Wheel-ground interaction in planetary rovers Test rig and preliminary tests

Transcription

1 Wheel-ground interaction in planetary rovers Test rig and preliminary tests G. Genta 1 F. Impinna 1 1 Department of Mechanical and Aerspace Engineering, Politecnico di Torino, Italy giancarlo.genta@polito.it, fabrizio.impinna@polito.it Keywords: : wheel-terrain interaction, elastic wheels, planetary rovers. SUMMARY. The data regarding the properties of the wheels needed for dynamic modeling of wheeled vehicles must be obtained experimentally, on specifically designed test rigs. This is standard practice in automotive technology, but in the case of the wheels used in planetary rovers, both robotic and manned, there is a substantial lack of experimental data even if many tests were performed in the past, starting from the 1970s for the Apollo LRV missions. This is particularly true when considering operation on regolith, like in the actual working conditions. The aim of the present paper is describing a test rig that can be used to characterize the wheelground interaction under different operating conditions. The test device allows adjusting the wheel setup at different sidesslip and camber angles to obtain a complete wheel characterization. The test rig can perform tests on both artificial, hard surfaces and on a stimulant for Mars or Moon regolith. A preliminary test campaign aimed at measuring the lateral performance on the wheels of a mobile robot is described. 1 INTRODUCTION All robotic rovers for planetary exploration and the vehicles used to carry astronauts on the surface of the Moon used wheels as running gear. The same applies to the majority of projects for future exploration missions, both of the unmanned and manned types. While the wheels used on the large majority of ground vehicles used for both on-road and offroad transportation on Earth are based on pneumatic tires, this kind of tires are considered unsuitable for airless worlds, particularly in case of a planet where there is a high level of ultraviolet and ionizing radiation. Many planetary rovers of the past had rigid wheels, mostly made of metal but, as it is well known, the great advantages of compliant wheels suggested to use elastic, non pneumatic (airless) tires [1]. Airless wheels were developed since the beginning of automotive technology, with the aim of avoiding the allegedly unreliable pneumatic tires, but with the improvements of the latter and the increased confidence of the users, they practically disappeared. Airless tires were applied again for planetary exploration vehicles and, in particular, the Lunar Roving Vehicle (LRV) of the Apollo program had wheels of this kind [2]. More recently, Michelin introduced the tweel [3], an airless elastic wheel, also for Earth application, and now is working with NASA for the next generation lunar and Mars rovers. Dynamic modeling of wheeled vehicles is a common practice in automotive technology, and commercial codes are usually employed. Such dynamic modeling however requires the knowledge of the wheel-terrain interaction that is usually beyond that available for the specific type of wheels designed for planetary rovers, in particular when they operate on regolith like in the actual

2 working conditions [4-6]. Several analytical wheel-terrain interaction models have been discussed in detail in the literature but, although many tests were performed in the past (starting from the 1970s for the Apollo LRV missions) there is a substantial lack of experimental data. Test campaigns aimed at characterizing the behavior of the specific non pneumatic, elastic but sometimes rigid, wheels designed for planetary rovers are required. The test must be performed on specific soils that simulate the terrain which can be found in the actual applications, the so-called planetary simulants. The aim of the present paper is to describe a test rig that can be used to characterize the wheelground interaction under different operating conditions. The sideslip and camber angles of the wheel can be adjusted in a wide range to obtain a complete wheel characterization. Different soils spanning from artificial hard surfaces to stimulants for Mars and Moon regolith can be used. 2 WHEEL TESTING The characteristics of tires can be measured using road or laboratory tests. In the most common testing machines the tire can roll either on the outer surface or on the inner surface of a drum simulating the ground surface (Fig. 1a). The actual conditions are in a way intermediate between those encountered on these two types of test machines. Figure 1: Tire testing machines. (a) Drum machines, with positive or negative curvature. 1: drum; 2: tire under test. (b) Belt machine. A: belt support; C: belt; R: wheel under test; V: shaker. To avoid the differences between the contact conditions occurring in drum machines and the actual ones, more modern machines use a steel belt (Fig. 1b). The belt is kept flat by a hydrostatic bearing, which can be connected to a shaker to simulate the motion on uneven road. The simulation of the road surface is easier on drum than on belt machines, on which the surface is usually a plain metal surface. In all testing machines the tire is fitted on a hub which is provided with a device able to measure the three components of the force and the three components of the moment. The various driving and braking conditions can be simulated by using two different motors for the wheel and the "road" and the wheel can be maintained at any sideslip and camber angle. Results of laboratory tests must be validated by road tests, which are performed using particular test vehicles. Road testing of tires require instrumented vehicles, usually provided with the same instrumentation common on testing machines. The wheel under testing is usually lowered from the vehicle, which rolls on its own wheels; when the first exerts lateral forces also the wheels of the vehicle work with a sideslip angle, which must be accounted for in measuring the sideslip angle of the wheel under test. The power needed for the test vehicle is very high if

3 high speed testing in strong braking or driving conditions is required. Testing in the lab using machines of this type has little significance in case of wheels for planetary rovers, where the nature of the ground must be simulated as accurately as possible. On the other side, while tires for standard vehicles must be tested in the whole speed range of the vehicle, and high speed test are the most important ones for the evaluation of both performances and safety, typical working conditions of planetary rovers, and in particular of robotic rovers, are characterized by low, or very low, speed. Since the typical velocity of robotic rovers span from some meters per hour to a few km/h, it is possible to devise laboratory testing machines that on one side are simpler, and on the other allow operation of the wheel on actual loose ground, and in particular on a suitable stimulant. Four alternatives are usually chosen: 1. rolling the wheel along a straight path on an elongated stretch of ground, 2. rolling the wheel, which rotates about a fixed axis, on a movable platform, 3. rolling the wheel on a circular path on a round patch of ground and 4. rolling the wheel, that rotates about a fixed axis, on a circular platform that in turn rotates about a vertical axis. The latter solutions allows for a test of longer duration, but do not allow rolling in straight direction. 3 TEST MACHINE DESIGN 3.1 Type of tests The test rig was designed for performing a number of different tests on the compliant or rigid wheels. The fact that the rig was built for testing wheels for planetary robotic rovers and, more in general, robots, results in the possibility of limiting the size of the wheel and the test speed. The types of tests planned are: Tests on free wheels: - Measurement of the rolling resistance, at various sideslip and camber angle; - Measurement of the side force, as function of the sideslip and camber angle; - Measurement of the aligning torque, as function of the sideslip and camber angle. Tests on driving and braking wheels: - Measurement of the longitudinal force, as a function of the longitudinal slip; - Measurement of the interaction between longitudinal and side forces and between the longitudinal force and the aligning torque. While tests on free wheels can be performed by assembling the wheel on a free-wheeling hub, for tests on driving and braking wheels the wheel must be supplied with its own driving motor, able to supply a torque in either direction (driving and braking). In this case a precise measurement of the wheel rotational speed, independently from the measurement of the longitudinal speed, must be performed. The speed can be easily measured by the motor driver, in case a brushless motor is used. 3.2 Basic requirements The test rig was built specifically for testing the wheels designed for the AMALIA rover [7, 8], but the specifications were drawn to allow testing wheels of a larger size and with more powerful motors. The following design specifications were stated: Overall test bench size (L W H) m

4 Max wheel diameter 600 mm Soil depth 200 mm Min. test time at top speed 40 s Max. speed 0.05 m/s = 180 m/h Travel distance 2 m Max. vertical load 0.8 kn Max. camber angle 10 Max. sideslip angle 25 Primary load sensors 6-component load cell, with sensing range of 500 N for forces and 20 Nm for torques and maximum overload for each axis 3 times the sensing range Primary displacement sensors 3 laser sensors to measure the absolute vertical distance of the wheel hub and of the ground before and after the passage of the wheel Test surface planetary regolith stimulant, but also sand, gravel and artificial surfaces like tarmac or concrete. The impossibility of realizing simultaneously all the specifications above is considered acceptable (for instance, the minimum test time can be reduced when testing a wheel with the maximum diameter at maximum speed). 3.3 General layout The first alternative, rolling the wheel along a straight path on an elongated stretch of ground, is here chosen, in spite of the fact that in this way long tests are made impossible. A drawing of the general layout of the machine is shown in Fig. 2. Figure 2: Wheel test rig built at the Mechatronics Lab of Politecnico di Torino. Front and side view showing the main components. The main constituents of the test rig are: A basement-structure subsystem. It includes a sandbox, with open bottom, so that when the sandbox is empty the test can be performed on the underlying hard surface, and a steel-tube structure. The basement is bolted to the ground so that the vertical forces acting on the wheel cannot lift it.

5 A linear guide with its electric motor. After a tradeoff among the different alternatives, a belt drive, wheel guided linear guide was chosen. The guide can be attached at different heights to the frame to compensate for the wheel diameter and the soil depth. A camber-steer subsystem, located between the slider of the guide and the suspension subsystem (Fig. 3a). The camber and the sideslip angle must be manually set before the test, and cannot be changed during the test. A suspension subsystem. The suspension is of the leading arm type with a preload spring. The preload must be manually set before the test using the output of the load cell. No preload changes during the test are possible. Owing to the low speed, no shock absorber is provided. A load cell unit. A 6-components load cell is mounted at the bottom end of the suspension unit. The load cell was supplied by IIT (Italian Institute of Technology) and has the required characteristics. The wheel subsystem, consisting of a spindle, the wheel under test and possibly an electric motor. The spindle is directly attached to the load cell. If the wheel is tested in the freewheeling configuration, there is no need to have a motor in the wheel. If, on the contrary the wheel is driving or braked, a motor providing the driving or braking torque must be inserted between the spindle and the wheel. This configuration was chosen since the wheels for the AMALIA rover have a built-in electric motor. Figure 3. a) Camber-steer subsystem. b) suspension subsystem. A displacement-sensor subsystem. 3 laser distance sensors are located on the fixed frame of the suspension (or better, o a fixture attached to it so that the reference point is located close to the center of the measuring range) and point on the wheel hub and on the ground forward and backward of the wheel. Sensors with a measuring range of 50 mm and a resolution better than 0.01 mm were chosen. 4. PRELIMINARY TESTS 4.1. Wheel under test The first tests were performed on a pneumatic wheel used on a wheeled robot with 10 wheels [9, 10]. The main data of the wheel, shown in Fig. 4, were the following: Outer tire diameter 390 mm Hub diameter 220 mm

6 Tire width Weight of the complete wheel-hub assembly 90 mm 87 N Figure 4. Test wheel. a): Wheel set at a sideslip angle α = 0; b): Wheel set at a sideslip angle α = 25. Since most of the tests of the robot were performed indoors, on the tiles of the floor of the lab, the tests were performed on the same type of terrain. Since the robot has no suspensions and the wheels remain perpendicular to the ground, all tests were performed with zero camber angle. The usual reference frame XYZ, with its X axis at the intersection of the ground plane with the midplane of the wheel and the Z axis perpendicular to the ground is used. The forces are measured with respect to the X Y Z reference frame of the load cell: since the camber angle is equal to zero, the two frames differ by the inclination angle β of the suspension arm (Fig. 5) The forces and moments referred to the first one are related to those measured by the load cell by the simple relationships: F = F cos(β ) + F sin (β ) X' Z' X FY = FY ' (1) F = F sin (β ) + F cos(β ) X' Z' Z M = M + d F sin (β ) + F cos (β ) R F F cos(β ) + F sin (β ) X' X' Z' L Y' X ' Z' X M Y = M Y ' + RL FX ' cos(β ) + FZ ' sin (β ) (2) M Z = M Z ' d FX ' cos(β ) + FZ ' sin (β ) [ [ [ ] ] ] In the preliminary tests only the lateral force Fy was measured as a function of the sideslip angle. The tests were performed at a speed of 0.02 m/s and using 3 different values of the load, namely Fz = 137, 187 and 287 N (spring preload of 50, 100 and 200 N). Test run of 30 s, corresponding to a travel of 600 mm, were performed. At the end of each run, the wheel was

7 returned to the original position with a return run performed at the same speed. The forces and moments were measured also during the return run. Figure 5. Reference frame of the wheel XYZ, centered in the center of the contact area P, and of the load cell X Y Z, centered in L Lateral behavior The procedure to investigating the lateral behavior was: 1. State a value of the vertical load; 2. State a value of the sideslip angle; 3. Start the machine and take 150 values of the forces and moments measured by the load cell at a rate of 5 reading per second; 4. At the end of the test run, a return run was monitored, to verify that the results were not strongly influenced by the direction of travel; 5. Increase the value of the sideslip angle and return to point 2; 6. When all the 10 intended values of the sideslip angle between 0 and 17.5 were exhausted, increase the load and return to point 1. The plot of the force versus the time during one of the tests, namely that for a load of 187 N and a sideslip angle of 10 (the sideslip angles allowed by the test rig are negative, following the usual conventions) is reported in Fig. 6. Clearly the force starts from 0 and there is an initial phase in which the force grows up to the steady-state value. In the following phase oscillations were recorded: these oscillations are apparently due to the presence of thick grousers on the periphery of the tire. At the end of the run the motion is inverted and the wheel returned to the original position. The steady-state value in the return run was not exactly equal to that measured in the forward run: this could be expected since no wheel is exactly symmetrical, even in the case in which it is nominally such. In particular the conicity of the wheel causes the value measured in the forward run to differ from that obtained in the return run. Only the force measured in the forward run was considered. The values of the forces measured in each test run were averaged, except for the first 50 values which were discarded to avoid effect due to the initial non-steady-state conditions. The averaged value in the case of Fig. 6 is 94.5 N and is reported in the plot. The results for the 3 values of the load are reported in Fig. 7a as functions of the sideslip angle.

8 Figure 6. Lateral force recorded during a test ad a function of time. Test with F z = 187 N and α 10. The curves F Y (α) were approximated by the simplest analytical relationship that has been used in cases of this type, namely C α FZ µ y ( ) p F = α µ Y sign FZ y 1 e (3) p Using a standard least square algorithm, the curves shown in Fig. 6a were obtained. The 3 values of the maximum value of the lateral traction coefficient µ yp and of the cornering stiffness C obtained for the 3 values of the load were again approximated using a linear approximation with coefficients obtained through a least square approach: 3 y = F Z µ (4) p C = F Z (5) where forces are in N and the cornering stiffness is measured in N/rad. Equations from (3) to (5) allow to approximate the cornering force as a function of the load acting on the wheel and of the sideslip angle in a wide range of these parameters. As a result, it is possible to assess that the wheel under test has a fairly low value of the lateral traction coefficient, that decreases with increasing load (as should be expected) in linear way (at least in the load range covered by the tests) with a slope larger than usual. These characteristics of the wheels are well explained by two considerations: 1. The wheel is a low-performance wheel designed for off-road use, with large grousers, that cannot be expected to behave well on a hard and smooth surface; 2. The wheel operates (during the test and in actual service) at a low temperature, owing to the low speed, and the duration of the test is too short to allow to reach the equilibrium temperature.

9 Figure 6. Results of the tests regarding the lateral behavior of the wheel. Cornering force (a) and lateral traction coefficient (b) as functions of the sideslip angle. Linear approximation of the maximum traction coefficient (c) and of the cornering stiffness (d) as functions of the load. 5. CONCLUSIONS A test rig for characterizing the wheel-ground interaction for wheels for planetary rovers and robots in general was designed and built. It allows to perform the tests on the actual surface although it is limited to low speeds. The characterization of the wheels in conditions similar to those encountered in space robotics (as opposite to those encountered in automotive applications, as usual in wheel characterization) is thus possible. The rig allows to set the sideslip and the camber angles within a wide range, and to load the wheel with a pre-determined force. However, the angles and the force must be manually set before each test run, which prevents from performing tests with varying parameters. A six-components load cell allows measuring the three components of the contact force and moment so that a complete characterization of the wheel can be obtained. A number of preliminary tests, aimed to measuring the lateral force as a function of the sideslip angle and of the load on a wheel used on a mobile robot where performed. They showed that the rig is easy to use and that the read-outs from the load cell can be easily processed using Matlab m- files. A first version of the software was written and proved to work satisfactorily. The lateral force characteristics of the test wheel was satisfactorily obtained and its trends are

10 found to be those expected for a wheel of that type. The research work must now proceed by completing the characterization of the wheel, measuring the rolling resistance and the effect of the camber angle on the lateral force. After that, a driving motor will be added in the wheel hub, so that the longitudinal force can be obtained as function of the longitudinal slip and the load. After completing the set-up of the test rig the elastic wheels of the AMALIA rover will be characterized. References [1] G. Genta, Introduction to the Mechanics of Space Robots, Springer, New York, [2] D. Baker, David, Lunar Roving Vehicle: Design Report, Spaceflight, 13, , July [3] T. B. Rhyne and S. M. Cron, Development of a Non-Pneumatic Wheel. Tire Science and Technology: September 2006, Vol. 34, No. 3, pp [4] Wang, Zhidan, and A. R. Reece, The Performance of Free Rolling Rigid and Flexible Wheels on Sand, Journal of Terramechanics, 2004, 41, p [5] Carrier III, W.D., Lunar Soil Simulation and Trafficability Parameters, Lunar Geotechnical Institute, Tech. Rep, [6] F. Chen, G. Genta, Dynamic modeling of wheeled planetary rovers: A model based on the Pseudo-coordinates approach, Acta Astronautica, Vol. 81, p [7] A. Della Torre, A. Ercoli Finzi, G. Genta, F. Curti, L. Schirone, G. Capuano, A. Sacchetti, I. Vukman, F. Mailland, E. Monchieri, A. Guidi, R. Trucco, I. Musso, C. Lombardi, The Conceptual Design Of The Team Italia Amalia Mission Rover, Candidate For Google Lunar X Prize Challenge, Acta Astronautica, 2010, Vol. 67, n. 7-8, Oct.-Nov. 2010, p [8] G. Genta, A. Genta, Modeling and Nonlinear Analysis of an Elastic Wheel for Low-Gravity Applications, XXXVIII Conv. Naz. AIAS, Torino, Sept [9] Genta G., Amati N., Bonfitto A., Carabelli S., Impinna F., A Wheeled Robot for Lunar Environment: Design, Modelling and Construction, 57 th International Astronautical Congress, Hyderabad, September [10] G. Genta, N. Amati, B. Bona, F. Impinna, M. Kaouk, C. Pristerà, G. Romeo, Mobile teleoperated manipulator for difficult and hazardous environments, Atti dell Accademia delle Scienze di Torino, Serie V, Vol. 32, p , [11] G. Genta, Introduction to the Mechanics of Space Robots, Springer, New York, 2011.