;
setting a starting point and an end point of the movement of the robot;
planning the moving path of the robot according to the A-algorithm;
marking a location of an obstacle in the global map;
re-planning the moving path of the robot according to the A-algorithm;
controlling the robot to move according to the planned path;
and when the robot reaches the terminal, the robot stops moving.
2. The method according to claim 1, characterized in that the a-algorithm comprises the following steps:
A. putting the starting point s into an open table;
B. traversing the sub-nodes in 8 directions around the s node;
C. judging whether the 8 child nodes are in an open table or a close table;
if the child node is in the open table, executing D;
if the child node is in the close table, executing F;
if the child node is not in the open table or the close table, executing H;
D. recalculating the value of the node h (n) + g (n) in the open table, and judging whether the value is reduced;
if so, executing E;
if no reduction occurs, executing I;
E. updating the h (n) + g (n) value of the node in the open table, and turning to I;
F. recalculating the h (n) + g (n) value of the node in the close table, and judging whether the h (n) + g (n) value is reduced or not;
if the number is reduced, executing G;
if no reduction occurs, executing I;
G. the child node is removed from the close table and put into the open table, turning to I;
H. calculating the h (n) + g (n) value of the child node and adding the h (n) + g (n) value into an open table;
I. sorting according to the values of h (n) + g (n), and selecting the node with the minimum value to be put into a close table;
J. judging whether h (n) is 0;
if the value is 0, executing K;
if not, executing B;
K. and finding an end point.
Wherein, the open table is used for storing the nodes which are generated but not examined;
the closed table is used to record the nodes that have been visited.
3. The method of claim 1 or 2, wherein the f (n) value is calculated by:
the adjacent nodes of the node n have eight search directions which are respectively upper, lower, left, right, left upper, left lower, right upper and right lower;
for each search direction, an estimation function is used to calculate an estimation value from the current point to the next point, and the direction with the smallest estimation value is set as the next motion direction.
4. The method according to claim 1 or 4, wherein the estimation function is
f(n)=g(n)+h(n)
Wherein,
f (n) is an estimate of the current point to the next point,
g (n) is the actual value from the starting point s to the node n, representing the preferential trend of the search breadth,
h (n) is an estimate of the best path from node n to target point D, including heuristic information in the search.
5. The method of claim 1, further comprising:
detecting an obstacle by using ultrasonic waves, and converting the position of the obstacle in a robot coordinate system into a position in a global map;
and setting an obstacle detection threshold value to be 1500mm, not processing when the obstacle detection threshold value exceeds 1500mm, and marking the obstacle in the global map when the obstacle detection threshold value is less than 1500 mm.
6. The method of claim 1, further comprising:
the planned path is represented by a two-dimensional array;
the number of rows of the two-dimensional array represents the number of straight line segments in a path, and the number of columns represents the grid position in each straight line segment;
the last point of each line defined by the two-dimensional array is a local target point in the path segment.
7. The method of claim 1, wherein the controlling the robot movement according to the planned path further comprises:
updating the position and the posture of the robot in real time in the motion process;
and calculating the deviation between the current position of the robot and the local target point, and correcting the deviation in real time in the walking process to realize the real-time control of the robot.
8. A system for obstacle avoidance and navigation of a mobile robot is characterized by comprising a control unit, a milemeter, an ultrasonic sensor and an attitude sensor, wherein,
the control unit is used for storing and adjusting the map, calculating an A-algorithm, controlling the robot to move and correcting the deviation of the robot movement;
the odometer is used for measuring the walking distance of the robot indoors;
the ultrasonic sensor is used for detecting the obstacle information around the robot;
the attitude sensor is used for detecting the attitude and the moving direction of the robot.
9. The method of claim 8, further comprising:
the control unit receives the measurement data from the odometer and calculates the position of the robot;
and the control unit calculates the deviation from the local target point in the planned path according to the position of the robot.
10. The method of claim 8, further comprising:
the control unit receives the measurement data of the attitude sensor and obtains the attitude and the moving direction of the robot;
and the control unit controls the motion of the robot in real time according to the calculated deviation and the posture of the robot.
CN201510571370.5A 2015-09-09 2015-09-09 Mobile robot obstacle avoidance navigation method and system Pending CN105116902A (en)

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CN105652838A (en) * 2016-01-29 2016-06-08 哈尔滨工大服务机器人有限公司 Multi-robot path planning method based on time window
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