CN108981717A

CN108981717A - A kind of paths planning method based on hyperbolic metric

Info

Publication number: CN108981717A
Application number: CN201810968156.7A
Authority: CN
Inventors: 王红军
Original assignee: Individual
Current assignee: Individual
Priority date: 2018-08-23
Filing date: 2018-08-23
Publication date: 2018-12-11

Abstract

The present invention is a kind of paths planning method based on hyperbolic metric, in the case where the distribution of known spatial object, influence of all objects to space potential energy can be calculated, according to these potential energy, suitable hyperbolic metric is equipped in known spatial, the homotopy homology theory of theory of geodesics and algebraic topology based on Differential Geometry, it considers further that the anti-collision safety distance of moving object on path and the length in path, several ways diameter connection start-stop two o'clock can globally be cooked up, suitable hyperbolic metric determines feasible path in engineering, to bring solid theory and practice basis to the autokinetic movement of object, to robot, unmanned plane, the fields such as pilotless automobile provide competitive technical advantage.

Description

Path planning method based on double curvature gauges

Technical Field

The invention relates to the technical concepts of artificial intelligence, machine vision, path planning and the like, in particular to a decision on how a robot selects an reachable path to autonomously move in a strange environment.

Background

With the development of industrial robots in recent years, the service robot industry is driven to be gradually excavated, meanwhile, the intelligent hardware field started in 2014 is also protruded, the sales volume of service robots in 2015 reaches 85 hundred million dollars according to the statistics of the international robot alliance, the higher 20% -30% growth rate is kept, according to the ai rui research, the global intelligent hardware loading volume in 2014 reaches 60 million machines in the intelligent hardware field, and 140 million machines in 2017 is expected.

The problem is also obvious behind the high-speed development of the market, on one hand, the market potential is not excavated, and on the other hand, the technical difficulties exist when the robot and the intelligent hardware enter the service industry.

Although the visual recognition of objects is a big difficulty, some technical attempts have been made to overcome this problem, for example, in the patents "a method for recognizing an entire object based on a three-dimensional grid map" and "a method for assisting in recognizing an object based on color features", a method "how to recognize an object from the aspects of shape, color, material, etc. is mentioned. Here we are to solve: how to plan the path in the environment space lays a solid foundation for autonomous movement.

Object of the Invention

The invention aims to solve the problem of how to plan a path when a machine moves autonomously, and provides a method which not only can calculate the accessibility of the path between a starting point and a stopping point, but also can calculate and optimize the path between the starting point and the stopping point.

Technical scheme

The purpose of the invention is realized as follows: the path planning method comprises the following steps of knowing an input environment space map and distribution position and size information of objects in the space on the map:

(1) establishing a hyperbolic gauge with uniform Gaussian curvature in a space to be analyzed, mapping hyperbolic space differential homomorphism to a new hyperbolic space for convenient calculation, and analyzing and calculating in the new hyperbolic space;

(2) modeling an environment potential function in the original space to be analyzed, and analyzing the influence of each obstacle on the space one by one, for example, the coordinate is ([ xi ] at the time t_i,τ_i,ε_i) Influence potential of the obstacle on the spatial position (x, y, z):

g is a constant;

after each obstacle is analyzed one by one, the influence potential of the position (x, y, z) at the time t can be obtained:

g is a constant as above;

(3) according to the previous stepAnd (3) correcting the double curvature gauge at the position (x, y, z) according to the following correction principle: correspondingly increasing the coefficient of the gauge at a place with a large influence potential value, and ensuring the hyperbolic property of the gauge;

(4) in a given hyperbolic space, a differential equation set of the geodesic line is established by utilizing a geodesic theory of differential geometry, the existence of solutions in the differential equation set indicates that the paths between the starting point and the stopping point are accessible, and the existence of a plurality of solutions in the differential equation set indicates that a plurality of paths between the starting point and the stopping point are accessible;

(5) and mapping the path in the hyperbolic space back to the original space to be analyzed.

The system used by the invention consists of: the system comprises a hyperbolic gauge initialization system, a potential field modeling system, a hyperbolic gauge correction system and a target path solving system. The four systems are software systems arranged according to functions, and the specific functions of each subsystem are as follows:

double curvature gauge initialization system: initializing a double curvature gauge at each position in a space to be analyzed to ensure that Gaussian curvatures at each position are equal,

potential field modeling system: calculating the spatial potential field distribution of all obstacles on a space to be analyzed,

double curvature gauge correction system: correcting the hyperbolic degree gauge at each position according to the potential field at each position in space,

target path solving system: and solving the geodesic line between the starting point and the stopping point on the double-curvature gauge space.

Description of the drawings:

FIG. 1 is a diagram showing the system configuration used in the method of the present invention

FIG. 2 is a spatial example diagram of an environment

FIG. 3 is a hyperbolic space diagram of an environment

FIG. 4 is a spatial potential field profile in an environment

FIG. 5 is a diagram of the reachable paths of two points at the beginning and end of the space in an environment

Detailed Description

The following describes an embodiment of the present invention in a two-dimensional space by way of example with reference to the accompanying drawings.

The overall structure of the system used in the method of the invention can refer to the attached figure 1, and the system comprises four subsystems and specifically comprises the following steps:

first step of

In a hyperbolic scale initialization system, a map of a known environment, as shown in fig. 2, is computed by mapping an environment spatial differential homomorphism onto a unit disk as follows: the environment space is considered as a part of the upper half plane in the two-dimensional Cartesian coordinate system O xy, and the mapping is utilized

Wherein,z₀＝i,z＝x+iy，

the upper x y half-plane is mapped to the unit disk as shown in FIG. 3.

A double curvature gauge is initialized on the unit disc, the gauge at position (x, y) being:

α(x,y)≡-1，

then the gaussian curvature K (x, y) ≡ α (x, y) — 1 at the position (x, y) determined by this hyperboloid on the unit disc.

Second step of

In a potential field modeling system, within a space O xy according to a two-dimensional potential function formula:

g is a constant;

the potential field distribution of all objects is calculated and the influence of all obstacles on the surrounding potential field is analyzed one by one, as shown in fig. 4.

The third step

In a double curvature correction system, the influence potential at the location (x, y) is corrected according to the above correction principleThe gauge was modified as follows:

α(a fourth step of x, y) ≡ -1

In the target path solving system, a second-order differential equation set of the geodesic is established according to the degree gauge g (x, y),

wherein: i, j, k ∈ {1,2}, and u¹＝x,u²＝y，

In the equationThe relation coefficient is adaptive to the metric g (x, y), in addition, it can be known that coordinate basis vectors are orthogonal in an original space and a hyperbolic unit disc space, and according to a Liouville formula, an equation set can be simplified into the following first-order differential equation set:

wherein E ═ g (x, y)₁₁,G′＝g(x,y)₂₂，

If the starting point S and the stopping point T are given, which is equivalent to the equation set having initial and boundary conditions, the equation set can be solved; if the solution of the equation set does not exist, the two starting and stopping points S and T are not reachable, and if the equation set has a plurality of solutions, the two starting and stopping points S and T are reachable by a plurality of homotopic paths.

After the reachable path is found on the unit disk, the inverse map w is used^-1A reachable path in the original environment space to be analyzed can be solved; through calculation, a plurality of reachable paths connecting the start and stop points S and T can be obtained, as shown in fig. 5.

In summary, we can see that on a given object or environment, through a two-dimensional or three-dimensional environment space map, if a start point and a stop point are given, we can determine the accessibility of the two points and plan a path between the two points, thereby providing a basic support for autonomous motion and collision prevention.

Claims

1. A path planning method based on a double-curvature gauge is characterized in that the double-curvature gauge with uniform Gaussian curvature is added to a space to be analyzed, then the double-curvature gauge is corrected on the basis of potential field distribution according to potential field distribution of all objects in the space, and finally, in the gauge space, if expected target conditions are given, the problem of path planning is converted into the problem of finding the optimal path connecting two points in the new double-curvature gauge space, and the method is realized according to the following steps:

(1) the method comprises the steps of knowing an input environment space map and distribution positions and sizes of objects in the space on the map;

(2) matching a double curvature gauge in a space map to be analyzed;

(3) establishing potential field distribution of the whole space according to a distance inverse ratio for all objects in a space map to be analyzed by a method similar to a gravitational field or a point charge electric field, and analyzing the influence of each obstacle on the whole space one by one, wherein the influence is represented by a potential function of the environment, and the potential function is represented by a potential functionRepresents the effect of all obstacles on the position at (x, y, z) at time t, as detailed below:

obstacle Q_i,i∈[1,n]Effect on position (x, y, z) at time t:

g is a constant;

(4) according to the previous step-correcting the gauge of the position (x, y, z);

(5) the method comprises the steps of establishing a differential equation of the geodesic by utilizing a geodesic theory of differential geometry, giving the positions of a start point and a stop point which are equivalent to the initial conditions and the boundary conditions of the differential equation, determining whether the solution of the differential equation exists or not according to the corresponding paths, determining the number of the solutions of the differential equation according to the number of the paths, and selecting one or more paths according to an optimization target.

2. A method for hyperbolic curve-based path planning as claimed in claim 1, wherein the environment space to be analyzed is regarded as a manifold, and the hyperbolic curve is added to the manifold to find the path between the start point and the stop point.

3. A method for hyperbolic-based path planning according to claim 1, wherein the hyperbolic is modified according to the effect of obstacles on the surrounding space.

4. The hyperbolic-rule-based path planning method according to claim 1, wherein the path planning method is applicable not only to a two-dimensional environment but also to a three-dimensional environment.

5. The method of claim 1, wherein the method is applicable not only to static environments but also to dynamic environments.

6. A hyperbolic-based path planning method according to claim 1, wherein one hyperbolic space differential homomorphism is mapped to another hyperbolic space for analysis and calculation.

7. The method of claim 1, wherein the path planning method is applicable not only to a continuous environment space but also to a discrete environment space.