Gyrodometry a new method for combining data from gyros and odometry in mobile robots
Proceedings of the 1996 IEEE International Conference on Robotics and Automation, Minneapolis, Apr. 22-28, 1996, pp. 423-428. Gyrodometry: A New Method for Combining Data from Gyros and Odometry in Mobile Robots
by
J. Borenstein and L. Feng
The University of Michigan
Advanced Technologies Lab, 1101 Beal Ave.
Ann Arbor, MI 48109-2110
Email: johannb@https://www.wendangku.net/doc/4a18097097.html, and Feng@https://www.wendangku.net/doc/4a18097097.html,
A BSTRACT
This paper presents a very simple, yet very effec-tive method for combining measurements from a gyro with measurements from wheel encoders (odometry). Sensor-fusion of this kind has been done before, usu-ally by means of a statistical model that describes the behavior of the gyro and the behavior of the odometry component. However, because these systems are based on models, they cannot anticipate the unpredictable and potentially "catastrophic" effect of larger bumps or objects occasionally encountered on the floor.
By contrast, our method, called Gyrodometry, has been developed based on a careful study of the physical interaction between the ground and the vehicle. We present experimental evidence that non-systematic odometry error sources (such as bumps) impact the vehicle only during very short periods; typically a fraction of a second for each encounter. During these short instances the readings from the gyro and from odometry differ significantly, while in the absence of large non-systematic errors the readings are very similar. Gyrodometry makes use of this observation by using odometry data only C most of the time, while substituting gyro data only during those brief instances during which gyro and odometry data differ substan-tially. This way the ill-effects of gyro drift are almost completely eliminated, and our method can thus make use of inexpensive gyros with large drift rates. Ex-perimental data is presented that demonstrates the effectiveness of this approach.1. I NTRODUCTION A ND B ACKGROUND
In most mobile robot applications two basic posi-tion-estimation methods are employed together: abso-lute and relative positioning [Byrne et al., 1992; Chenavier and Crowley, 1992; Evans, 1994]. Absolute positioning methods usually rely on navigation bea-cons, active or passive landmarks, map matching, or satellite-based navigation signals. Each of these abso-lute positioning approaches can be implemented by a variety of methods and sensors. Yet, none of the cur-rently existing systems is particularly elegant, and usually these systems are somewhat expensive. A comprehensive survey on mobile robot positioning methods is given in [Borenstein et al., 1995].
Relative positioning is usually based on odometry. Odometry is simple, inexpensive, and easy to accom-plish in real-time. The disadvantage of odometry is its unbounded accumulation of errors.
With the introduction of optical fiber gyros the use of gyros has become more attractive for mobile robot applications. However, gyros have relatively large drift rates, which cause unbounded growth in orientation errors.
Because of their potential for unbounded growth of errors, odometry and gyros can only be used in con-junction with periodic absolute position updates. Nonetheless, improving odometry and gyro accuracy helps increase the travel distance in-between absolute position updates, and thus results in lower installation and operating costs for the whole system.
1.1 Properties of odometry errors
In this section we discuss properties of odometry as they relate to differential-drive vehicles (i.e., vehicles that have two independently driven wheels). Optical encoders are typically mounted on the drive motors to count the wheel revolutions. Using simple geometric equations, it is straight-forward to compute the mo-mentary position of the vehicle relative to a known starting position. This computation is called odometry. It is important to note that when considering errors in odometry, orientation errors are the main source of concern. This is so because once incurred, orientation errors grow without bound into lateral position errors [Feng et al., 1993].
Odometry is based on the assumption that wheel revolutions can be translated into linear displacement relative to the floor. This assumption is only of limited validity. One extreme example is wheel slippage: if one wheel was to slip on, say, an oil spill, then the associated encoder would register wheel revolutions even though these revolutions would not correspond to a linear displacement of the wheel.
Besides this extreme case of total slippage, there are several other, more subtle reasons for inaccuracies in the translation of wheel encoder readings into linear motion. All of these error sources fit into one of two categories: (1) systematic errors and (2) non-systematic errors.
1. Systematic errors
a.Unequal wheel diameters
b.Average of both wheel diameters differs from
nominal diameter
c.Misalignment of wheels
d.Uncertainty about the effective wheelbase (due to
non-point wheel contact with the floor)
e.Limited encoder resolution
f.Limited encoder sampling rate
2. Non-systematic errors
a.Travel over uneven floors
b.Travel over unexpected objects on the floor
c.Wheel-slippage
In recent work we introduced "UMBmark," a method for measuring and correcting systematic odometry errors in differential-drive mobile robots [Borenstein and Feng, 1995a; 1995b]. With this method we were able to reduce the systematic odome-try error of an uncalibrated LabMate robot [TRC] by one order of magnitude. However, this measure alone cannot guarantee trouble-free odometry, because occa-sional bumps, cracks or other large disturbances can cause unpredictable "catastrophic" odometry errors that can easily lead to the complete failure of the ro-bot's mission. The method presented in this paper is designed to detect and correct such "catastrophic" non-systematic odometry errors.
1.2 The use of gyros in mobile robot applica-tions
An extensive study of the use of gyroscopes in mo-bile robots was conducted by [Barshan and Durrant-Whyte, 1995]. One of the tested instruments was the ENV-O5S Gyrostar from [MURATA] and the other was the Solid State Angular Rate Transducer (START) gyroscope manufactured by [GEC]. Barshan and Dur-rant-Whyte evaluated the performance of these two gyros and found that they suffered relatively large drift, on the order of 5 to 15E/min. The Oxford re-searchers then developed a sophisticated error model for the gyros, which was subsequently used in an Ex-tended Kalman Filter (EKF). At the end of a 5-minute experiment, the START had accumulated a heading error of -70.8E while the error of the Gyrostar was -59E. With the EKF, the accumulated errors were much smaller: 12E was the maximum heading error for the START gyro, while that of the Gyrostar was -
3.8E. Overall, the results from applying the EKF show
a 5 to 6-fold reduction in the angular measurement after a five-minute test period. However, even with the EKF, a drift rate of 1 to 3o/min can still be expected.
Komoriya and Oyama [1994] conducted a study of a system that used the OFG-3 [HITACHI] optical fiber gyroscope in conjunction with odometry information. This fusion of information from these two different sensor systems was realized through a Kalman Filter. Komoriya and Oyama tested their method in actual experiments with a mobile robot. In one set of experi-ments their robot was instructed to follow a triangular path of 5 m total length. The robot's maximum speed was 0.14 m/s and that speed was further reduced at the corners of the path. The results of this experiment in-dicate an average position error of about 5 mm. How-ever, it is not immediately evident how this error was found. We interpret the quoted results as showing a position error that was computed by the onboard com-puter, but not measured absolutely.
In both of the above studies a Kalman Filter ap-proach was taken to reduce the drift and to fuse odometry and gyro data. Kalman filters require a de-tailed model of the sensors and the interaction between the wheels and the floor (i.e., odometry). To model
odometry researchers typically define "error ellipsis"that describe the probability of the robot to be indeed at the location its odometry has determined. These models are usually based on the robot's systematic er-rors, but they cannot take into account non-systematic errors and especially "catastrophic" events like the encounter of a bump, crack, or other irregularity of the floor.
To overcome this problem, we took a different ap-proach. We studied the physical interaction between the floor and the wheels during "catastrophic" events.We present relevant results of this study in Section 2.Based on these results we developed Gyrodometry , a method for improving odometric accuracy with gyros regardless of the gyro's drift rate (see Section 3). Sec-tion 4 presents initial experimental results from im-plementing Gyrodometry on a LabMate robot.In the experiments described in the following sec-tions we used the Murata Gyrostar [Murata] model ENV-05H (see Fig. 1). The Gyrostar is a piezoelectric vibrating gyroscope with analog voltage output that varies linearly with the measured rate of rotation. con-nection to a computer. The drift rate we measured in practice was 3 to 15E /min (similar to the drift ob-served by [Barshan and Durrant-Whyte, 1995] for their Gyrostar sensor). We will assume an average drift rate of 10E /min = 0.166E /s. A detailed discussion of gyroscopes for mobile robot applications is given in [Borenstein et al., 1996].
2. A NALYSIS
When the left wheel (W L ) of a differential-drive ro-bot like the LabMate travels over a bump (or crack, or other irregularity), then W L 's total travel distance would have to increase by an amount )D if the robot was to maintain straight-line motion. )D is a function of the wheel diameter and the height of the bump (see [Borenstein, 1995] for a detailed analysis). However,for straight-line motion the low-level controller of a conventional differential-drive mobile robot will try to keep the rotational velocities of both wheels equal .Thus, the horizontal distance traveled by W L will be )D less than that of W R , causing a curved motion into the direction of the bump. After traversing the bump,the vehicle will continue in straight-line motion, but with a constant orientation error )2bump , given by )2bump – )D /b , where b is the wheelbase of the robot.One further effect that is noticeable while travers-ing a bump is that the vehicle will first turn toward the bump, then away from it. This is so because the wheel that encounters the bump (W L ) slows down momentar-ily as some of the kinetic energy from the forward mo-tion is converted into potential energy associated with the higher elevation of the vehicle on top of the bump.Then, when the robot rolls off the bump, it regains its velocity and turns back (almost) to its original orien-tation. The wheel encoders are aware of the change in velocity and will provide correct data on the event.However, the wheel encoders are not aware that W L traveled the extra distance )D . Because of this, the robot does not turn back completely in the original direction of motion, thereby establishing the constant orientation error )2bump described above.
Figure 2 provides experimental data in support of the above model. In the experiment of Fig. 2 a Lab-Mate robot traveled at a slow speed of 10 cm/s on a smooth concrete floor. The custom-built motor con-troller that we installed on that vehicle uses a so-called cross-coupling control algorithm [Feng et al., 1993]that tries to maintain equal encoder pulses from both wheels at all times. The vehicle ran for 140 s (.14 m)and artificial bumps (see Table I) were introduced by placing pieces of different-diameter household exten-sion cables under the right wheel at roughly 1-m inter-vals.
The momentary orientation of the vehicle based on odometry is plotted and labeled 2odo in Fig. 2. Since the odometry computation is unaware of the error D,the bumps cause only a short swerve for each encoun-ter, but the vehicle returns to it original orientation (at
least, that's what the odometry algorithm "thinks").
Figure 1: The Murata Gyrostar ENV-05H was used in the experiments in this paper.
The momentary orientation of the robot as measured with the Gyrostar is plotted and la-beled gyro in Fig. 2. The mag-nitude of the swerve as meas-ured by the gyro is similar to that measured by odometry. However, the gyro-plot shows that after each swerve there is a clearly discernible residual in-crement in the orientation of the vehicle, on the order of 0.5o - 0.8o for the larger bumps.
Since the odometry compu-tation is unaware of the error )D, the bumps cause only a short swerve for each encoun-ter, but the vehicle returns to it original orientation (at least, that's what the odometry algo-rithm "thinks").
The momentary orientation
of the robot as measured with the Gyrostar is plotted and labeled 2gyro in Fig. 2.
While Fig. 2 explains some of the physical aspects of the robot's encounter with bumps, the figure does not provide information on the accuracy of the gyro data. For example, we cannot tell the actual drift of the gyro from examining Fig. 2. An absolute measure of the robot's momentary orientation is needed, against which the gyro-data can be plotted. To obtain such an absolute measure we installed a simple wall-following system, based on two sideways facing Polaroid ultra-sonic sensors. Then, when traveling along a continu-ous, straight wall, it is possible to measure the absolute orientation of the robot to within typically "0.25o. The momentary orientation of the robot, according to the sonar wall-following sensor, is shown and labeled 2sonar in Fig. 2. According to the sonars, at the end of this run the accumulated orientation error is -9o. One can also see now that the gyro readings were off by approximately 4.2o at the end of the run. We attribute this discrepancy to the drift rate of the gyro; here about 4.2o/140 s = 0.03o/s = 1.8o/min.
The effect of a single bump on the robot's sensors is shown in Fig. 3. The plot shows the change in ori-entation of the robot per sampling interval, as meas-ured by odometry ()2odo) and by the gyro ()2gyro). The experiment is similar to that of Fig. 2, except that the data for Fig. 3 came from an earlier test with a differ-ent gyro and a single bump was encountered by the left wheel, at t = 73 s. The sampling interval in this ex-periment was T = 0.1 s.
Figure 3 shows how the vehicle first turns toward the bump (ccw, positive portion of the curve) while the affected wheel climbs up the bump, then away from the bump (cw), while the affected wheel rolls off the bump. Since the robot controller is set up to maintain equal encoder pulse counts, the robot steers back to its "original" direction after traversing the bump. How-ever, since odometry missed some of the initial turn-ing, the robot does not completely turn back to its original orientation and thus retains a large residual orientation error.
We interpret the gyro-measured change of orienta-tion, )2gyro, as an almost accurate representation of the actual rotation performed by the vehicle. We do so because the typical drift rate of the Gyrostar (0.03o/s) is negligible when compared to the peak rate of rota-tion, which is reached at t = 72.9 s and which amounts to 0.7o/0.1s = 7o/s. Based on these values, the drift rate of the Gyrostar (we assumed an average drift of 0.166E/s in Section 1) introduces an acceptable inac-curacy of 0.166/7 . 2.37% compared to the peak rate.
Table 1: Objects used to create the bumps in Fig. 2 Bumps 1-5Bumps 6-10Bumps 11-15
6-mm dia. cable 9-mm dia.
Cable
12-mm dia
cable
3. G YRODOMETRY
In this section we introduce Gyrodometry C a new method for fusing data from a gyro with data ob-tained from odometry. As we explained in Section 1, one of the most serious problems with odometry is the potential for "catastrophic" non-systematic errors, such as those caused by bumps or other large irregularities on the ground. We also argued that the robot cannot be calibrated to compensate for non-systematic errors, nor that is it possible to predict the frequency or magni-tude of these errors. Similarly, we recalled that the foremost problem with gyros is their inherent drift, which results in continuous and unbounded growth of the orientation error. Gyrodometry reduces the ill-effects of these problems.
The Gyrodometry method is based on the hypothe-sis that the discrepancy between the odometry curve and the gyro curve persists only over a very short amount of time. The experimental data in Fig. 3 lends credence to this hypothesis, as can be seen by investi-gating the line labeled )2gyro - )2odo in Fig. 3. This line shows the difference between the odometry and the gyro measurements, defined as
)G-O = )2gyro - )2odo.
The Gyrodometry method now simply compares )G-O to a preset threshold, for example )2thres = 0.125o/T. Then, if |)G-O| > )2thres, the robot's momentary orientation 2i is computed based on )2gyro; if |)G-O| < )2thres, then 2i is computed based on )2odo. The complete implementation of the Gyrodometry method can thus be expressed by this simple pseudo-code statement:
if (|)G-O,i| > )2thres)
then2i = 2i-1 + )2gyro,i T
else2i = 2i-1 + )2odo,i T
One can see in Fig. 3 that |θG-O|> thres is true for only three sampling intervals (=0.3 s). Yet, this short amount of time accounts for most of the difference between θgyro and θodo. Consequently, the robot's dead-reckoning systems relies on the gyro data only for a small fraction of the total travel time, keeping the system largely free of the drift associated with the gy-roscope. On the other hand, the gyro data covers those intervals in which the odometry error would have been largest. The effectiveness of the Gyrodometry method is illustrated by experimental results presented in the next section.
In this section we present experimental results that illustrate the effectiveness of the Gyrodometry method. For the sake of consistency, we have used the same set of experimental data that was used in Figure 2 for Fig-ure 4 in this section. One should note, though, that we have actually conducted many experimental runs C all with similarly good results as those shown here.
Before we present the experimental results we have to define the following orientation errors (recall that we consider the sonar-based orientation measurements as "completely correct").
,odo = 2odo - 2sonar(2a) ,gyro = 2gyro - 2sonar(2b) ,go = 2go - 2sonar(2c) where
2odo, 2gyro, 2sonar, 2go C Momentary orientation as computed by odometry, the gyro, the sonars, and the Gyrodometry method, respectively.
,odo, ,gyro, ,go C Momentary orientation error as computed by odometry, the gyro, and the Gyrodometry method, respectively.
Although the experimental data used in Fig. 4 is identical to the data used for Fig. 2, Fig. 4 differs in that it shows a plot of the orientation errors,odo, ,gyro, and ,go as defined above. Interestingly, it appears that
Figure 3: Effect of a single bump on the vehicle's change of orientation per sampling interval, as meas-ured by odometry and by the gyro. The bump was a 9-mm dia. cable placed under the left wheel.
the Gyrodometry error ,go does not increase with either the odometry-only error nor with the gyro-only drift. The maximal error ,go (during normal travel, i.e., not during a transient) stayed well under "0.5o. Thus the Gy-rodometry error was about 18 times smaller than the odometry-only error and about eight times smaller than the gyro-only error at the end of the ex-periment (-4o). It is also evident from Fig. 4 that had we continued the ex-periment further, the performance of the Gyrodometry method relative to the gyro would have increased further. However, the length of travel was lim-ited to the length of the largest unin-terrupted wall we could find in our laboratory, for using the sonar wall-following sensor. Running at a lower speed than 10 cm/s is unfeasible with
the LabMate robot.
5. C ONCLUSIONS
This paper introduces a new method for combining data from gyros and from odometry. This method, called Gyrodometry, is exceedingly easy to implement, yet it appears to be very effective in reducing odometry errors due to non-systematic "catastrophic" errors such as those caused by bumps or other large irregularities on the floor.
Although our current set of experiments covers only straight line motion, we are optimistic that the method can be extended easily to turning motion as well. This is so because the Gyrodometry method acts upon the difference between momentary odometry and gyro readings. This difference should behave similarly during turning and straight-line motion. We will in-vestigate this matter in the immediate future. Acknowledgment:
This research was funded by Department of Energy Grant DE-FG02-86NE37969.
6. R EFERENCES
1.Barshan, B. and Durrant-Whyte, H.F., 1995,
"Inertial Navigation Systems for Mobile Robots."
IEEE Transactions on Robotics and Automation, Vol. 11, No. 3, June 1995, pp. 328-342.
2.Borenstein, J., 1995, "Internal Correction of Dead-
reckoning Errors With the Compliant Linkage Ve-hicle." Journal of Robotic Systems, Vol. 12, No. 4, April 1995, pp. 257-273.
3.Borenstein, J. and Feng. L., 1995a, "Correction of
Systematic Dead-reckoning Errors in Mobile Ro-bots." Proceedings of the 1995 International Con-ference on Intelligent Robots and Systems (IROS '95), Pittsburgh, Pennsylvania, August 5-9, 1995, pp. 569-574.
4.Borenstein, J. and Feng. L., 1995b, "UMBmark: A
Benchmark Test for Measuring Dead-reckoning Errors in Mobile Robots." 1995 SPIE Conference on Mobile Robots, Philadelphia, October 22-26, 1995.Borenstein, J., Everett, H.R. , and Feng, L., 1996, "Navigating Mobile Robots: Systems and Techniques" Publisher: AK Peters., Wellesley, MA, ISBN 1-56881-058-X, Projected Publication Date: 2/96.
5.Byrne, R.H., KIarer, P.R., and Pletta, J.B., 1992,
"Techniques for Autonomous Navigation," Sandia Report SAND92-0457, Sandia National Laborato-ries, Albuquerque, NM, March.
6.Chenavier, F. and Crowley, J., 1992, "Position
Estimation for a Mobile Robot Using Vision and Odometry." Proceedings of IEEE International Conference on Robotics and Automation, Nice, France, May 12-14, pp. 2588-2593. Evans, J. M.,
1994, "HelpMate: An Autonomous Mobile Robot Courier for Hospitals." 1994 International Confer-ence on Intelligent Robots and Systems (IROS '94).
M h nchen, Germany, September 12-16, 1994, pp.
1695-1700.
7.Everett, H.R., 1995, "Sensors for Mobile Robots,"
A K Peters, Ltd., Wellesley, MA.
8.Feng, L, Koren, Y., and Borenstein, J., 1993, "A
Cross-Coupling Motion Controller for Mobile Ro-bots." IEEE Journal of Control Systems. Decem-ber, pp. 35-43.9.Komoriya, K. and Oyama, E., 1994, "Position
Estimation of a mobile Robot Using Optical Fiber Gyroscope (OFG)." International Conference on Intelligent Robots and Systems (IROS '94). Mu-nich, Germany, September 12-16, pp. 143-149.
10.[GEC] Avionics, Kent, U.K.
11.[HITACHI] - Hitachi Cable America, Inc., New
York Office, 50 Main Street, 12th floor, White Plains, NY 10606.
12.[MURATA] - Murata Erie North America, 2200
Lake Park Drive, Smyrna, GA 30080.
13.[TRC] (Transition Research Corporation), Shelter
Rock Lane, Danbury, CT, 06810-8159.
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[标签:标题] 篇一：关于汽车的英语作文 好的 Nowadays, with the rapid improvement of people’s living standards, cars have become an indispensable part of people's lives,so that more and more people have a car of their own, especially in cities. It brings some benefits for us but also causes many problems at the same time. For one thing,there’s no doubt that cars provide much convenience for people to go where they want to quickly and easily. Especially on weekday,driving a car can save a lot of time for us to go to work.When some places are too far away from our home, driving our own car is also convenient, we can go wherever we want. However,for another, too many cars will lead to the pressure of public transport, a series of problems will appear.First of all,it will bring about more air pollution,a large amount of polluted air given off by cars do great harm to our health.What’s more, as the existing roads are not so wide for the increasing number of cars,undoubtedly,traffic jams will become more and more serious. Last but not least, cars also place burden on the public facilities in providing more parking lots. As far as I am concerned,everything has its advantages and disadvantages. It’s high time that effective action must be token to limit the ever growing number of cars, the government should take measures to control the air pollution from the cars. Some roads should be widened and more new roads should be constructed. Only in this way，will people benefit from the popularity of cars. 坏的 Nowadays, with the rapid improvement of people's living standards, cars have become an indispensable part of people's lives,so that more and more people have a car of their own, especially in cities.It brings some benefit for us but also causes many problems at the same time. For one thing,it's no doubt that that cars provide much convenience for people to go where they want to quickly and easily. Especially on weekday,driving a car can save a lot of time for us to go to work.When some places are too far away from our home, driving our own car is also convenient, we can go wherever we want. However,for another, too many cars will lead to the pressure of public transport, a series of problems will appear.First of all,it will bring about more air pollution,a large amount of polluted air given off by cars do great harm to our health .What's more, as the existing roads are not so wide for the increasing number of cars,undoubtedly,traffic jams will become more and more serious. Last but not least, cars also place burden on the public facilities in providing more parking lots. As far as I am concerned,everything has its advantages and disadvantages. It's high time that effective action must be token to limit the ever growing number of cars, the government should take measures to control the air pollution from the cars. Some roads should be widened and more new roads should be constructed. Only in this way,will people benefit from the popularity of cars. 篇二：雅思作文高分范文：私家车的利与弊 智课网IELTS备考资料 雅思作文高分范文：私家车的利与弊
2课下作业三十二
课下作业(三十二) 、选择题 1．哲学基本问题又称哲学的根本问题、哲学的最高问题。这一问题包括( ) ①物质和意识的辩证关系问题 ②思维和存在何者是本原的问题 ③思维和存在有没有同一性的问题 ④唯物主义和唯心主义关系问题 A ．①② B ．②③ C .③④ D .①③ 解析：选 B 。哲学基本问题包括两个方面的内容：一是思维和存在何者是本原的问题；二是思维和存在有没有同一性的问题，②③入选。 2. 唯物主义是哲学上两个敌对的基本派别之一，是同唯心主义相对立的思想体系。划分唯物 主义和唯心主义的唯一标准是( ) A .物质和意识的关系问题 B .客观与主观的关系问题 C .思维和存在何者是本原的问题 D ?思维和存在有没有同一性的问题 解析：选C。对思维和存在何者是本原问题的不同回答，是划分唯物主义和唯心主义的唯一 标准， C 入选。 3. “二月春分八月秋分昼夜不长不短；三年一闰五年再闰阴阳无差无错。”这副对联从一个侧面反映了( ) ①思维和存在具有同一性 ②认识与自然的吻合具有必然性 ③认识以实证和猜测为基础 ④意识活动具有主动创造性 A .①③ B .②④ C .①④ D .②③ 解析：选C o材料反映人们可以认识和把握自然界的运动规律,说明思维和存在具有同一性 反映了意识活动具有主动创造性，①④符合题意；认识与自然的吻合不具有必然性，②错误；实践是认识的基础，③错误。 4 .(2019河南中原名校联考)“为天地立心，为生民立命，为往圣继绝学，为万世开太平”是北宋张载的名言。由于其言简意宏，一直被人们传颂不衰。下列观点符合“为天地立心”的
是( ) ①形存则神存，形谢则神灭②吾心即是宇宙，宇宙即是吾心 ③思维着的精神是地球上最 美的花朵④“天不生仲尼，万古长如夜” A ．①② B ．①③ C .③④ D .②④ 解析：选C。“为天地立心”的意思是为天地确立一种核心价值理念，强调精神的作用，③ ④强调思维着的精神的作用，符合题意；①强调物质决定意识，②片面夸大意识的作用，均不合题意。 5.有位生物学学者认为，唯有生物学才能带领人类探究物种本源、生从何来死往何方等问题，他确信构成生物的眼见为实的物质比辩证唯物主义判断猜想的物质还正确。这种认识( ) ①没弄清辩证唯物主义的物质概念与构成生物的物质之间的关系 ②坚持了唯物主义根本方向，但属于古代朴素唯物主义的思想 ③犯了近代形而上学唯物主义错误，具有机械性、形而上学性 ④是在自然科学基础上对辩证唯物主义和历史唯物主义的发展 A .①② B .①③ C .②③ D .③④ 解析：选B。材料中的生物学学者没有看到哲学对具体科学的意义，认为哲学中的物质是猜 想的，没有看到哲学中的物质与自然科学中的物质是共性与个性的关系，因而具有机械性、 形而上学性，①③正确，②④错误。 6.18世纪法国哲学家丹尼斯狄德罗认为：“自然界由数目无穷、性质不同的异质元素构成。” 这种观点( ) ①承认世界的物质性，但把物质归结为自然科学意义上的元素②建立在自然科学成就的基 础上，丰富和发展了唯物主义③坚持物质第一性，但对物质的认识没有科学依据④认为世界是物质的，正确揭示了物质世界的基本规律 A .①② B .③④ C .①③ D .②④ 解析：选A。“狄德罗认为：‘自然界由数目无穷、性质不同的异质元素构成。'” 这种观点承认世界的物质性，但把物质归结为自然科学意义上的元素，①正确；狄德罗生活在18世纪，其观点建立在自然科学成就的基础上，丰富和发展了唯物主义，属于近代形而上学唯物主义，②入选；③④ 说法错误。 7 ?“宇宙创造过程中，上帝没有位置……没有必要借助上帝来为宇宙按下启动键”。这是斯
课后巩固作业(十九) 3.2.1
温馨提示： 此套题为Word版，请按住Ctrl,滑动鼠标滚轴，调节合适的观看比例，答案解析附后。 课后巩固作业（十九） (30分钟50分) 一、选择题(每题4分，共16分) 1.下列试验中，是古典概型的是( ) (A)发射一颗卫星能否成功 (B)从高一(18)班60名同学中任选一人测量其身高 (C)抛掷一枚骰子，出现1点或2点 (D)射击选手射击一次，恰中靶心 2.(2011·温州高一检测)抛掷两个骰子,则两个骰子点数之和大于4的概率为 ( ) (A)13 18 (B)8 9 (C)7 12 (D)5 6 3.从{1,2,3,4,5}中随机选取一个数为a，从{1,2,3}中随机选取一个数为b，则 b>a的概率是( ) (A)4 5 (B)3 5 (C) 2 5 (D)1 5 4.用1，2，3，4这四个数字，组成比2 000大且无重复数字的四位数的概率是 ( ) (A)1 4 (B)1 2 (C)3 4 (D)1 3 二、填空题(每题4分，共8分) 5.(2011·江苏高考)从1，2，3，4这四个数中一次随机取两个数，则其中一个
数是另一个的两倍的概率是_____. 6.(2011·永定高二检测)扔两枚骰子出现的点数为m,n，以(m,n)为坐标的点出现在x2+y2=16内的概率为_____. 三、解答题(每题8分，共16分) 7.一个袋中装有四个形状大小完全相同的球，球的编号分别为1，2，3，4. (1)从袋中随机抽取两个球，求取出的球的编号之和不大于4的概率； (2)先从袋中随机取一个球，该球的编号为m，将球放回袋中，然后再从袋中随机取一个球，该球的编号为n，求n 介绍北京的英语作文1篇 篇一MyFamily Ilovemyfamily,becauseIhaveahappyfamily. MyfatherisanEnglishteacher.HisnameisJacky.Heisthirty-eight.Helikesplay ingbasketball.What’smymotherjop?Issheateacher?Yes,you’reright!Mymotherisverykindandnice,sheisthirty-seven.Mymotherisalways laboriouswork.Ilovemyparents! OnStaurdayandSunday,Ioftengotothelibraryandplaythepiano,Myfathergot oplaybasketball.Sometimes,wewatchTVandlistentomusicathome. Ilovemyfamily.BecauseI’mveryhappytolivewithmyparentstogether! 篇二MyFamily MyFamily Everyonehasafamily.Weliveinitandfeelverywarm.Therearethreepersonsin myfamily,mymother,fatherandI.Welivetogetherveryhappilyandtherearema nyinterestingstoriesaboutmyfamily. Myfatherisahard-workingman.Heworksasadoctor.Healwaystrieshisbesttoh elpevery,patientandmakepatientscomfortable.Butsonetimesheworkssohard thathecan”trememberthedate. 人教版二年级下册语文 每课作业 HEN system office room 【HEN16H-HENS2AHENS8Q8-HENH1688】 1、找春天 一、看拼音写词语。 tuō xiàjiědònɡxī shuǐmián yī tàn tóu yáo tóu?yě huā duǒcánɡ 二、按课文内容填空。 1、春天来了！我们几个孩子，_______棉袄，________家门，________田野，去_______春天。春天像个___________，遮遮掩掩，躲躲藏藏。我们________地找啊，找啊。 2、春天来了！我们______到了她，我们______到了她，我们______到了她，我们______到了她。她在柳枝上_________，在风筝尾巴上_________；她在喜鹊、杜鹃__________，在桃花、杏花__________…… 三、填空。 藏藏丁丁遮遮 慌慌清清摇摇 四、照样子写词语。 遮掩遮遮掩掩认真 开心（） （）（） 五、在正确读音下面画横线。 1、我家院子里有几（jǐ jī）只小鸡，这些小鸡真可爱！ 2、我家的客厅里的茶几（jǐ jī）上有两杯水。 ★照样子，写句子。 小草从地下探出头来，那是春天的眉毛吧？ ，是 2、古诗两首 一、看拼音写词语。 Wèi lái zhuī gǎn shūdiàn kūhuáng guāng róng yěcài zhù sù gāo shāo 二、抄写古诗《草》 题目： 作者：三、比一比，组词语。 未（）烧（）枯（）徐（） 末（）浇（）姑（）除（） ★这两首诗都是描写季景色的。 ★《草》是朝大诗人写的，诗中“， 。”句最为有名，它描写了草顽强的生命力。诗中还有一对反义词，分别是________和________。★《宿新市徐公店》描写了种景物，分别是 。诗中最有意思的一句 是、 。 3、笋芽儿 一、拼一拼，写一写。 shì jiè sǔn yá hūhuàn shān gāng hōng dòng 二、读一读，并照样子，写一写。 啊，多么明亮、多么美丽的世界呀！ 三、按课文内容填空。 1、笋芽儿被叫醒了。她（）眼睛，（）懒腰，（）四周一片漆黑，撒娇地说：“是谁在叫我呀” 2、春雨姑娘（）着她，（）着她。太阳公公（）着她，（）着她。笋芽儿脱下一件件衣服，长成了一株（）的竹子。她站在山冈上，（）地喊着：“我长大啦！”四、比一比，再组词。 岗（）界（）笋（）牙（）喊 （）呼（） 刚（）介（）笛（）芽（）减 （）乎（） 部编版三年级语文下册同步练习 20. 肥皂泡 一、看拼音写词语。 féi zào cháng láng mù wǎn tòu míng jiāo ruǎn yǎng tóu yí chuàn fēi yuè yīng ér xī wàng 二、给下列加点字选择正确的读音，打“√”。 1、几个同学散．（sǎn sàn）漫得在操场上散．（sǎn sàn）步。 2、若用扇．(shān shàn)子在下面轻轻地扇．(shān shàn)送,有时它能飞得很高很高。 三、比一比，再组词。 皂（）透（）婴（）娇（）希（） 泉（）诱（）耍（）骄（）杀（） 四、照样子，完成练习。 例：无声地散裂无声地（）无声地（） 例：轻轻地扇轻轻地（）轻轻地（） 例：颤巍巍（ABB式）（）（）（）（） 五、我会查字典，给加点字选择正确的解释。 “仰”字按部首查字法应先查（）部，再查（）画。按音序查字法应先查大写字母（），再查音节（）。“仰”字在字典里的解释有：①脸向上，与“俯”相对；②敬慕；③依赖；给下列加点字选择正确的解释，填序号。 仰．起头（）久仰．大名（）仰．仗（） 六、择合适的词语填空。（填序号） ①颤巍巍②软悠悠③轻飘飘④慢腾腾 1.不知为什么，我这几天头晕眼花，走起路来感觉________的。 2.轻轻地一提，那轻圆的球儿便从管上落了下来，_______地在空中飘游。 3.他做事总是像老牛拉破车，_______的。 4.有时吹得太大了，扇得太急了，这脆薄的球，会扯成长圆的形式，______的，光影零乱。 七、按要求完成句子练习。 1. 把句子写具体。 ①薄球就散裂了。___________________________________________________________ ②浮光在球面上乱转。______________________________________________________ 2.我把用剩的碎肥皂放在一只小木碗里。（改为“被”字句） ____________________________________________________________________________ 3.小时候，我喜欢玩吹泡泡、滚铁环、西瓜等游戏。（修改病句） ___________________________________________________________________________ 七、阅读课文片段,完成练习 方法是把用剩的碎肥皂放在一只小木碗里，加上点水，（），使它融化，然后 ．．用一 支竹笔的套管，蘸上那黏稠的肥皂水，（）地吹起，吹起一个（）的网球大小 的泡儿，再．（）地一提，那轻圆的球儿，便从管上落了下来，（）地在空中飘游。若用扇子在下面（）地扇送，有时它能飞得很高很高。 1.根据课文内容填空。 2.这是写（）肥皂泡和（）肥皂泡的过程。 3.用“”画出做肥皂水方法的句子。 4.用“先……然后……再……”说一说吹肥皂泡的过程。 . 八、快乐阅读。 种一片树叶 冰心 埋下一片树叶，固执地相信它终会长成一棵参天大树。这便是儿时最美的梦。 我4岁那年的秋天，枯黄的叶子从高高的树枝上飘落，正在院中玩耍的我俯身拾起一片， 觉得很美。玩赏了半天，我忽发一个奇怪的想法：这个曾经是树伯伯身上一部分的叶，把它 种进土里之后，必定可以长出一棵同样的大树! 于是我捡了许多片叶子，虔诚地跪在地上挖了个小坑，把树叶全埋到了土里。就像妈妈 生下了我，我也会渐渐长大—样，我坚定地相信我的梦马上可以实现。 我天天蹲在种树叶的地方等待我的大树，直到大雪纷飞。我想叶子大概怕冷，所以不敢 出来，等明年开春，一定会长得更好!我依旧固执地坚守着自己的梦，直到燕子衔泥，杨树吐 汽车的重要性《英语作文》 The automobile has become one of the most important means/ways of transportation in the world since it was invented. The automobile has completely changed the lifestyles of almost all the people in the world. In the past, animals like horses and camels were used for traveling and transporting goods. Automobiles are more comfortable and faster. Automobiles have also made it possible for us to transport large quantities of goods and people at the same time. Besides, the invention of the automobile has provided jobs for millions of people all over the world. 翻译： 汽车已经成为世界上最重要的交通工具之一，因为它是发明的。汽车已经完全改变了世界上几乎所有的人的生活方式。 在过去，像马和骆驼的动物被用来运送货物。汽车更舒适，更快速。汽车也使我们能够在同一时间运送大量货物和人。 此外，汽车的发明为全世界上百万的人提供了工作。 三一文库（https://www.wendangku.net/doc/4a18097097.html,） 〔我想去北京英语作文〕 我想去北京的英语作文如何写？那么，下面是小编给大家整理收集的我想去北京英语作文，供大家阅读参考。 我想去北京英语作文1 I’d like to go to a beautiful place. I think it would be Beijing. Beijing is not only our capital city, but also a famous city with long history and wonderful culture. Beijing is also China’s political and cultural center. There’re many old places of great interest, such as the Great Wall, the Summer Palace, the Forbidden City, the Temple of Heaven, and Tiananmen Square. Once you see Tiananmen Square, you will think of Beijing. It has been the symbol of Beijing since 1949. 我想去北京英语作文2 I went to Beijing more than eight times. Beijing is the capital of China. It’s a big city. I am very familiar with Beijing. It takes an hour and forty minutes from Nantong to Beijing by plane. There are many tall buildings in Beijing. It’s a modern city. My family visited the Great Wall, the Summer 必修2 Unit 1 课下作业（一~三） 课下作业（一）考点过关针对练 Ⅰ.单词拼写 1．Jim insisted that the book Mr.Black referred to was worth (值得的) reading. 2．She took one look at the horse and her heart sank (下沉)． 3．It was not until he removed (摘掉) his sunglasses that I recognized him. 4．I'll be waiting for you at the entrance (入口) to Guangzhou station. 5．The coal industry is now barely half its former (以前的) size. 6．The door opened and in came a troop of children in all sorts of fancy (奇特的) dresses. 7．Some animals are hunted illegally, so they become rare (珍贵的；稀有的)． 8．To make my room look nicer, I had the walls decorated (装饰) with paper cuts last year. Ⅱ.语境语法填空 1．?Having_removed (remove) from his hometown to the city, Zhang Qiang didn't know what ?to_do (do) at first.Under the guidance of his friend Li Ping, he made ?a fortune by doing business.He launched a campaign which ?was_designed (design) to help those in need in return ?for the society.He has done so much for the poor in his community that we can't think ?highly (high) of him enough. 2．As is known to all, cultural relics belong ?to human beings rather than individuals, so they are well worth ?protecting (protect)．However, some people are in search ?of them and take possession of them illegally.Some of them have been damaged while only a few survive.Therefore, every one of us should make all efforts to protect them from ?being_destroyed (destroy)．There is no doubt ?that it is our duty to protect cultural relics. 3．The old piano I bought years ago took up too much room, so ?by the light of the room, I ?took (take) it apart.I sold it to a waste recycling center at a low price. Ⅲ.语境改错 1．文中共有3处错误，每句中最多有两处，请找出并改正。 After removed dirt from the vase, the expert was amazed to find that it survived the Tang Dynasty.The vase was so amazingly designed that it was very worth buying at such a reasonable price. 答案：第一句：removed→removing; survived后加from 第二句：very→well 2．文中共有3处错误，每句中最多有两处，请找出并改正。 汽车英文演讲稿 篇一：汽车英语演讲稿 Good morning everyone ,today, the topic of my lecture（演讲） is “Do you love automobiles（'tmbilz）”. before I start my speech ,I want to ask a question,did there anybody present had seen the movie”the Fast and the Furious['fjrs]”.There are many cars of different styles in the movie,for example ,when you see the movie,you can find roadsters（跑车） just like Porsche（保时捷） GT3,sports utility (通用的）vehicles （车）SUV such as Volkswagen ['f:lks,va:gn]Touareg ['twɑ:reɡ](大众途锐）,even armored cars ,all of them are so powerful and beautiful. When I was a child,I dreamed I can have a car like FORD GT 40,this racing bike（跑车） is amazing and fantastic,but as time goes on ,my hobby is changing,now my favorite car is Jeep Rubicon,this is a car I really want ,it’s dynamic performance（性能） and off-road （越野） performance is top-ranking（一流的） ,which other ordinary SUV is unable to compare; the shape and color of this car is magnificent (华丽的） [mg'nfs()nt],and it’s gear-shift system（齿轮转 小学一年级介绍北京的英语作文 Beijing is an ancient city with a long history. Back in 3000 years ago in Zhou dynasty, Beijing, which was called Ji at the moment, had been named capital of Yan. Thereafter, Liao, Jin, Yuan, Ming and Qing dynasty all made Beijing their capital. Therefore, Beijing was famous for "Capital of a thousand years". The long history leaves Beijing precious cultural treasure. Winding for several kilometers in Beijing area, the Great Wall is the only man-made structure that could been seen in the space. The Summer Palace is a classic composition of ancient royal gardens, and the Forbidden City is the largest royal palaces in the world. Tiantan is where the emperor used to fete their ancestors, and also the soul of Chinese ancient constructions. The four sites above has been confirmed world cultural heritage by UNESCO. However, the best representatives for Beijing are the vanishing Hutongs and square courtyards. Through hundreds of years, they have become symbol of Beijing's life. Tian'anmen square being still brilliant today with cloverleaf junctions and skyscrapers everywhere, the old-timey scene and modern culture are combined to present a brand new visage of Beijing. As Beijing has been confirmed home city of Olympics 2008, the spirit of "green Olympics, scientific Olympics and humanized Olympic" will surely bring more and more changes to Beijing, promote the development of sports and Olympics in China as well as in the world, and strengthen the friendly communications between Chinese and foreign people. 北京是一个有着悠久历史的古城。 早在 3000 年前的周朝,北京,这叫霁,被命 名为首都燕。此后,辽、金、元、明、清都是北京首都。因此,北京著名的一千年 的“资本”。 悠久的历史使北京宝贵的文化瑰宝。绕组在北京地区几公里,长城是唯一的 人造结构,可以在空间。 颐和园是古代皇家园林的经典组合,和故宫是世界上最大 的皇家宫殿。 天坛是皇帝用来祭祀他们的祖先的地方,也是中国古代建筑的灵魂。 上面的四个网站已经确认被联合国教科文组织世界文化遗产。然而,北京最好的 代表是消失的胡同和广场庭院。数百年来,他们已经成为北京的生活的象征。天 安门广场到处都在今天依然灿烂的蝶式路口和摩天大楼的,古色古香的场景和现 代文化相结合,提出一个全新的北京的面貌。 随着北京 2008 年奥运会已被证实的家乡,精神的“绿色奥运、科技奥介绍北京的英语作文1篇 .doc
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