CN111583644B - Control method for network connection automatic vehicle of ramp convergence area on hybrid traffic express way - Google Patents

Control method for network connection automatic vehicle of ramp convergence area on hybrid traffic express way Download PDF

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CN111583644B
CN111583644B CN202010383230.6A CN202010383230A CN111583644B CN 111583644 B CN111583644 B CN 111583644B CN 202010383230 A CN202010383230 A CN 202010383230A CN 111583644 B CN111583644 B CN 111583644B
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CN111583644A (en
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孙棣华
刘忠诚
赵敏
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Chongqing University
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    • G—PHYSICS
    • G08—SIGNALLING
    • G08G—TRAFFIC CONTROL SYSTEMS
    • G08G1/00—Traffic control systems for road vehicles
    • G08G1/01—Detecting movement of traffic to be counted or controlled
    • G08G1/0104—Measuring and analyzing of parameters relative to traffic conditions
    • G08G1/0108—Measuring and analyzing of parameters relative to traffic conditions based on the source of data
    • G08G1/0116—Measuring and analyzing of parameters relative to traffic conditions based on the source of data from roadside infrastructure, e.g. beacons
    • G—PHYSICS
    • G08—SIGNALLING
    • G08G—TRAFFIC CONTROL SYSTEMS
    • G08G1/00—Traffic control systems for road vehicles
    • G08G1/01—Detecting movement of traffic to be counted or controlled
    • G08G1/0104—Measuring and analyzing of parameters relative to traffic conditions
    • G08G1/0125—Traffic data processing
    • G—PHYSICS
    • G08—SIGNALLING
    • G08G—TRAFFIC CONTROL SYSTEMS
    • G08G1/00—Traffic control systems for road vehicles
    • G08G1/01—Detecting movement of traffic to be counted or controlled
    • G08G1/0104—Measuring and analyzing of parameters relative to traffic conditions
    • G08G1/0137—Measuring and analyzing of parameters relative to traffic conditions for specific applications
    • G—PHYSICS
    • G08—SIGNALLING
    • G08G—TRAFFIC CONTROL SYSTEMS
    • G08G1/00—Traffic control systems for road vehicles
    • G08G1/01—Detecting movement of traffic to be counted or controlled
    • G08G1/052—Detecting movement of traffic to be counted or controlled with provision for determining speed or overspeed
    • G—PHYSICS
    • G08—SIGNALLING
    • G08G—TRAFFIC CONTROL SYSTEMS
    • G08G1/00—Traffic control systems for road vehicles
    • G08G1/09—Arrangements for giving variable traffic instructions
    • G08G1/0962—Arrangements for giving variable traffic instructions having an indicator mounted inside the vehicle, e.g. giving voice messages
    • G08G1/0967—Systems involving transmission of highway information, e.g. weather, speed limits
    • G08G1/096708—Systems involving transmission of highway information, e.g. weather, speed limits where the received information might be used to generate an automatic action on the vehicle control
    • G—PHYSICS
    • G08—SIGNALLING
    • G08G—TRAFFIC CONTROL SYSTEMS
    • G08G1/00—Traffic control systems for road vehicles
    • G08G1/09—Arrangements for giving variable traffic instructions
    • G08G1/0962—Arrangements for giving variable traffic instructions having an indicator mounted inside the vehicle, e.g. giving voice messages
    • G08G1/0967—Systems involving transmission of highway information, e.g. weather, speed limits
    • G08G1/096766—Systems involving transmission of highway information, e.g. weather, speed limits where the system is characterised by the origin of the information transmission
    • G08G1/096783—Systems involving transmission of highway information, e.g. weather, speed limits where the system is characterised by the origin of the information transmission where the origin of the information is a roadside individual element
    • G—PHYSICS
    • G08—SIGNALLING
    • G08G—TRAFFIC CONTROL SYSTEMS
    • G08G1/00—Traffic control systems for road vehicles
    • G08G1/16—Anti-collision systems
    • G08G1/166—Anti-collision systems for active traffic, e.g. moving vehicles, pedestrians, bikes
    • G—PHYSICS
    • G08—SIGNALLING
    • G08G—TRAFFIC CONTROL SYSTEMS
    • G08G1/00—Traffic control systems for road vehicles
    • G08G1/16—Anti-collision systems
    • G08G1/167—Driving aids for lane monitoring, lane changing, e.g. blind spot detection

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Abstract

The invention discloses a method for controlling a network-connected automatic vehicle of a ramp converging area on a hybrid traffic expressway, which comprises the following steps of: the method comprises the steps of dividing road sections near a ramp into a control area and a sensing area, constructing a vehicle kinematics model, distributing numbers for vehicles in all the sensing areas, and realizing an event-triggered switching control mechanism according to different algorithms. The invention comprehensively considers all vehicle information in the sensing area, thereby providing comprehensive data information for the convergence control of the network automatic vehicle ramps, adopting an event-triggered switching control mechanism to control the convergence of the network automatic vehicle, adopting different control strategies according to the position and the speed of each network automatic vehicle, ensuring the safety and improving the traffic efficiency.

Description

Control method for network connection automatic vehicle of ramp convergence area on hybrid traffic express way
Technical Field
The invention belongs to the field of intelligent automobile motion control, and particularly relates to a method for controlling a network-connected automatic automobile on a ramp converging area on a hybrid traffic expressway.
Background
At present, vehicles with unmanned functions are sold in the market, and some vehicles are provided with advanced driving assistance systems (ADA step), and the systems can realize self-adaptive auxiliary driving under certain working conditions by using self safety assistance sensors of the vehicles, including videos, microwaves, millimeter waves, laser radars and the like. However, due to technical development and legal restrictions, hybrid traffic consisting of networked autopilot and traditional human drive will be the main form of future traffic for some time in the future.
In hybrid traffic, the efficiency of the control method for the ramp junction of the automatic driving vehicle under ideal conditions is reduced, and even negative effects can be brought to the traffic. For this reason, it is necessary to design a new merge area control method for the internet-connected autonomous vehicle in the hybrid traffic.
Disclosure of Invention
In view of the above, the present invention provides a method for controlling a networked automatic vehicle on a ramp junction area on a hybrid traffic expressway, so as to optimize the traffic condition of the ramp on the expressway when the occupancy of the networked automatic vehicle is not high. The method improves the control effect and improves the traffic capacity by introducing an event trigger switching control mechanism on the basis of the original strategy. The purpose of the invention is realized by the following technical scheme:
step 1: dividing a ramp confluence area on an express way and an extension 300-plus 400-meter road section thereof into two circular areas by taking the center point of the confluence area as the center of a circle: the range of the sensing area is larger than that of the control area; wherein, a sensing device is arranged at one side of a road in the sensing area, and the control area is an area for triggering switching control by an application event of the networked automatic driving vehicle;
step 2: constructing a vehicle kinematic model as a reference model;
and step 3: detecting the positions and the speeds of all vehicles in a sensing area every 0.1-0.8 second by using roadside sensing equipment, sequentially distributing a control number to the vehicles from small to large according to the distance from each vehicle to a confluence area, and mapping the control numbers to a virtual vehicle fleet according to the distance from each vehicle to the confluence area;
and 4, step 4: judging whether the current control number of the networked automatic driving vehicle in the traffic is 1, if so, turning to a step 8, and otherwise, turning to a step 5;
and 5: judging whether a front vehicle exists in the same lane by the network connection automatic driving vehicle in traffic, if not, turning to the step 6, otherwise, turning to the step 7;
step 6: judging whether the network connection automatic driving vehicle in traffic can reach a convergence area before the vehicle in the virtual lane, if so, turning to a step 8, otherwise, turning to a step 10;
and 7: judging whether a safe distance is kept between the networked automatic driving vehicle and a front vehicle in the same lane or not by the networked automatic driving vehicle in traffic, if so, turning to a step 9, and otherwise, turning to a step 10;
and 8: and (3) applying a vehicle automatic control algorithm I by the internet automatic driving vehicle according to the data acquired in the step 3:
un(t)＝ant+bn
wherein u isn(t) is the input of the nth vehicle at time t, an,bnThe following matrix equation is satisfied:
Figure GDA0003311519930000021
in the above formula:
sn(t) is the position of the nth vehicle at time t;
vn(t) is the speed of the nth vehicle at time t;
Figure GDA0003311519930000022
for the nth vehicle at the moment
Figure GDA0003311519930000023
The expected position is usually taken as the starting point or the end point of the confluence area;
Figure GDA0003311519930000024
for the nth vehicle at the moment
Figure GDA0003311519930000025
The expected speed is usually taken as the lowest speed limit of the current road;
Figure GDA0003311519930000026
calculating the time when the nth vehicle enters the convergence region by dividing the distance from the current vehicle to the entrance of the convergence region by the current vehicle speed;
and step 9: and the networked automatic driving vehicle applies a vehicle automatic control algorithm II according to the collected data:
Figure GDA0003311519930000027
Figure GDA0003311519930000028
wherein: a isn(t) is the acceleration of the nth vehicle at time t, and is also the input of the nth vehicle at time t; v. ofn(t) the speed of the nth vehicle at the time t; Δ vn(t)＝vn-1(t)-vn(t) is the relative speed of the nth-1 vehicle and the nth vehicle at the time t; v. ofmaxIs the maximum vehicle speed; sn(t)＝pn-1(t)-pn(t) is the inter-vehicle distance between the nth vehicle and the (n-1) th vehicle at time t, pn(t) is the position of the nth vehicle at time t; a is 1m/s2，b＝2m/s2TT is 1.1s, theta is an integer of 1-4, s0Taking a nonnegative number in the range of 0-10;
Figure GDA0003311519930000031
when the velocity is vn(t) velocity difference Δ vn(t) a desired inter-vehicle distance for the nth vehicle;
step 10: and the networked automatic driving vehicle applies a vehicle automatic control algorithm III according to the collected data:
Figure GDA0003311519930000032
wherein
Figure GDA0003311519930000033
The acceleration obtained after the vehicle automatic control algorithm II is applied; p is a radical ofn(t) is the position of the nth vehicle at time t; a isn(t) is the acceleration of the nth vehicle at time t, and is also the input of the nth vehicle at time t; f (p)n) In the interval (L)0,S0) Is monotonically decreased and 0 ≦ f (p)n) 1 or less, wherein L0As a starting point of the control zone, S0Is the starting point of the confluence area.
Further, the vehicle kinematic model expression in step 2 is:
Figure GDA0003311519930000034
wherein:
Figure GDA0003311519930000035
yn＝[pn,vn]T，un＝anis an acceleration input; p is a radical ofnIs the position of the nth vehicle; v. ofnThe speed of the nth vehicle; τ (t) is the input delay of the vehicle.
Further, f (p) in the step 10n) The expression of (a) is:
Figure GDA0003311519930000036
wherein, omega is a relaxation coefficient and is a certain value between 0.1 and 4 according to actual requirements.
Further, f (p) in the step 10n) The expression of (a) is:
Figure GDA0003311519930000037
wherein, omega is a relaxation coefficient and is a certain value between 0.1 and 4 according to actual requirements.
Due to the adoption of the technical scheme, the invention has the following beneficial effects:
the control method of the networked automatic vehicle comprehensively considers all vehicle information in the sensing area, thereby providing comprehensive data information for controlling the convergence of the networked automatic vehicle ramps and laying a data foundation for improving the safety and the traffic efficiency of the vehicle; the invention adopts an event-triggered switching control mechanism to control the confluence of the networked automatic vehicles, and adopts different control strategies according to the position and the speed of each networked automatic vehicle, thereby not only ensuring the safety, but also improving the traffic efficiency.
Additional advantages, objects, and features of the invention will be set forth in part in the description which follows and in part will become apparent to those having ordinary skill in the art upon examination of the following or may be learned from practice of the invention. The objectives and other advantages of the invention may be realized and attained by the means of the instrumentalities and combinations particularly pointed out hereinafter.
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In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention will be further described in detail with reference to the accompanying drawings:
FIG. 1 is a schematic diagram of an embodiment;
FIG. 2 is a control number assignment flow diagram;
FIG. 3 is a flow chart of event triggered handover control dynamic control.
Detailed Description
The present invention will be further described with reference to the following examples.
Example 1
As shown in fig. 1-3, a method for controlling a network-connected automatic vehicle in a ramp converging area on a hybrid traffic expressway comprises the following steps:
step 1: dividing a ramp confluence area on an express way and an extended 400-meter road section thereof into two circular areas by taking a central point of the confluence area as a circle center: the range of the sensing area is larger than that of the control area; wherein, a sensing device is arranged at one side of a road in the sensing area, and the control area is an area for triggering switching control by an application event of the networked automatic driving vehicle;
step 2: constructing a vehicle kinematic model as a reference model;
and step 3: detecting the positions and speeds of all vehicles in a sensing area every 0.1s by using road side sensing equipment, sequentially distributing a control number to the vehicles from small to large according to the distance from each vehicle to a confluence area, and mapping the control numbers to a virtual vehicle fleet according to the distance from each vehicle to the confluence area;
and 4, step 4: judging whether the current control number of the networked automatic driving vehicle in the traffic is 1, if so, turning to a step 8, and otherwise, turning to a step 5;
and 5: judging whether a front vehicle exists in the same lane by the network connection automatic driving vehicle in traffic, if not, turning to the step 6, otherwise, turning to the step 7;
step 6: judging whether the network connection automatic driving vehicle in traffic can reach a convergence area before the vehicle in the virtual lane, if so, turning to a step 8, otherwise, turning to a step 10;
and 7: judging whether a safe distance is kept between the networked automatic driving vehicle and a front vehicle in the same lane or not by the networked automatic driving vehicle in traffic, if so, turning to a step 9, and otherwise, turning to a step 10;
and 8: and (3) applying a vehicle automatic control algorithm I by the internet automatic driving vehicle according to the data acquired in the step 3:
un(t)＝ant+bn
wherein a isn,bnSatisfies the following conditions:
Figure GDA0003311519930000051
wherein:
Figure GDA0003311519930000052
the time when the nth vehicle enters the confluence area is taken as the time;
tfthe calculation method is that the distance from the current vehicle to the entrance of the confluence area is divided by the current vehicle speed;
and step 9: the networked automatic driving vehicle applies an IDM algorithm according to the collected data:
Figure GDA0003311519930000053
Figure GDA0003311519930000054
wherein: v. ofn(t) the speed of the nth vehicle at the time t; Δ vn(t)＝vn-1(t)-vn(t) is the relative speed of the nth-1 vehicle and the nth vehicle at the time t; v. ofmax120km/h is the maximum vehicle speed; sn(t)＝pn-1(t)-pn(t) the inter-vehicle distance, p, between the nth vehicle and the (n-1) th vehicle at time tn(t) is the position of the nth vehicle at time t; a is 1m/s2，b＝2m/s2，TT＝1.1s，θ＝4，s0＝0m；
And step 9: and the networked automatic driving vehicle applies a vehicle automatic control algorithm III according to the collected data:
Figure GDA0003311519930000061
wherein
Figure GDA0003311519930000062
The acceleration obtained after the vehicle automatic control algorithm II is applied; p is a radical ofn(t) is the position of the nth vehicle at time t; a isn(t) is the acceleration of the nth vehicle at time t, and is also the input of the nth vehicle at time t; f (p)n) In the interval (L)0,S0) Is monotonically decreased and 0 ≦ f (p)n) 1 or less, wherein L0As a starting point of the control zone, S0Is the starting point of the confluence area.
The vehicle kinematic model expression in the step 2 is as follows:
Figure GDA0003311519930000063
wherein:
Figure GDA0003311519930000064
wherein: y isn＝[pn,vn]T，un＝anIs an acceleration input; p is a radical ofnIs the position of the nth vehicle; v. ofnThe speed of the nth vehicle; τ (t) is the input delay of the vehicle.
F (p) in said step 9n) The expression of (a) is:
Figure GDA0003311519930000065
where ω is a relaxation coefficient, and is usually a value between 0.1 and 4 according to actual needs.
Example 2
The method for controlling the networked automatic vehicle for the ramp converging area on the hybrid traffic express way comprises the following steps of:
step 1: dividing a junction area of a ramp on an express way and an extended 300-meter road section of the junction area into two circular areas by taking a center point of the junction area as a circle center: the range of the sensing area is larger than that of the control area; wherein, a sensing device is arranged at one side of a road in the sensing area, and the control area is an area for triggering switching control by an application event of the networked automatic driving vehicle;
step 2: constructing a vehicle kinematic model as a reference model;
and step 3: detecting the positions and speeds of all vehicles in a sensing area every 0.8s by using road side sensing equipment, sequentially distributing a control number to the vehicles from small to large according to the distance from each vehicle to a confluence area, and mapping the control numbers to a virtual vehicle fleet according to the distance from each vehicle to the confluence area;
and 4, step 4: judging whether the current control number of the networked automatic driving vehicle in the traffic is 1, if so, turning to a step 8, and otherwise, turning to a step 5;
and 5: judging whether a front vehicle exists in the same lane by the network connection automatic driving vehicle in traffic, if not, turning to the step 6, otherwise, turning to the step 7;
step 6: judging whether the network connection automatic driving vehicle in traffic can reach a convergence area before the vehicle in the virtual lane, if so, turning to a step 8, otherwise, turning to a step 10;
and 7: judging whether a safe distance is kept between the networked automatic driving vehicle and a front vehicle in the same lane or not by the networked automatic driving vehicle in traffic, if so, turning to a step 9, and otherwise, turning to a step 10;
and 8: and (3) applying a vehicle automatic control algorithm I by the internet automatic driving vehicle according to the data acquired in the step 3:
un(t)＝ant+bn
wherein a isn,bnSatisfies the following conditions:
Figure GDA0003311519930000071
wherein:
Figure GDA0003311519930000072
the time when the ith vehicle enters the confluence area is taken as the time;
tfthe calculation method is that the distance from the current vehicle to the entrance of the confluence area is divided by the current vehicle speed;
and step 9: the networked automatic driving vehicle applies an IDM algorithm according to the collected data:
Figure GDA0003311519930000073
Figure GDA0003311519930000081
wherein: v. ofn(t) the speed of the nth vehicle at the time t; Δ vn(t)＝vn-1(t)-vn(t) is the relative speed of the nth-1 vehicle and the nth vehicle at the time t; v. ofmax120km/h is the maximum vehicle speed; sn(t)＝pn-1(t)-pn(t) the inter-vehicle distance, p, between the nth vehicle and the (n-1) th vehicle at time tn(t) is the position of the nth vehicle at time t; a is 1m/s2，b＝2m/s2，TT＝1.1s，θ＝4，s0＝0m；
And step 9: and the networked automatic driving vehicle applies a vehicle automatic control algorithm III according to the collected data:
Figure GDA0003311519930000082
wherein
Figure GDA0003311519930000083
Acceleration obtained after application of the vehicle automatic control algorithm II, f (p)n) In the open interval (L)0,S0) Is monotonically decreased and 0 ≦ f (p)n)≤1。
The vehicle kinematic model expression in the step 2 is as follows:
Figure GDA0003311519930000084
wherein:
Figure GDA0003311519930000085
wherein: y isn＝[pn,vn]T，un＝anIs an acceleration input; p is a radical ofnIs the position of the nth vehicle; v. ofnThe speed of the nth vehicle.
F (p) in said step 9n) The expression of (a) is:
Figure GDA0003311519930000086
where ω is a relaxation coefficient, and is usually a value between 0.1 and 4 according to actual needs.
Finally, the above embodiments are only for illustrating the technical solutions of the present invention and not for limiting, although the present invention has been described in detail with reference to the preferred embodiments, it should be understood by those skilled in the art that modifications or equivalent substitutions may be made on the technical solutions of the present invention without departing from the spirit and scope of the technical solutions, and all of them should be covered in the protection scope of the present invention.

Claims (4)

1. A control method for a network connection automatic vehicle of a ramp converging area on a hybrid traffic expressway is characterized by comprising the following steps:
step 1: dividing a ramp confluence area on an express way and an extension 300-plus 400-meter road section thereof into two circular areas by taking the center point of the confluence area as the center of a circle: the range of the sensing area is larger than that of the control area; wherein, a sensing device is arranged at one side of a road in the sensing area, and the control area is an area for triggering switching control by an application event of the networked automatic driving vehicle;
step 2: constructing a vehicle kinematic model as a reference model;
and step 3: detecting the positions and the speeds of all vehicles in a sensing area every 0.1-0.8 second by using roadside sensing equipment, sequentially distributing a control number to the vehicles from small to large according to the distance from each vehicle to a confluence area, and mapping the control numbers to a virtual vehicle fleet according to the distance from each vehicle to the confluence area;
and 4, step 4: judging whether the current control number of the networked automatic driving vehicle in the traffic is 1, if so, turning to a step 8, and otherwise, turning to a step 5;
and 5: judging whether a front vehicle exists in the same lane by the network connection automatic driving vehicle in traffic, if not, turning to the step 6, otherwise, turning to the step 7;
step 6: judging whether the network connection automatic driving vehicle in traffic can reach a convergence area before the vehicle in the virtual lane, if so, turning to a step 8, otherwise, turning to a step 10;
and 7: judging whether a safe distance is kept between the networked automatic driving vehicle and a front vehicle in the same lane or not by the networked automatic driving vehicle in traffic, if so, turning to a step 9, and otherwise, turning to a step 10;
and 8: and (3) applying a vehicle automatic control algorithm I by the internet automatic driving vehicle according to the data acquired in the step 3:
un(t)＝ant+bn
wherein u isn(t) is the input of the nth vehicle at time t, an,bnThe following matrix equation is satisfied:
Figure FDA0003311519920000011
in the above formula:
sn(t) is the position of the nth vehicle at time t;
vn(t) is the speed of the nth vehicle at time t;
Figure FDA0003311519920000021
for the nth vehicle at the moment
Figure FDA0003311519920000022
The expected position is usually taken as the starting point or the end point of the confluence area;
Figure FDA0003311519920000023
for the nth vehicle at the moment
Figure FDA0003311519920000024
The expected speed is usually taken as the lowest speed limit of the current road;
Figure FDA0003311519920000025
calculating the time when the nth vehicle enters the convergence region by dividing the distance from the current vehicle to the entrance of the convergence region by the current vehicle speed;
and step 9: and the networked automatic driving vehicle applies a vehicle automatic control algorithm II according to the collected data:
Figure FDA0003311519920000026
Figure FDA0003311519920000027
wherein: a isn(t) is the acceleration of the nth vehicle at time t, and is also the input of the nth vehicle at time t; v. ofn(t) the speed of the nth vehicle at the time t; Δ vn(t)＝vn-1(t)-vn(t) is the relative speed of the nth-1 vehicle and the nth vehicle at the time t; v. ofmaxIs the maximum vehicle speed; sn(t)＝pn-1(t)-pn(t) is the inter-vehicle distance between the nth vehicle and the (n-1) th vehicle at time t, pn(t) is the position of the nth vehicle at time t; a is 1m/s2，b＝2m/s2TT is 1.1s, theta is an integer of 1-4, s0Taking a nonnegative number in the range of 0-10;
Figure FDA0003311519920000028
when the velocity is vn(t) velocity difference Δ vn(t) a desired inter-vehicle distance for the nth vehicle;
step 10: and the networked automatic driving vehicle applies a vehicle automatic control algorithm III according to the collected data:
Figure FDA0003311519920000029
wherein
Figure FDA00033115199200000210
The acceleration obtained after the vehicle automatic control algorithm II is applied; p is a radical ofn(t) is the position of the nth vehicle at time t; a isn(t) is the acceleration of the nth vehicle at time t, and is also the input of the nth vehicle at time t; f (p)n) In the interval (L)0,S0) Is monotonically decreased and 0 ≦ f (p)n) 1 or less, wherein L0As a starting point of the control zone, S0Is the starting point of the confluence area.
2. The method for controlling the networked automatic vehicle for the junction area of the ramp on the hybrid traffic express way according to claim 1, wherein the method comprises the following steps: the vehicle kinematic model expression in the step 2 is as follows:
Figure FDA0003311519920000031
wherein:
Figure FDA0003311519920000032
yn＝[pn,vn]T，un＝anis an acceleration input; p is a radical ofnIs the position of the nth vehicle; v. ofnThe speed of the nth vehicle; τ (t) is the input delay of the vehicle.
3. Root of herbaceous plantThe method for controlling the networked automatic vehicle for the junction area of the ramp on the hybrid traffic express way according to claim 1, wherein the method comprises the following steps: f (p) in said step 10n) The expression of (a) is:
Figure FDA0003311519920000033
wherein, omega is a relaxation coefficient and is a certain value between 0.1 and 4 according to actual requirements.
4. The method for controlling the networked automatic vehicle for the junction area of the ramp on the hybrid traffic express way according to claim 1, wherein the method comprises the following steps: f (p) in said step 10n) The expression of (a) is:
Figure FDA0003311519920000034
wherein, omega is a relaxation coefficient and is a certain value between 0.1 and 4 according to actual requirements.
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