CN113759900A - Inspection robot track planning and real-time obstacle avoidance method and system based on obstacle area prediction - Google Patents
Inspection robot track planning and real-time obstacle avoidance method and system based on obstacle area prediction Download PDFInfo
- Publication number
- CN113759900A CN113759900A CN202110923744.0A CN202110923744A CN113759900A CN 113759900 A CN113759900 A CN 113759900A CN 202110923744 A CN202110923744 A CN 202110923744A CN 113759900 A CN113759900 A CN 113759900A
- Authority
- CN
- China
- Prior art keywords
- obstacle
- potential field
- inspection robot
- dynamic
- model
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Granted
Links
- 238000007689 inspection Methods 0.000 title claims abstract description 75
- 238000000034 method Methods 0.000 title claims abstract description 40
- 239000013598 vector Substances 0.000 claims abstract description 31
- 230000033001 locomotion Effects 0.000 claims abstract description 28
- 230000004888 barrier function Effects 0.000 claims description 53
- 230000006870 function Effects 0.000 claims description 36
- 230000003068 static effect Effects 0.000 claims description 24
- 239000011159 matrix material Substances 0.000 claims description 14
- 238000004364 calculation method Methods 0.000 claims description 6
- 238000004590 computer program Methods 0.000 claims description 6
- 230000005484 gravity Effects 0.000 claims description 6
- 238000005259 measurement Methods 0.000 claims description 6
- 238000012546 transfer Methods 0.000 claims description 4
- 230000007704 transition Effects 0.000 claims description 4
- 238000004422 calculation algorithm Methods 0.000 abstract description 14
- 230000008859 change Effects 0.000 abstract description 4
- 238000005265 energy consumption Methods 0.000 abstract description 4
- 230000008569 process Effects 0.000 description 6
- 238000010586 diagram Methods 0.000 description 4
- 238000010276 construction Methods 0.000 description 3
- 230000004048 modification Effects 0.000 description 3
- 238000012986 modification Methods 0.000 description 3
- 230000003287 optical effect Effects 0.000 description 3
- 238000011161 development Methods 0.000 description 2
- 230000018109 developmental process Effects 0.000 description 2
- 238000005381 potential energy Methods 0.000 description 2
- 206010063385 Intellectualisation Diseases 0.000 description 1
- 240000007651 Rubus glaucus Species 0.000 description 1
- 235000011034 Rubus glaucus Nutrition 0.000 description 1
- 235000009122 Rubus idaeus Nutrition 0.000 description 1
- 230000001133 acceleration Effects 0.000 description 1
- XAGFODPZIPBFFR-UHFFFAOYSA-N aluminium Chemical compound [Al] XAGFODPZIPBFFR-UHFFFAOYSA-N 0.000 description 1
- 229910052782 aluminium Inorganic materials 0.000 description 1
- 238000004458 analytical method Methods 0.000 description 1
- 230000006399 behavior Effects 0.000 description 1
- 230000005540 biological transmission Effects 0.000 description 1
- 238000001514 detection method Methods 0.000 description 1
- 238000005868 electrolysis reaction Methods 0.000 description 1
- 238000005516 engineering process Methods 0.000 description 1
- 238000005188 flotation Methods 0.000 description 1
- 230000006872 improvement Effects 0.000 description 1
- 230000001788 irregular Effects 0.000 description 1
- 238000004519 manufacturing process Methods 0.000 description 1
- 230000008447 perception Effects 0.000 description 1
- 238000011160 research Methods 0.000 description 1
- 230000011218 segmentation Effects 0.000 description 1
- 230000000007 visual effect Effects 0.000 description 1
Images
Classifications
-
- G—PHYSICS
- G05—CONTROLLING; REGULATING
- G05D—SYSTEMS FOR CONTROLLING OR REGULATING NON-ELECTRIC VARIABLES
- G05D1/00—Control of position, course, altitude or attitude of land, water, air or space vehicles, e.g. using automatic pilots
- G05D1/02—Control of position or course in two dimensions
- G05D1/021—Control of position or course in two dimensions specially adapted to land vehicles
- G05D1/0212—Control of position or course in two dimensions specially adapted to land vehicles with means for defining a desired trajectory
- G05D1/0214—Control of position or course in two dimensions specially adapted to land vehicles with means for defining a desired trajectory in accordance with safety or protection criteria, e.g. avoiding hazardous areas
-
- G—PHYSICS
- G05—CONTROLLING; REGULATING
- G05D—SYSTEMS FOR CONTROLLING OR REGULATING NON-ELECTRIC VARIABLES
- G05D1/00—Control of position, course, altitude or attitude of land, water, air or space vehicles, e.g. using automatic pilots
- G05D1/02—Control of position or course in two dimensions
- G05D1/021—Control of position or course in two dimensions specially adapted to land vehicles
- G05D1/0212—Control of position or course in two dimensions specially adapted to land vehicles with means for defining a desired trajectory
- G05D1/0223—Control of position or course in two dimensions specially adapted to land vehicles with means for defining a desired trajectory involving speed control of the vehicle
-
- 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
- Y02T—CLIMATE CHANGE MITIGATION TECHNOLOGIES RELATED TO TRANSPORTATION
- Y02T10/00—Road transport of goods or passengers
- Y02T10/10—Internal combustion engine [ICE] based vehicles
- Y02T10/40—Engine management systems
Landscapes
- 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)
- Manipulator (AREA)
Abstract
The invention discloses an inspection robot track planning and real-time obstacle avoidance method and system based on obstacle area prediction, wherein a two-dimensional high-precision grid map is established through a two-dimensional high-precision laser radar and a depth camera, a dynamic obstacle reachable area prediction model based on state updating is established, the motion characteristic and the geometric dimension of an obstacle are fully considered, an adjustment allowance is reserved, the reachable area of the dynamic obstacle is determined in advance, a multi-step elliptic envelope potential field, a novel Sigmoid square obstacle potential field and a circular obstacle potential field are defined to correct a logarithm Lyapunov gravitational field model, a real-time obstacle avoidance algorithm in an obstacle space is obtained, an expected driving angle and an expected speed vector of a robot are obtained through the obstacle avoidance algorithm, and finally, a dynamic obstacle avoidance path of the robot is obtained in real time The energy consumption is lower, the safety is higher and the maximum driving angle change amplitude is smaller.
Description
Technical Field
The invention mainly relates to the technical field of process industry and obstacle avoidance trajectory planning, in particular to an inspection robot trajectory planning and real-time obstacle avoidance method and system based on obstacle area prediction.
Background
The autonomous inspection mobile robot has the advantages of low price, flexible operation, wide motion range and the like, is successfully applied to the fields of electric power and security protection, and has great application potential in the industrial fields of processes such as aluminum electrolysis, flotation and the like. The research trend of the inspection mobile robot in the future is intellectualization and autonomy, and the safety and real-time obstacle avoidance are one of key technologies for improving the autonomous planning capability of the inspection mobile robot, but compared with the unmanned aerial vehicle, the underwater mobile robot and other motion platforms, the factory environment where the inspection mobile robot is located is more complex, and if operation workers, large static obstacles and the like exist, the requirement for the autonomous obstacle avoidance capability of the industrial inspection mobile robot is higher. With the advance of China towards industry 4.0 and the manufacture of the Qiangguo 2025, the contradiction between increasingly complex and changeable industrial environment and the insufficient autonomous planning capability of the inspection mobile robot is increasingly prominent, and the contradiction becomes a bottleneck for restricting the autonomous and intelligent development of the industrial inspection robot in China.
The autonomous obstacle avoidance problem of the industrial inspection robot is that according to information of an industrial field or environment information sensed in real time from a sensor (such as a depth camera, a laser radar and the like), such as obstacle information, target information and the like, autonomous planning is carried out to make decisions and control the obstacle avoidance behavior of an inspection mobile machine, so that the inspection robot moves to a target point and avoids various obstacles. The difficulty of the problem lies in the non-structural property of the environment (such as the existence of the problems of non-convex area and multiple types of obstacles), the dynamic property of the environment (such as the existence of dynamic obstacles, moving targets and the like of operators or other inspection robots), and the non-determinacy of the environment information (such as the difficulty in obtaining part of the environment information, the lack of some local information in a short time due to the long obtaining time of the environment information, and the like). Through development for many years, the autonomous obstacle avoidance method of the inspection robot has achieved various achievements, but most of the autonomous obstacle avoidance methods are only suitable for simple industrial environments such as barrier-free or static obstacles, and the autonomous obstacle avoidance method of the inspection robot still needs to be further researched under complex industrial environments with static and dynamic obstacles.
Disclosure of Invention
The invention provides a method and a system for routing inspection robot track planning and real-time obstacle avoidance based on obstacle area prediction, which solve the technical problem that the existing routing inspection robot cannot avoid obstacles in real time under a complex factory environment.
In order to solve the technical problems, the inspection robot track planning and real-time obstacle avoidance method based on obstacle area prediction provided by the invention comprises the following steps:
establishing a dynamic barrier reachable area prediction model based on state updating;
acquiring an elliptic reachable area under the predicted step number based on a dynamic barrier reachable area prediction model;
establishing a multi-step ellipse enveloping potential field model based on the ellipse reachable region under the predicted step number;
establishing a square obstacle potential field model and a circular obstacle potential field model of a novel Sigmoid function based on a static obstacle model;
acquiring an expected driving angle and an expected speed vector of the inspection robot based on a multi-step ellipse enveloping potential field model, a square obstacle potential field model of a novel Sigmoid function, a circular obstacle potential field model and a logarithm Lyapunov gravitational field model;
and obtaining an obstacle avoidance path of the robot based on the expected driving angle and the expected speed vector.
Further, obtaining the elliptical reachable area under the preset step number based on the dynamic obstacle reachable area prediction model comprises:
initializing a movement velocity variance, a measurement noise variance and an initial variance transfer matrix of the dynamic obstacle;
obtaining the variance of the centroid of the dynamic obstacle in the motion direction and the vertical motion direction under the predicted step number according to a p-step predicted variance equation, wherein the p-step predicted variance equation specifically comprises the following steps:
wherein, Pk+j|kPredicting time kThe variance matrix of step number j, P (0) is the initial variance transfer matrix, AjUpdating a matrix for the state transition of the predicted step number j, wherein Q is a measurement covariance matrix;
obtaining the centroid position of the dynamic barrier under the predicted step number according to the centroid updating equation of the dynamic barrier;
and constructing an elliptical reachable area under the preset step number according to the position of the centroid of the dynamic obstacle and the variance of the centroid of the dynamic obstacle in the motion direction and the vertical motion direction under the predicted step number.
Further, according to the position of the centroid of the dynamic obstacle and the variance of the centroid of the dynamic obstacle in the motion direction and the vertical motion direction under the predicted step number, the specific steps for constructing the elliptical reachable area under the preset step number are as follows:
and (3) taking the centroid position of the previous step of the preset step number as the center, and taking the 3-time variance of the centroid of the dynamic barrier in the motion direction and the vertical motion direction as the major axis and the minor axis under the preset step number to construct an elliptical reachable area.
Further, establishing a multi-step ellipse enveloping potential field model based on the ellipse reachable region under the prediction step number comprises:
expanding the reachable area of the ellipse under the predicted step number by a preset radius;
obtaining an ellipse enveloping potential field according to the ellipse reachable region under the prediction step number after the preset radius is expanded;
according to the elliptical enveloping potential field, a multi-step elliptical enveloping potential field model is established, and the multi-step elliptical enveloping potential field model specifically comprises the following steps:
wherein, U1In the case of a multi-step elliptical envelope potential field,
UAB(M1)、UCD(M1) Respectively as any point M in the multi-step elliptic envelope potential field1In the ellipse reachable region N1N2Oval reachable region P1P2Straight line AB and straight line CD, and the ellipse can reach the region P1P2And elliptical reachable region N1N2The predicted step number j is 1, and the predicted step number j is P, and the straight line AB and the straight line CD are the elliptical reachable areas P1P2And elliptical reachable region N1N2Envelope common tangent line of (c).
Further, based on the static obstacle model, a specific formula for establishing a square obstacle potential field model of the novel Sigmoid function is as follows:
wherein, U2(M2) Any point M in a square obstacle potential field model which is a novel Sigmoid function2Square obstacle potential field of (k)riGain coefficient being a new Sigmoid function, r being an influence coefficient related to the influence range of a square obstacle, SiMathematical expression of a function representing the ith plane of a square obstacle, hc(M2) Any point M in a square obstacle potential field model which is a novel Sigmoid function2The square barrier function expression of (2).
Further, based on the static obstacle model, a concrete formula for establishing the circular obstacle potential field model is as follows:
wherein, U3(M3) Is any point M in the potential field model of the circular obstacle3λ is the coefficient of the potential field of the circular obstacle, rcRadius of a circular obstacle, hc(M3) Is any point M in the potential field model of the circular obstacle3Expression of the circular barrier function of, p0Is the influence distance of a circular obstacle.
Further, obtaining an expected driving angle and an expected speed vector of the inspection robot based on a multi-step ellipse enveloping potential field model, a square obstacle potential field model of a novel Sigmoid function, a circular obstacle potential field model and a logarithm Lyapunov gravitational field model comprises:
correspondingly obtaining a multi-step elliptical envelope potential field, a square obstacle potential field of a novel Sigmoid function, a circular obstacle potential field and a logarithm Lyapunov vector gravity according to the multi-step elliptical envelope potential field model, the square obstacle potential field model of the novel Sigmoid function, the circular obstacle potential field and the logarithm Lyapunov gravity field model;
respectively solving negative gradients of the multistep elliptic enveloping potential field, the square obstacle potential field of the novel Sigmoid function and the circular obstacle potential field, and correspondingly obtaining multistep elliptic enveloping potential field repulsive force, the square obstacle potential field repulsive force of the novel Sigmoid function and the circular obstacle potential field repulsive force;
and obtaining an expected driving angle and an expected speed vector of the inspection robot according to the repulsion of the multi-step elliptical envelope potential field, the repulsion of the square obstacle potential field of the novel Sigmoid function, the repulsion of the circular obstacle potential field and the logarithm Lyapunov vector attraction.
Further, based on the expected driving angle and the expected speed vector, a calculation formula for obtaining the obstacle avoidance path of the robot is as follows:
θ(t+1)＝θ(t)+ωθ△t
wherein q isd(t +1) and qd(t) represents the positions of the inspection robot at time t +1 and time t, vxAnd vyRepresenting the speeds of the inspection robot in the x and y directions, theta (t +1) and theta (t) representing the orientation angles of the inspection robot at the time t +1 and the time t, and omegaθIndicating the angular velocity of the inspection robot.
The invention provides an inspection robot track planning and real-time obstacle avoidance system based on obstacle area prediction, which comprises:
the invention provides a patrol robot track planning and real-time obstacle avoidance method based on obstacle area prediction, which comprises a memory, a processor and a computer program stored on the memory and capable of running on the processor, wherein the processor realizes the steps of the patrol robot track planning and real-time obstacle avoidance method based on obstacle area prediction when executing the computer program.
Compared with the prior art, the invention has the advantages that:
the invention provides a method and a system for planning a track and avoiding an obstacle of an inspection robot in real time based on obstacle area prediction, which are used for obtaining an elliptical reachable area under the predicted step number by establishing a dynamic obstacle reachable area prediction model based on state updating, establishing a multi-step elliptical enveloping potential field model based on the elliptical reachable area under the predicted step number, establishing a square obstacle potential field model and a circular obstacle potential field model of a novel Sigmoid function based on a static obstacle model, obtaining an expected driving angle and an expected speed vector of the inspection robot based on the multi-step elliptical enveloping potential field model, the square obstacle potential field model of the novel Sigmoid function, the circular obstacle potential field model and a logarithm Lyapunov gravitational field model, obtaining an obstacle avoiding path of the inspection robot based on the expected driving angle and the expected speed vector, and solving the technical problem that the conventional inspection robot cannot avoid the obstacle in real time under a complex factory environment, the method comprises the steps of establishing a dynamic barrier reachable area prediction model based on state updating, fully considering the motion characteristics and the geometric dimensions of barriers and reserving adjustment allowance, determining a reachable area of the dynamic barrier in advance, defining a multi-step elliptical envelope potential field, a novel Sigmoid square barrier potential field and a circular barrier potential field to modify a logarithm Lyapunov gravitational field model, and obtaining a real-time barrier avoidance algorithm in a barrier space, so that the barrier avoidance path of the inspection robot in complex environments such as static and dynamic environments is shorter in length, lower in energy consumption, higher in safety and smaller in maximum driving angle change amplitude, and under the condition of performance constraint of the inspection robot, the proposed algorithm can more effectively realize the barrier avoidance task of the inspection robot in the complex factory environment.
Drawings
Fig. 1 is a flowchart of a method for routing inspection robot trajectory planning and real-time obstacle avoidance based on obstacle area prediction according to an embodiment of the present invention;
fig. 2 is a flowchart of a second inspection robot trajectory planning and real-time obstacle avoidance method based on obstacle area prediction according to an embodiment of the present invention;
FIG. 3 is a diagram of a predicted time domain T according to a second embodiment of the present inventionpThe center of mass of the dynamic obstacle is 4 Delta t, and the area can be reached;
FIG. 4 is a diagram of the predicted time domain T according to the second embodiment of the present inventionpAn ellipse enveloping a dynamic barrier reachable region of 3 delta t;
FIG. 5 is a side view of a multi-step elliptical envelope potential field based on dynamic obstacle reachable region prediction according to a second embodiment of the present invention;
FIG. 6 is a top view of a multi-step elliptical envelope potential field based on dynamic obstacle reachable area prediction according to a second embodiment of the present invention;
fig. 7 is a schematic diagram of a geodetic coordinate system of the inspection robot according to the second embodiment of the invention;
fig. 8 is a structural block diagram of the inspection robot trajectory planning and real-time obstacle avoidance system based on obstacle area prediction according to the present invention.
Reference numerals:
10. a memory; 20. a processor.
Detailed Description
In order to facilitate an understanding of the invention, the invention will be described more fully and in detail below with reference to the accompanying drawings and preferred embodiments, but the scope of the invention is not limited to the specific embodiments below.
The embodiments of the invention will be described in detail below with reference to the drawings, but the invention can be implemented in many different ways as defined and covered by the claims.
Example one
Referring to fig. 1, a method for routing a trajectory of an inspection robot and avoiding an obstacle in real time based on obstacle area prediction according to an embodiment of the present invention includes:
step S101, establishing a dynamic obstacle reachable area prediction model based on state updating;
step S102, acquiring an ellipse reachable area under the predicted step number based on a dynamic obstacle reachable area prediction model;
step S103, establishing a multi-step ellipse enveloping potential field model based on the ellipse reachable region under the prediction step number;
step S104, establishing a square obstacle potential field model and a circular obstacle potential field model of a novel Sigmoid function based on a static obstacle model;
step S105, obtaining an expected driving angle and an expected speed vector of the inspection robot based on a multi-step ellipse enveloping potential field model, a square obstacle potential field model of a novel Sigmoid function, a circular obstacle potential field model and a logarithm Lyapunov gravitational field model;
and step S106, obtaining an obstacle avoidance path of the robot based on the expected driving angle and the expected speed vector.
The inspection robot track planning and real-time obstacle avoidance method based on obstacle area prediction provided by the embodiment of the invention obtains the elliptical reachable area under the predicted step number by establishing a dynamic obstacle reachable area prediction model based on state updating, establishes a multi-step elliptical enveloping potential field model based on the elliptical reachable area under the predicted step number, establishes a square obstacle potential field model and a circular obstacle potential field model of a novel Sigmoid function based on a static obstacle model, obtains an expected driving angle and an expected speed vector of an inspection robot based on the multi-step elliptical enveloping potential field model, the square obstacle potential field model and the circular obstacle potential field model of the novel Sigmoid function and a logarithm Lyapunov gravitational field model, obtains an obstacle avoidance path of the robot based on the expected driving angle and the expected speed vector, and solves the technical problem that the existing inspection robot cannot avoid obstacles in real time under a complex factory environment, the method comprises the steps of establishing a dynamic barrier reachable area prediction model based on state updating, fully considering the motion characteristics and the geometric dimensions of barriers and reserving adjustment allowance, determining a reachable area of the dynamic barrier in advance, defining a multi-step elliptical envelope potential field, a novel Sigmoid square barrier potential field and a circular barrier potential field to modify a logarithm Lyapunov gravitational field model, and obtaining a real-time barrier avoidance algorithm in a barrier space, so that the barrier avoidance path of the inspection robot in complex environments such as static and dynamic environments is shorter in length, lower in energy consumption, higher in safety and smaller in maximum driving angle change amplitude, and under the condition of performance constraint of the inspection robot, the proposed algorithm can more effectively realize the barrier avoidance task of the inspection robot in the complex factory environment.
Example two
Referring to fig. 2, the inspection robot trajectory planning and real-time obstacle avoidance method based on obstacle area prediction provided by the second embodiment of the invention includes establishment of an initial world grid map, a static obstacle map layer and a dynamic obstacle map layer, prediction of a reachable area of a dynamic obstacle substance center and construction of a multi-step elliptic envelope potential field model based on reachable area prediction, modification of a logarithm Lyapunov gravitational vector field based on construction of a square obstacle potential field and a circular potential field of a novel Sigmoid function, calculation of an expected speed vector and an expected driving angle of a robot by using a total potential field force on a raspberry dispatching controller, transmission of a calculation result to a lower computer STM32 single chip microcomputer through a serial port, and return of a mileage meter and positioning information to an ROS operating system so as to facilitate next calculation. The method specifically comprises the following steps:
step 1: and establishing a two-dimensional ultrahigh-precision world grid map in an actual industrial scene, and acquiring map layer information of the moving obstacle in real time. And establishing an ultrahigh-precision grid map and a real-time updated high-speed and low-speed moving obstacle grid map under a complex industrial environment according to the multithreading ultrahigh-precision laser radar data or red, yellow and blue three-channel data containing depth information in the optical system of the Audio.
Because the static barrier can be cut into a circular or square barrier, the position of the static barrier is fixed, all circular and square barriers can be arranged in the global static grid map through program mapping, and once the static grid map is arranged, the static map layer does not need to be updated as long as the barrier is not manually moved; for moving objects, the robot can greatly detect local appearance information of the moving objects through the laser radar and the binocular camera or the monocular depth three-channel camera, so that the occupied area of the dynamic objects on the barrier map and corresponding position coordinates can be changed, and each moving object is stored in a relatively independent map layer as an unrelated object.
Specifically, in the embodiment, a laser radar or an optical depth camera in an optical contrast is used for scanning an actual scene, a two-dimensional high-precision grid map is established, and a static obstacle model including a square obstacle map model and a circular obstacle map model is established on the basis of an obstacle obtained by scanning; wherein the square obstacle map model is represented with a center position at (x)r,yr) Side length of lr1,lr2Can define a function h with respect to the coordinates (x, y)r(x, y), specifically:
wherein the circular obstacle map model is represented with a center position at (x)c,yc) Radius rcCan be obtained as a function h of the coordinates (x, y)c(x, y) is as follows:
when h is generatedr(x,y)>0,hr(x,y)＝0,hr(x,y)<And 0 represents the outer area, the surface area and the inner area of the square barrier respectively. When h is generatedc(x,y)>0,hc(x,y)＝0,hc(x,y)<When 0, the outer region, the surface region and the inner region of the circular obstacle are shown.
Step 2: the method aims at dynamic obstacles in an intelligent factory, such as operators, various mobile robots and the like. In order to describe the dynamic obstacle more effectively, the center of mass of the dynamic obstacle is taken as the center of a circle, and the radius r is used at a certain momentcThe circular envelope of (a) represents the current area of the dynamic obstacle, and the following assumptions are made: motion speed of dynamic obstacle in prediction time domain TpConstant within p Δ t, but with uncertain gaussian noise. Defining a state vector of a dynamic obstacle as
Wherein x0,y0Is the position of the center of mass of the dynamic obstacle,
is a dynamic obstacle x0The component of the velocity of the direction of the,
is a dynamic obstacle y0The velocity component of the direction, the state equation and the measurement equation of the dynamic obstacle are as follows:
wherein:
Discretizing the state equation and the measurement equation of the dynamic barrier to obtain a state updating equation under each time step, so that the inspection robot updates the dynamic barrier centroid area in real time according to the barrier centroid position obtained by scanning of the laser radar and the dynamic barrier state updating equation in the barrier grid map layer.
xobs_d(k+1)＝Axobs_d(k)+ωs(k) (4)
Where a is the state update matrix for the dynamic barrier,
is the state vector of the obstacle, each item from left to right in the square bracket comprises the abscissa of the center of mass of the dynamic obstacle, the ordinate of the center of mass of the dynamic obstacle and the x of the dynamic obstacle under the perception of the robot0Direction velocity, dynamic obstacle y0A direction speed; Δ t is the control step time of the robot, μsN (0, Q), Q is a state update covariance matrix of the form:
and step 3: and (3) according to the state updating equation of the dynamic obstacle centroid area in the step (2), providing a dynamic obstacle reachable area prediction algorithm.
Firstly, an equation is updated based on the state of the dynamic obstacle, and the future motion state of the dynamic obstacle is predicted according to the obstacle information detected in real time. Then setting a prediction time domain TpP is a positive integer. Construction of prediction time domain T based on optimal prediction theorypAnd finally, solving the reachable area of the dynamic obstacle centroid of the predicted step number p steps.
If the predicted step number j is 1,2 … p, the prediction error is determined
Wherein
Optimal prediction
Due to the fact that
A zero mean gaussian sequence. The p-step prediction variance formula is as follows:
p-step predictive variance formulaIn AjP(0)AjFor the transition terms caused by the variance matrix,
for noise-induced variance increase, P (0) is an initial variance transfer matrix of the form:
the variance sigma of the centroid of the dynamic obstacle in the motion direction is obtained by a p-step prediction variance formulaxAnd variance σ in the vertical motion directionyThen the reachable region of its centroid is available (x)0(k),y0(k) ) has a major axis of 3 σ as a centeryMinor axis of 3 σxAs shown in fig. 3. Based on the above analysis, a dynamic obstacle reachable area prediction algorithm based on state update is proposed as follows:
and 4, step 4: and (4) establishing a multi-step ellipse enveloping potential field model based on dynamic obstacle reachable area prediction according to the dynamic obstacle reachable area centroid prediction algorithm provided in the step (3). Firstly, because the obstacle has a certain size, in order to improve the calculation efficiency, the reachable area of the dynamic obstacle is firstly expanded to rc. Setting the position of the mass center of the dynamic obstacle as O1And the predicted step number j is 1 ellipse P1P2Center of (A), P1And P2Its major and minor axes are denoted 2a for its focal point1,2b1Focal length is 2c1(ii) a Predicted step number j ═ p ellipse N1N2Has a focal point of N1And N2And the major and minor axes thereof are denoted as 2a2,2b2Focal length is 2c2(ii) a Two straight lines around the ellipse are envelope common tangent lines of the predicted reachable region; radius r for dynamic barrier at a certain momentcCircular envelope description of (1), achievable region extension rc. Using geometric knowledge, ellipse P1P2The major axis and the minor axis of (a) are respectively re-corrected to 2 (a)1+rc),2(b1+rc) The focal length is newly found to be
Ellipse N1N2Respectively find 2 (a) again for the major axis and the minor axis of2+rc),2(b2+rc) The focal length becomes
The envelope common tangent of the predicted reachable area is revised and recorded as AB and CD; let a point position in space be denoted as M (x, y), the elliptical envelope potential field is described as follows:
wherein: d1＝|2(a1+rc)-||MN1||-||MN2|||，d2＝|||AB||-||MB||-||MA|||，
And UAB(M) are each an ellipse N1N2And the potential field produced by the straight line AB part, | | MN1I is robot to focus N1Distance of, | | MN2I is robot to focus N2Distance of d0Is the influence distance, k, of the dynamic obstacle potential fieldfAnd kABAre respectively an ellipse N1N2And an ellipse P1P2Coefficient of influence of the repulsive force field. With the same principle of obtaining dynamic obstaclesThe multi-step elliptical envelope potential is as follows:
the negative gradient of the envelope potential energy is obtained, and the repulsion force can be obtained:
wherein: o is2Is a focal point N1And a focal point N2Is marked as the midpoint
Psi and lambda respectively represent the included angle between the connecting line from the point M (x, y) to the two ends of the AB and the AB; ellipse N1N2Has a major axis of 2a2Minor axis of 2b2；
Are respectively
FABThe direction vector, the direction of which points to the outside of the obstacle, is shown in fig. 5 and fig. 6 for the side view and the top view of the multi-step elliptical envelope potential field of the present embodiment based on the dynamic obstacle reachable area prediction.
In the same way, the total repulsion of the dynamic potential field is:
and 5: in the obstacle avoidance process of the robot, the robot can meet not only dynamic obstacles, but also various dynamic obstacles. In general, semantic segmentation and visual target detection can be realized through laserThe method for measuring comprises the steps of dividing irregular static barriers into square barriers and circular barriers, and further establishing a square barrier potential field model of a novel Sigmoid function on the basis of establishing a static barrier model according to the step 1. Repulsive force function F of a square obstacle2Negative gradient as a function of repulsive potential energy:
wherein k isriIs the gain coefficient of a novel Sigmoid function, the coefficient r is related to the influence range of a square obstacle, SiMathematical expression of a function representing the ith plane of a square obstacle, hcIs a square barrier function expression, ri＝[sinβi-sinαi,cosαi-cosβi]TThe sum of two unit vectors formed by two end points on the ith surface of the square obstacle and the position of the robot respectively points to the outer side of the square obstacle.
Step 6: on the basis of establishing a static obstacle model in a circular obstacle map model according to the step 1, further establishing a potential field of a circular obstacle, which is defined as follows:
where ρ is0Is the influence distance of a circular obstacle.
And 7: step 4-step 6, multistep elliptical envelope potential field repulsion F1Novel square obstacle potential field repulsion F of Sigmoid function2Circular obstacleRepulsive force F of object3Logarithmic Lyapunov vector gravity FattrAnd total potential field force Ftotal＝F1+F2+F3+Fattr＝[Ftotalx,Ftotaly]TReferring to fig. 7, the desired velocity vector v of the robot in the total potential field is showndAnd desired driving angle
Can be determined by solving the following system of equations:
||vd||＝vd,arctan(vd)＝arctan(Ftotal)＝θd (18)
wherein the logarithmic Lyapunov gravity vector field is represented as
Represents the Euclidean distance between the current position of the inspection robot and the position of the target point,
and 8: the robot calculates an expected driving angle and an expected speed vector in real time through the step 7 in the ros operating system, then controls an instruction to the STM32 single chip microcomputer through a serial port, controls the pose of the robot in real time through proportional integral feedback and forward feedback, and finally obtains an obstacle avoidance path of the robot through a track deduction formula.
The track deduction formula is as follows:
θ(t+1)＝θ(t)+ωθ△t (20)
wherein, [ v ]x,vy]T，qdAnd (t) and omega respectively represent the speed of the inspection robot in the geodetic coordinate system, the position of the robot at the time t and the angular speed.
Compared with the traditional method, the real-time obstacle avoidance algorithm provided by the embodiment considers the movement trend and the geometric size of the obstacle, and can ensure that the path length is shorter, the energy consumption is lower, and the path smoothness and the maximum driving angle change amplitude are smaller in the obstacle avoidance process of the inspection robot. Under the condition of performance constraint of the inspection robot, the provided algorithm can more effectively realize the obstacle avoidance task of the inspection robot in a complex factory environment. Meanwhile, the robot can avoid obstacles locally and safely, and can solve the problems that the path is around and the obstacle is not kept away in time. The average linear acceleration and the average angular velocity of the robot are both larger than corresponding indexes of the obstacle avoidance algorithm provided by the text under the dynamic window algorithm, which can provide higher performance requirements for a voltage driving module of the inspection mobile robot and can also cause the connection device to be worn more easily. Based on this, the algorithm is more reasonable and practical.
Referring to fig. 8, the inspection robot trajectory planning and real-time obstacle avoidance system based on obstacle area prediction according to the embodiment of the present invention includes:
the system comprises a memory 10, a processor 20 and a computer program stored on the memory 10 and capable of running on the processor 20, wherein the processor 20 implements the steps of the inspection robot trajectory planning and real-time obstacle avoidance method based on obstacle area prediction proposed in the embodiment when executing the computer program.
The specific working process and working principle of the inspection robot trajectory planning and real-time obstacle avoidance system based on obstacle area prediction in this embodiment can refer to the working process and working principle of the inspection robot trajectory planning and real-time obstacle avoidance method based on obstacle area prediction in this embodiment.
The above is only a preferred embodiment of the present invention, and is not intended to limit the present invention, and various modifications and changes will occur to those skilled in the art. Any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the protection scope of the present invention.
Claims (9)
1. A method for routing inspection robot track planning and real-time obstacle avoidance based on obstacle area prediction is characterized by comprising the following steps:
establishing a dynamic barrier reachable area prediction model based on state updating;
acquiring an elliptic reachable area under the prediction step number based on the dynamic barrier reachable area prediction model;
establishing a multi-step ellipse enveloping potential field model based on the ellipse reachable region under the predicted step number;
establishing a square obstacle potential field model and a circular obstacle potential field model of a novel Sigmoid function based on a static obstacle model;
obtaining an expected driving angle and an expected speed vector of the inspection robot based on the multi-step ellipse enveloping potential field model, the square obstacle potential field model of the novel Sigmoid function, the circular obstacle potential field model and the logarithm Lyapunov gravitational field model;
and obtaining an obstacle avoidance path of the robot based on the expected driving angle and the expected speed vector.
2. The inspection robot trajectory planning and real-time obstacle avoidance method based on obstacle area prediction according to claim 1, wherein obtaining an elliptical reachable area under a preset number of steps based on the dynamic obstacle reachable area prediction model comprises:
initializing a movement velocity variance, a measurement noise variance and an initial variance transfer matrix of the dynamic obstacle;
obtaining the variance of the centroid of the dynamic obstacle in the motion direction and the vertical motion direction under the predicted step number according to a p-step prediction variance equation, wherein the p-step prediction variance equation specifically comprises the following steps:
wherein, Pk+j|kPredict the variance matrix of step number j for time k, P (0) is the initial variance transition matrix, AjUpdating a matrix for the state transition of the predicted step number j, wherein Q is a measurement covariance matrix;
obtaining the centroid position of the dynamic barrier under the predicted step number according to the centroid updating equation of the dynamic barrier;
and constructing an elliptical reachable area under the preset step number according to the position of the centroid of the dynamic obstacle and the variance of the centroid of the dynamic obstacle in the motion direction and the vertical motion direction under the predicted step number.
3. The inspection robot trajectory planning and real-time obstacle avoidance method based on obstacle area prediction according to claim 2, wherein the specific steps of constructing the elliptical reachable area under the preset number of steps are as follows according to the position of the centroid of the dynamic obstacle and the variance of the centroid of the dynamic obstacle in the motion direction and the vertical motion direction under the predicted number of steps:
and (3) taking the centroid position of the previous step of the preset step number as the center, and taking the 3-time variance of the centroid of the dynamic barrier in the motion direction and the vertical motion direction as the major axis and the minor axis under the preset step number to construct an elliptical reachable area.
4. The inspection robot trajectory planning and real-time obstacle avoidance method based on obstacle area prediction according to claim 1 or 2, wherein the establishing of the multi-step ellipse enveloping potential field model based on the ellipse reachable area under the prediction step number comprises:
expanding the reachable area of the ellipse under the predicted step number by a preset radius;
obtaining an ellipse enveloping potential field according to the ellipse reachable region under the prediction step number after the preset radius is expanded;
establishing a multi-step elliptical envelope potential field model according to the elliptical envelope potential field, wherein the multi-step elliptical envelope potential field model specifically comprises the following steps:
wherein, U1In the case of a multi-step elliptical envelope potential field,
UAB(M1)、UCD(M1) Respectively as any point M in the multi-step elliptic envelope potential field1In the ellipse reachable region N1N2Oval reachable region P1P2Straight line AB and straight line CD, and the ellipse can reach the region P1P2And elliptical reachable region N1N2The predicted step number j is 1, and the predicted step number j is P, and the straight line AB and the straight line CD are the elliptical reachable areas P1P2And elliptical reachable region N1N2Envelope common tangent line of (c).
5. The inspection robot trajectory planning and real-time obstacle avoidance method based on obstacle area prediction as claimed in claim 4, wherein a concrete formula of a square obstacle potential field model for establishing a novel Sigmoid function based on a static obstacle model is as follows:
wherein, U2(M2) Any point M in a square obstacle potential field model which is a novel Sigmoid function2Square obstacle potential field of (k)riGain coefficient being a new Sigmoid function, r being an influence coefficient related to the influence range of a square obstacle, SiMathematical expression of a function representing the ith plane of a square obstacle, hc(M2) Any point M in a square obstacle potential field model which is a novel Sigmoid function2The square barrier function expression of (2).
6. An inspection robot trajectory planning and real-time obstacle avoidance method based on obstacle area prediction as claimed in claim 4, wherein the specific formula for establishing the circular obstacle potential field model based on the static obstacle model is as follows:
wherein, U3(M3) Is any point M in the potential field model of the circular obstacle3λ is the coefficient of the potential field of the circular obstacle, rcRadius of a circular obstacle, hc(M3) Is any point M in the potential field model of the circular obstacle3Expression of the circular barrier function of, p0Is the influence distance of a circular obstacle.
7. The inspection robot trajectory planning and real-time obstacle avoidance method based on obstacle area prediction according to claim 6, wherein obtaining the expected driving angle and the expected speed vector of the inspection robot based on the multi-step elliptical envelope potential field model, the square obstacle potential field model of the novel Sigmoid function, the circular obstacle potential field model, and the logarithmic Lyapunov gravitational field model comprises:
correspondingly obtaining a multi-step elliptical envelope potential field, a square obstacle potential field of a novel Sigmoid function, a circular obstacle potential field and a logarithm Lyapunov vector gravity according to the multi-step elliptical envelope potential field model, the square obstacle potential field model of the novel Sigmoid function, the circular obstacle potential field and the logarithm Lyapunov gravity field model;
respectively solving negative gradients of the multi-step elliptic enveloping potential field, the square obstacle potential field of the novel Sigmoid function and the circular obstacle potential field, and correspondingly obtaining a multi-step elliptic enveloping potential field repulsive force, a square obstacle potential field repulsive force of the novel Sigmoid function and a circular obstacle potential field repulsive force;
and obtaining an expected driving angle and an expected speed vector of the inspection robot according to the multistep elliptical envelope potential field repulsive force, the square obstacle potential field repulsive force of the novel Sigmoid function, the circular obstacle potential field repulsive force and the logarithm Lyapunov vector attractive force.
8. The inspection robot trajectory planning and real-time obstacle avoidance method based on obstacle area prediction according to claim 7, wherein a calculation formula for obtaining an obstacle avoidance path of the robot based on the expected travel angle and the expected speed vector is as follows:
θ(t+1)＝θ(t)+ωθ△t
wherein q isd(t +1) and qd(t) represents the positions of the inspection robot at time t +1 and time t, vxAnd vyRepresenting the speeds of the inspection robot in the x and y directions, theta (t +1) and theta (t) representing the orientation angles of the inspection robot at the time t +1 and the time t, and omegaθIndicating the angular velocity of the inspection robot.
9. A system for planning a track of an inspection robot and avoiding obstacles in real time based on obstacle area prediction comprises:
memory (10), processor (20) and computer program stored on the memory (10) and executable on the processor (20), characterized in that the steps of the method according to any of the preceding claims 1 to 8 are implemented when the computer program is executed by the processor (20).
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN202110923744.0A CN113759900B (en) | 2021-08-12 | 2021-08-12 | Method and system for track planning and real-time obstacle avoidance of inspection robot based on obstacle region prediction |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN202110923744.0A CN113759900B (en) | 2021-08-12 | 2021-08-12 | Method and system for track planning and real-time obstacle avoidance of inspection robot based on obstacle region prediction |
Publications (2)
| Publication Number | Publication Date |
|---|---|
| CN113759900A true CN113759900A (en) | 2021-12-07 |
| CN113759900B CN113759900B (en) | 2023-05-02 |
Family
ID=78789080
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN202110923744.0A Active CN113759900B (en) | 2021-08-12 | 2021-08-12 | Method and system for track planning and real-time obstacle avoidance of inspection robot based on obstacle region prediction |
Country Status (1)
| Country | Link |
|---|---|
| CN (1) | CN113759900B (en) |
Cited By (7)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN114384919A (en) * | 2022-01-17 | 2022-04-22 | 北京格睿能源科技有限公司 | Vehicle obstacle avoidance path planning method and system based on large obstacle shape information |
| CN114578827A (en) * | 2022-03-22 | 2022-06-03 | 北京理工大学 | Distributed multi-agent cooperative full coverage path planning method |
| CN114610040A (en) * | 2022-04-02 | 2022-06-10 | 天津大学 | Autonomous obstacle avoidance learning control method and device applied to unmanned operating system |
| CN114637302A (en) * | 2022-04-15 | 2022-06-17 | 安徽农业大学 | Automatic advancing obstacle avoidance method and system based on computer vision |
| CN115309169A (en) * | 2022-10-11 | 2022-11-08 | 天地科技股份有限公司 | Underground unmanned vehicle control method and device |
| CN115454061A (en) * | 2022-08-31 | 2022-12-09 | 安徽机电职业技术学院 | Robot path obstacle avoidance method and system based on 3D technology |
| CN117474190A (en) * | 2023-12-28 | 2024-01-30 | 磐石浩海(北京)智能科技有限公司 | Automatic inspection method and device for cabinet |
Citations (5)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN103558856A (en) * | 2013-11-21 | 2014-02-05 | 东南大学 | Service mobile robot navigation method in dynamic environment |
| CN108827312A (en) * | 2018-08-08 | 2018-11-16 | 清华大学 | A kind of coordinating game model paths planning method based on neural network and Artificial Potential Field |
| CN111337941A (en) * | 2020-03-18 | 2020-06-26 | 中国科学技术大学 | Dynamic obstacle tracking method based on sparse laser radar data |
| CN112904842A (en) * | 2021-01-13 | 2021-06-04 | 中南大学 | Mobile robot path planning and optimizing method based on cost potential field |
| US20220016778A1 (en) * | 2019-04-02 | 2022-01-20 | Brain Corporation | Systems, apparatuses, and methods for cost evaluation and motion planning for robotic devices |
-
2021
- 2021-08-12 CN CN202110923744.0A patent/CN113759900B/en active Active
Patent Citations (5)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN103558856A (en) * | 2013-11-21 | 2014-02-05 | 东南大学 | Service mobile robot navigation method in dynamic environment |
| CN108827312A (en) * | 2018-08-08 | 2018-11-16 | 清华大学 | A kind of coordinating game model paths planning method based on neural network and Artificial Potential Field |
| US20220016778A1 (en) * | 2019-04-02 | 2022-01-20 | Brain Corporation | Systems, apparatuses, and methods for cost evaluation and motion planning for robotic devices |
| CN111337941A (en) * | 2020-03-18 | 2020-06-26 | 中国科学技术大学 | Dynamic obstacle tracking method based on sparse laser radar data |
| CN112904842A (en) * | 2021-01-13 | 2021-06-04 | 中南大学 | Mobile robot path planning and optimizing method based on cost potential field |
Non-Patent Citations (3)
| Title |
|---|
| NARAYAN SRINIVASA等: "A bio-inspired kinematic controller for obstacle avoidance during reaching tasks with real robots", 《ES》 * |
| 张化锴 等: "基于路径预测人工势场法的自动跟随小车路径规划", 《计算机测量与控制》 * |
| 彭帆 等: "基于障碍物可达区域预测的机器人实时避障算法", 《东北大学学报（自然科学版）》 * |
Cited By (12)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN114384919A (en) * | 2022-01-17 | 2022-04-22 | 北京格睿能源科技有限公司 | Vehicle obstacle avoidance path planning method and system based on large obstacle shape information |
| CN114384919B (en) * | 2022-01-17 | 2023-06-27 | 北京格睿能源科技有限公司 | Vehicle obstacle avoidance path planning method and system based on large obstacle form information |
| CN114578827A (en) * | 2022-03-22 | 2022-06-03 | 北京理工大学 | Distributed multi-agent cooperative full coverage path planning method |
| CN114610040A (en) * | 2022-04-02 | 2022-06-10 | 天津大学 | Autonomous obstacle avoidance learning control method and device applied to unmanned operating system |
| CN114637302A (en) * | 2022-04-15 | 2022-06-17 | 安徽农业大学 | Automatic advancing obstacle avoidance method and system based on computer vision |
| CN114637302B (en) * | 2022-04-15 | 2022-10-18 | 安徽农业大学 | Automatic advancing obstacle avoidance method and system based on computer vision |
| CN115454061A (en) * | 2022-08-31 | 2022-12-09 | 安徽机电职业技术学院 | Robot path obstacle avoidance method and system based on 3D technology |
| CN115454061B (en) * | 2022-08-31 | 2024-03-29 | 安徽机电职业技术学院 | Robot path obstacle avoidance method and system based on 3D technology |
| CN115309169A (en) * | 2022-10-11 | 2022-11-08 | 天地科技股份有限公司 | Underground unmanned vehicle control method and device |
| AU2023201045B1 (en) * | 2022-10-11 | 2023-04-13 | Ccteg Energy Technology Development Co., Ltd. | Method for controlling side mining unmanned vehicle and device |
| CN117474190A (en) * | 2023-12-28 | 2024-01-30 | 磐石浩海(北京)智能科技有限公司 | Automatic inspection method and device for cabinet |
| CN117474190B (en) * | 2023-12-28 | 2024-02-27 | 磐石浩海(北京)智能科技有限公司 | Automatic inspection method and device for cabinet |
Also Published As
| Publication number | Publication date |
|---|---|
| CN113759900B (en) | 2023-05-02 |
Similar Documents
| Publication | Publication Date | Title |
|---|---|---|
| CN113759900B (en) | Method and system for track planning and real-time obstacle avoidance of inspection robot based on obstacle region prediction | |
| Saravanakumar et al. | Multipoint potential field method for path planning of autonomous underwater vehicles in 3D space | |
| Baek et al. | Optimal path planning of a target-following fixed-wing UAV using sequential decision processes | |
| CN111982114B (en) | Rescue robot for estimating three-dimensional pose by adopting IMU data fusion | |
| CN114355981B (en) | Method and system for autonomous exploration and mapping of four-rotor unmanned aerial vehicle | |
| US20220057804A1 (en) | Path determination method | |
| Zhu et al. | Global dynamic path planning based on fusion of a* algorithm and dynamic window approach | |
| Wu et al. | Robust LiDAR-based localization scheme for unmanned ground vehicle via multisensor fusion | |
| Do Quang et al. | An approach to design navigation system for omnidirectional mobile robot based on ROS | |
| Steiner et al. | Open-sector rapid-reactive collision avoidance: Application in aerial robot navigation through outdoor unstructured environments | |
| Bayer et al. | Speeded up elevation map for exploration of large-scale subterranean environments | |
| Huang et al. | A novel particle swarm optimization algorithm based on reinforcement learning mechanism for AUV path planning | |
| Wang et al. | A fuzzy logic path planning algorithm based on geometric landmarks and kinetic constraints | |
| Spitzer et al. | Fast and agile vision-based flight with teleoperation and collision avoidance on a multirotor | |
| WO2022232415A1 (en) | Reactive collision avoidance for autonomous vehicles considering physical constraints | |
| Lai et al. | Hierarchical incremental path planning and situation-dependent optimized dynamic motion planning considering accelerations | |
| Tusseyeva et al. | 3D global dynamic window approach for navigation of autonomous underwater vehicles | |
| Aldair et al. | Navigation of mobile robot with polygon obstacles avoidance based on quadratic bezier curves | |
| Li et al. | A method for collision free sensor network based navigation of flying robots among moving and steady obstacles | |
| Dapena et al. | An Algebraic Collision Avoidance Approach for Unmanned Aerial Vehicle. | |
| Li et al. | Design and Implementation of Autonomous Navigation System Based on Tracked Mobile Robot | |
| Fleckenstein et al. | Smooth local planning incorporating steering constraints | |
| Wu et al. | Application of 6-Dof Robot Motion Planning in Fabrication | |
| Xing et al. | Real-time robot path planning using rapid visible tree | |
| Paz-Delgado et al. | Combined path and motion planning for workspace restricted mobile manipulators in planetary exploration |
Legal Events
| Date | Code | Title | Description |
|---|---|---|---|
| PB01 | Publication | ||
| PB01 | Publication | ||
| SE01 | Entry into force of request for substantive examination | ||
| SE01 | Entry into force of request for substantive examination | ||
| GR01 | Patent grant | ||
| GR01 | Patent grant |