CN108762256B - Method for robot to avoid relatively high-speed obstacle - Google Patents

Method for robot to avoid relatively high-speed obstacle Download PDF

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CN108762256B
CN108762256B CN201810421961.8A CN201810421961A CN108762256B CN 108762256 B CN108762256 B CN 108762256B CN 201810421961 A CN201810421961 A CN 201810421961A CN 108762256 B CN108762256 B CN 108762256B
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CN108762256A (en
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许天野
成慧
谢志鹏
龙有炼
江泽宇
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Sun Yat Sen University
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    • G05—CONTROLLING; REGULATING
    • G05D—SYSTEMS FOR CONTROLLING OR REGULATING NON-ELECTRIC VARIABLES
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    • G05D1/02—Control of position or course in two dimensions
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Abstract

The invention relates to the technical field of robots, in particular to a method for avoiding a relatively high-speed obstacle by a robot. The method provided by the invention is used for dynamically avoiding the high-speed obstacle under the condition that the maximum speed of the robot is limited. The method makes up the situation that a feasible solution cannot be obtained easily under the condition of facing a high-speed obstacle in the traditional speed obstacle method. The method provides a thought for expanding a speed obstacle area, and the speed obstacle is expanded into two parts, wherein one part is the speed obstacle area obtained by the traditional speed obstacle method, and the other part is the speed area which can cause that the next control cycle can not obtain a feasible solution under the current speed area. By adopting the method, the maximum speed of the robot can be guaranteed to be limited, and the next control period can be kept to be solved, so that the risk that the robot collides with an obstacle is reduced. And a method for a wheeled mobile robot is proposed based on the algorithm.

Description

Method for robot to avoid relatively high-speed obstacle
Technical Field
The invention relates to the technical field of robots, in particular to a method for avoiding a relatively high-speed obstacle by a robot.
Background
With the development of science and technology, robotics is gradually combined with human production work, and is widely applied to military, industry and service industry. Especially, the ground mobile robot can replace human labor force in mapping and transportation due to high safety and reliability. In a complex scene, there may be obstacles in rest and motion, and the robot works in such an environment, and it is first to avoid collision between itself and the obstacles, so how to effectively avoid cooperative and non-cooperative obstacles in an unknown environment is a key issue in the field of robot research. The traditional obstacle avoidance problem is mainly to avoid static obstacles or consider the obstacles as static in one control cycle, so as to plan the motion of the robot at the current moment. The simplified method is only suitable for a completely static environment or a scene with slow obstacle movement, and the real-time performance is poor. Since there may be many uncertain factors in the moving speed and direction of an obstacle in a dynamic obstacle, it is necessary to perform dynamic obstacle avoidance on the obstacle. Meanwhile, higher requirements are provided for the accuracy and the speed of the sensor of the robot and the real-time performance of the algorithm.
The local dynamic obstacle avoidance problem is emphasized, and during the movement of the robot, the self speed is adjusted in real time after the information fed back by the sensor is received to change the self track, so that the collision with an obstacle is avoided, wherein the detection strategy and the obstacle avoidance control algorithm of the sensor are crucial.
In the prior art, the artificial potential field method is one of simple and easy methods. The artificial potential field method regards a scene as a potential field space, and a target point of the robot is the lowest potential energy point of the whole potential field and is attractive to the robot; each barrier generates repulsion action on the robot and generates high potential energy. The robot is more inclined to move to a low potential energy point in the moving process, namely under the combined action of repulsion and attraction, the robot finishes avoiding the obstacle and moves to a desired point. The artificial potential field method is a simple and easy-to-use method and can be well utilized in low-complexity and low-speed changing scenes. However, in a complex scene of an obstacle, the effect of repulsion cannot be infinite due to model constraints of the robot. Meanwhile, when the obstacle is in a moving state, the artificial potential field method is easy to generate the problems of shock, untimely response and the like. In a scene with a large number of obstacles and a complex scene, the artificial potential field method is easy to fall into local optimization so as to stop moving.
The speed obstacle method restrains the movement speed of the robot by establishing a speed obstacle area, ensures that the speed of the mobile robot cannot collide with the obstacle within a time window tau as long as the speed of the mobile robot is outside the speed obstacle area, and can be used for collision avoidance of static and dynamic obstacles. The research and implementation of the VO algorithm is a current topical topic. The earliest speed barrier methods were proposed in 1998, and many different improved versions were derived over the years to solve the deficiencies and shortcomings of different VO methods. Jur van den Berg research team proposed a Reciprocal obstacle Avoidance algorithm (RCA) based on the velocity obstacle method. The method avoids the obstacle by respectively bearing partial responsibility among the multiple robots, solves the problem that the VO algorithm must bear all responsibility, increases the speed feasible region of the robots, and solves the problem of oscillation generated when the robots and the obstacle robots adopt the same obstacle avoidance strategy, so that the method is widely applied to the field of multi-robot obstacle avoidance. The speed obstacle method has higher requirements on the accuracy of a robot sensor and the positioning accuracy in actual use, and meanwhile, the robot is required to ignore the constraint of acceleration within a certain range due to the fact that the robot is solved in a speed domain, so that the situation that obstacle avoidance is not timely occurs in some scenes. Meanwhile, when a high-speed obstacle exists in a scene, the speed obstacle method is easy to generate a situation without solution.
Disclosure of Invention
The invention provides a method for avoiding a relatively high-speed obstacle by a robot in order to overcome at least one defect in the prior art, and provides a solution for solving the problem that a feasible solution can not be easily generated in a scene that the robot faces the relatively high-speed obstacle. The scheme is based on an improved reciprocal velocity barrier algorithm, proposes a thought for expanding a velocity barrier region, predicts a position point which can cause no solution next time, and simultaneously maps to a current new velocity selection to expand a new velocity barrier region. After a new speed obstacle area is generated, the obtained speed feasible solution can ensure that a new speed feasible solution can still be generated in the next time window, and further the risk that the robot cannot avoid the obstacle in the obstacle avoiding process is reduced. A method for applying the method to a wheeled mobile robot is also provided.
The scheme provides a solution for the problem that a feasible solution can not be easily generated in a scene that the robot faces a relatively high-speed obstacle. The scheme is based on an improved reciprocal velocity barrier algorithm, proposes a thought for expanding a velocity barrier region, predicts a position point which can cause no solution next time, and simultaneously maps to a current new velocity selection to expand a new velocity barrier region. After a new speed obstacle area is generated, the obtained speed feasible solution can ensure that a new speed feasible solution can still be generated in the next time window, and further the risk that the robot cannot avoid the obstacle in the obstacle avoiding process is reduced. The scheme is suitable for the condition that the speed and the direction of the barrier cannot be changed violently in a short time.
The technical scheme of the invention is as follows: a method of a robot for evading a relatively high speed obstacle, comprising the steps of:
s1, sensing the position and the speed of a peripheral obstacle by using a robot airborne sensor, and obtaining the relative position and the relative speed of the robot and the obstacle. Because the position information and the speed information are detected by the airborne sensor, the obtained data are relative values. Meanwhile, the speed of the robot can be obtained according to the onboard sensor of the robot, and the actual speed of the fault obstacle can be obtained by adding the relative speed and the speed of the robot.
S2, radius of the robot A and radius of the obstacle O are defined to be r respectivelyA、rOIn the position pO|A＝pO-pA. The collision zone under the location domain is defined as:
D(pO-pA,rA+rO)＝{q|q-(pO-pA)<rA+rO}
let τ be a predefined time window (i.e., how long no collision will occur). And analyzing the current robot in a position domain through a time window coefficient tau, and converting the current robot into analysis in a speed domain. In other words, the sum of the relative position and the radius is divided by the time coefficient τ, and the sum can be converted from the position domain to the velocity domain. D (p, r) ═ { q | | | q-p | | non-woven cells<r represents a circular region with a radius r centered at p. D (0, v)i max) Representing the speed limit of the robot. The speed barrier with time window may be defined as:
Figure BDA0001650966460000021
s3, the VO speed obstacle space is expanded by the following steps. The relative speed of the robot and the obstacle is vA|O＝vA-vO. Definition of
Figure BDA0001650966460000031
Is the new relative position and relative velocity of the robot.
Figure BDA0001650966460000032
Because the time window is short, the speed and direction of the obstacle are not changed in a short time. Coordinates of the next position of the obstacle
Figure BDA0001650966460000033
The new relative position can be expressed as
Figure BDA0001650966460000034
S4, if the next control period is reached, the new relative position is adopted
Figure BDA0001650966460000035
So as to draw a new speed obstacle area
Figure BDA0001650966460000036
Comprising a speed-constrained region of the robot
Figure BDA0001650966460000037
(here, the relative position) the robot cannot escape the new velocity obstacle area. The formula can be expressed as
Figure BDA0001650966460000038
When this is doneOf time of day
Figure BDA0001650966460000039
Is selected at
Figure BDA00016509664600000310
In the region, the next time τ will cause the above-mentioned situation where no feasible solution can be generated. Therefore, it is necessary to expand the original speed barrier
Figure BDA00016509664600000311
The new speed obstacle area is
Figure BDA00016509664600000312
And
Figure BDA00016509664600000313
the intersection of (a).
S5, selecting a new speed rule. Defining a desired relative velocity pointing to a target point of the robot as
Figure BDA00016509664600000314
The new speed selection of the robot requires escaping the extended speed obstacle area defined above.
Figure BDA00016509664600000315
S6, aiming at the wheeled mobile robot, kinematic model constraint exists, namely a constraint area of the speed is not a circle. It is no longer assumed that the maximum rotational speed of each wheel is
Figure BDA00016509664600000316
The advancing speed and the rotating speed of the differential wheel type robot are limited by the wheel speed. The following equation represents the maximum constraint of the linear speed and the rotational speed of the forward drive, where KsFor the conversion coefficient of the wheel rotating speed and the linear speed, different values may be obtained in different scenes:
|v(t)|≤vmax-l|ω(t)|/2
Figure BDA00016509664600000317
Figure BDA00016509664600000318
s7, due to the limit of the linear speed and the rotating speed, errors can be generated on the track when the wheeled mobile robot follows the expected speed. The idea is to control this error to be within a fixed range epsilon and thus to derive a new velocity constraint based on epsilon. According to the geometrical relationship, there are:
Figure BDA0001650966460000041
wherein v isdAnd thetadA desired speed and a desired speed bearing angle. It can be seen that the above formula is a quadratic function with respect to velocity v when v is at a stagnation point vmThe error has a minimum value.
Figure BDA0001650966460000042
Figure BDA0001650966460000043
Where T is the time to rotate to the desired angle and needs to be preset. If the T setting is too small,
Figure BDA0001650966460000044
less than omegamaxThe robot will use all wheel speeds to meet the desired angular velocity.
S8, assuming that the robot meets the requirement of reaching a desired angle preferentially, a speed and angular speed map (according to a kinematic model of the differential wheel type robot) transmitted to the robot actuator under the condition that the magnitude and direction of the desired speed are known can be obtained.
Figure BDA0001650966460000045
After the angular velocity and the linear velocity are mapped in the above equation in three cases, respectively, different maximum errors can be obtained for the three cases:
Figure BDA0001650966460000046
when the desired angle theta isdAfter fixation, the above formula is one with v onlydSize dependent piecewise functions. Due to epsilonmaxIs preset, and v can be obtaineddMaximum value and theta can be takendThe relationship (2) of (c).
S9. according to vdAnd thetadCan obtain a closed speed feasible region containing a nonlinear boundary, which is marked as SND. The linear simplified speed feasible region is PNDDefine velocity v relative to the obstacleOHas a relative velocity feasible region of PND-O。
S10, obtaining a new speed feasible region, and expressing the new speed selection method by using a formula as follows:
Figure BDA0001650966460000051
and S11, after the new relative speed is obtained, the speed of the robot is added to obtain the new expected speed of the robot. The new speed is transmitted as the desired speed to the actuators of the lower tier.
Figure BDA0001650966460000052
Compared with the prior art, the beneficial effects are: the scheme provides a solution for the problem that a feasible solution can not be easily generated in a scene that the robot faces a relatively high-speed obstacle. The scheme is based on an improved reciprocal velocity barrier algorithm, proposes a thought for expanding a velocity barrier region, predicts a position point which can cause no solution next time, and simultaneously maps to a current new velocity selection to expand a new velocity barrier region. After a new speed obstacle area is generated, the obtained speed feasible solution can ensure that a new speed feasible solution can still be generated in the next control period, and further the risk that the robot cannot avoid the obstacle in the obstacle avoiding process is reduced. Meanwhile, the scheme of applying the method to the wheeled mobile robot is provided.
Drawings
Fig. 1 is a diagram showing a positional relationship between an obstacle and a robot in a scene.
Fig. 2 is a schematic diagram of a region where the robot cannot escape from a speed obstacle.
Fig. 3 is an example diagram of an extended velocity barrier area.
Fig. 4 is a diagram of a kinematic model of the wheeled mobile robot.
Fig. 5 is a diagram of a velocity constraint region obtained by the wheeled mobile robot.
Fig. 6 shows a combination of wheel robot speed constraint and MVO.
Detailed Description
The drawings are for illustrative purposes only and are not to be construed as limiting the patent; for the purpose of better illustrating the embodiments, certain features of the drawings may be omitted, enlarged or reduced, and do not represent the size of an actual product; it will be understood by those skilled in the art that certain well-known structures in the drawings and descriptions thereof may be omitted. The positional relationships depicted in the drawings are for illustrative purposes only and are not to be construed as limiting the present patent.
Example 1
In order to solve the technical problems proposed above, the technical solution proposed by the present invention is:
an improved speed obstacle method expands the speed obstacle area of an original VO algorithm, and comprises the following specific implementation steps:
s1, sensing the position and the speed of a peripheral obstacle by using a robot airborne sensor, and obtaining the relative position and the relative speed of the robot and the obstacle. Because the position information and the speed information are detected by the airborne sensor, the obtained data are relative values. Meanwhile, the self speed can be obtained according to the robot onboard sensor, and the actual speed of the fault obstacle can be obtained by adding the relative speed and the self speed of the robot, as shown in fig. 1.
S2, radius of the robot A and radius of the obstacle O are defined to be r respectivelyA、rOIn the position pO|A＝pO-pA. The collision zone under the location domain is defined as:
D(pO-pA,rA+rO)＝{q|q-(pO-pA)<rA+rO}
let τ be a predefined time window (i.e., how long no collision will occur). And analyzing the current robot in a position domain through a time window coefficient tau, and converting the current robot into analysis in a speed domain. In other words, the sum of the relative position and the radius is divided by the time coefficient τ, and the sum can be converted from the position domain to the velocity domain. D (p, r) ═ { q | | | q-p | | non-woven cells<r represents a circular region with a radius r centered at p.
Figure BDA0001650966460000061
Representing the speed limit of the robot. The situation where a speed barrier with a time window cannot escape from the speed barrier can be defined as:
Figure BDA0001650966460000062
as shown in fig. 2, if the speed is always within the speed obstacle area, it will collide with the obstacle after the time window τ time.
S3, the VO speed obstacle space is expanded by the following steps. The relative speed of the robot and the obstacle is vA|O＝vA-vO. Definition of
Figure BDA0001650966460000063
Is the new relative position and relative velocity of the robot.
Figure BDA0001650966460000064
Because the time window is short, the speed and direction of the obstacle are not changed in a short time. Coordinates of the next position of the obstacle
Figure BDA0001650966460000065
The new relative position can be expressed as
Figure BDA0001650966460000066
S4, if the next control period is reached, the new relative position is adopted
Figure BDA0001650966460000067
So as to draw a new speed obstacle area
Figure BDA0001650966460000068
Comprising a speed-constrained region of the robot
Figure BDA0001650966460000069
(here, the relative position) the robot cannot escape the new velocity obstacle area. The formula can be expressed as
Figure BDA0001650966460000071
When this moment is
Figure BDA0001650966460000072
Is selected at
Figure BDA0001650966460000073
In the region, the next time τ will cause the above-mentioned situation where no feasible solution can be generated. Therefore, it is necessary to expand the original speed barrier
Figure BDA0001650966460000074
The new speed obstacle area is
Figure BDA0001650966460000075
And
Figure BDA0001650966460000076
e.g. fig. 3.
S5, selecting a new speed rule. Defining a desired relative velocity pointing to a target point of the robot as
Figure BDA0001650966460000077
The new speed selection of the robot requires escaping the extended speed obstacle area defined above.
Figure BDA0001650966460000078
S6, aiming at the wheeled mobile robot, kinematic model constraint (figure 4) exists, namely the constraint area of the speed is not a circle. It is no longer assumed that the maximum rotational speed of each wheel is
Figure BDA0001650966460000079
The advancing speed and the rotating speed of the differential wheel type robot are limited by the wheel speed. The following equation represents the maximum constraint of the linear speed and the rotational speed of the forward drive, where KsFor the conversion coefficient of the wheel rotating speed and the linear speed, different values may be obtained in different scenes:
|v(t)|≤vmax-l|ω(t)|/2
Figure BDA00016509664600000710
Figure BDA00016509664600000711
s7, due to the limit of the linear speed and the rotating speed, errors can be generated on the track when the wheeled mobile robot follows the expected speed. The idea is to control this error to be within a fixed range epsilon and thus to derive a new velocity constraint based on epsilon. According to the geometrical relationship, there are:
Figure BDA00016509664600000712
wherein v isdAnd thetadA desired speed and a desired speed bearing angle. It can be seen that the above formula is a quadratic function with respect to velocity v when v is at a stagnation point vmThe error has a minimum value.
Figure BDA0001650966460000081
Figure BDA0001650966460000082
Where T is the time to rotate to the desired angle and needs to be preset. If the T setting is too small,
Figure BDA0001650966460000083
less than omegamaxThe robot will use all wheel speeds to meet the desired angular velocity.
S8, assuming that the robot meets the requirement of reaching a desired angle preferentially, a speed and angular speed map (according to a kinematic model of the differential wheel type robot) transmitted to the robot actuator under the condition that the magnitude and direction of the desired speed are known can be obtained.
Figure BDA0001650966460000084
After the angular velocity and the linear velocity are mapped in the above equation in three cases, respectively, different maximum errors can be obtained for the three cases:
Figure BDA0001650966460000085
when the desired angle theta isdAfter fixation, the above formula is one with v onlydSize dependent piecewise functions. Due to epsilonmaxIs preset, and v can be obtaineddMaximum value and theta can be takendThe relational expression (c) of (c).
S9, obtaining a closed speed feasible region containing a nonlinear boundary according to the formula, and marking as SND. The linear simplified speed feasible region is PND(see fig. 5), defining velocity v relative to the obstacleOHas a relative velocity feasible region of PND-O. Because the speed constraint area is not changed in rotation, the speed direction can be assumed to be the positive direction of the x axis, and the constraint area is drawn and then rotated according to the current movement direction. Such as the black rectangle in fig. 5.
S10, obtaining a new speed feasible region, and expressing the new speed selection method by using a formula as follows:
Figure BDA0001650966460000091
the new speed selection method is shown in fig. 6.
And S11, after the new relative speed is obtained, the speed of the robot is added to obtain the new expected speed of the robot. The new speed is transmitted as the desired speed to the actuators of the lower tier.
Figure BDA0001650966460000092
The method provides a solution for solving the problem that a feasible solution can not be easily generated in a scene that a robot faces a relatively high-speed obstacle. The scheme is based on an improved reciprocal velocity barrier algorithm, proposes a thought for expanding a velocity barrier region, predicts a position point which can cause no solution next time, and simultaneously maps to a current new velocity selection to expand a new velocity barrier region. After a new speed obstacle area is generated, the obtained speed feasible solution can ensure that a new speed feasible solution can still be generated in the next control period, and further the risk that the robot cannot avoid the obstacle in the obstacle avoiding process is reduced. Meanwhile, the scheme of applying the method to the wheeled mobile robot is provided.
The desired speed at the current time is selected in the "next cycle not resolvable" region
Figure BDA0001650966460000093
The next time instant τ will result in a situation where no feasible solution can be generated. Extend the original speed obstacle
Figure BDA0001650966460000094
The new speed obstacle area is
Figure BDA0001650966460000095
And
Figure BDA0001650966460000096
the intersection of (a). The scheme gives an example of the extended velocity barrier solution and the new velocity barrier area after extension.
The new method is combined with a wheel type mobile robot model, and a scheme for applying the new method to the wheel type mobile robot is provided.
It should be understood that the above-described embodiments of the present invention are merely examples for clearly illustrating the present invention, and are not intended to limit the embodiments of the present invention. Other variations and modifications will be apparent to persons skilled in the art in light of the above description. And are neither required nor exhaustive of all embodiments. Any modification, equivalent replacement, and improvement made within the spirit and principle of the present invention should be included in the protection scope of the claims of the present invention.

Claims (1)

1. A method of a robot for evading a relatively high speed obstacle, comprising the steps of:
s1, sensing the position and the speed of a peripheral obstacle by using a robot airborne sensor, and obtaining the relative position and the relative speed of the robot and the obstacle; because the position information and the speed information are detected by the airborne sensor, the obtained data are relative values; meanwhile, the self speed can be obtained according to the robot onboard sensor, and the actual speed of the fault obstacle can be obtained by adding the relative speed and the self speed of the robot;
s2, radius of the robot A and radius of the obstacle O are defined to be r respectivelyA、rOIn the position pO|A＝pO-pA(ii) a The collision zone under the location domain is defined as:
D(pO-pA,rA+rO)＝{q|q-(pO-pA)<rA+rO}
defining tau as a predefined time window coefficient; analyzing the current robot in a position domain through a time window coefficient tau, and converting the current robot into analysis in a speed domain; in other words, the sum of the relative position and the radius is divided by the time window coefficient τ respectively, so that the sum can be converted from the position domain to the representation in the speed domain; d (p, r) ═ { q | | | q-p | | non-woven cells<r, representing a circular domain with p as the center and r as the radius; d (0, v)A max) Represents a speed limit of the robot; the speed barrier with time window may be defined as:
Figure FDA0003022985120000011
s3, expanding the space of the speed obstacle; the relative speed of the robot and the obstacle is vA|O＝vA-vO(ii) a Definition of
Figure FDA0003022985120000012
Is the new relative position and relative velocity of the robot;
Figure FDA0003022985120000013
the time window is short, so that the speed and the direction of the obstacle are not changed in a short time; coordinates of the next position of the obstacle
Figure FDA0003022985120000014
The new relative position can be expressed as
Figure FDA0003022985120000015
S4, if the next control period is reached, the new relative position is adopted
Figure FDA0003022985120000016
So as to draw a new speed obstacle area
Figure FDA0003022985120000017
Comprising a speed-constrained region of the robot
Figure FDA0003022985120000018
The robot cannot escape from the new speed obstacle area; the formula can be expressed as
Figure FDA0003022985120000021
When this moment is
Figure FDA0003022985120000022
Is selected at
Figure FDA0003022985120000023
In the region, the next τ will cause the above formula to fail to produce a feasible solution; therefore, it is necessary to expand the original speed barrier
Figure FDA0003022985120000024
The new speed obstacle area is
Figure FDA0003022985120000025
And
Figure FDA0003022985120000026
the intersection of (a);
s5, selecting a new speed rule; defining a desired relative velocity pointing to a target point of the robot as
Figure FDA0003022985120000027
The new speed selection of the robot needs to escape from the defined expanded speed obstacle area;
Figure FDA0003022985120000028
s6, aiming at the wheeled mobile robot, kinematic model constraint exists, namely a constraint area of the speed is not a circle; assuming a maximum rotational speed of each wheel of
Figure FDA0003022985120000029
The advancing speed and the rotating speed of the differential wheel type robot are limited by the wheel speed; the following equation represents the maximum constraint of the linear speed and the rotational speed of the forward drive, where KsThe conversion coefficient of the wheel rotating speed and the linear speed is different in value in different scenes;
|v(t)|≤vmax-l|ω(t)|/2
Figure FDA00030229851200000210
Figure FDA00030229851200000211
s7, due to the limitation of the linear speed and the rotating speed, errors can be generated on the track when the wheeled mobile robot follows the expected speed; controlling the error to be within a fixed range epsilon, so as to obtain a new speed constraint according to epsilon; according to the geometrical relationship, there are:
Figure FDA00030229851200000212
wherein v isdAnd thetadA desired speed and a desired speed bearing angle; it can be seen that the above formula is a quadratic function with respect to velocity v when v is at a stagnation point vmWhen, the error has a minimum value;
Figure FDA0003022985120000031
Figure FDA0003022985120000032
wherein T is the time for rotating to a desired angle and needs to be preset; if the T setting is too small,
Figure FDA0003022985120000033
less than omegamaxThe robot will use all wheel speeds to meet the desired angular velocity;
s8, assuming that the robot meets the requirement of reaching the expected angle preferentially, the speed and angular speed mapping transmitted to the robot actuator under the condition that the expected speed and the expected speed direction are known can be obtained;
Figure FDA0003022985120000034
after the angular velocity and the linear velocity are mapped in the above equation in three cases, respectively, different maximum errors can be obtained for the three cases:
Figure FDA0003022985120000035
when the desired angle theta isdAfter fixation, the above formula is one with v onlydA size dependent piecewise function; due to epsilonmaxIs preset, and v can be obtaineddMaximum value and theta can be takendThe relationship of (1);
s9. according to vdAnd thetadCan obtain a closed speed feasible region containing a nonlinear boundary, which is marked as SND(ii) a The linear simplified speed feasible region is PNDDefine velocity v relative to the obstacleOHas a relative velocity feasible region of PND-O；
S10, obtaining a new speed feasible region, and expressing the new speed selection method by using a formula as follows:
Figure FDA0003022985120000041
s11, after obtaining the new relative speed, adding the speed of the robot to obtain a new expected speed of the robot; the new speed is transmitted to the actuator at the lower layer as the expected speed;
Figure FDA0003022985120000042
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