Proposal of Walking to Prevent a Fall of a Planetary Exploration Legged Rover Using Effect of Loose Soil Caused by a Propagation of Vibration

A.MECHANISM THAT ROVER FALLS DOWN ON THE LOOSE GROUND WITH A SLOPE

In this section, the necessity of a walking method that prevents a fall of a legged rover is explained. First, the mechanism that a rover falls down on the loose ground with a slope is explained. In this study, the moment that is generated by the weight of a rover on a slope is called M_os (moment on a slope). The illustration of the forces that a rover is received on the loose ground with a slope is shown in Fig. 1. Fig. 1 shows the simple forces in a two-dimensional coordinate system. In Fig. 1, M_os is caused around P_R (the touching point between the ground and a rear leg). The term M_os is calculated from (1)

Fig. 1. Conceptual diagram of the moment on a slope.

where θ_G is the slope angle of the ground and θ_S is the angle of a rover’s posture, which is generated by the leg subsidence and calculated from (3)

The reason that legged rovers are easy to fall on the loose ground is explained here. The term l_z is large because the centers of gravity of legged rovers are higher than that of rovers using other moving mechanisms. Moreover, the loose ground is easy to deform by receiving external force. On the slope, s_R is larger than s_F because the weight of a rover that a rear leg is received is larger than one that front a leg is received. Therefore, θ_s is increased on the slope ( eq. (3)). The term M_os is decreased by increasing these values. The risk that a rover falls down is increased by decreasing M_os. Therefore, a walking method is needed, which prevents a fall of a legged rover.

B.PROPOSED WALKING METHOD USING VIBRATION

In this section, a walking method that prevents a fall of a legged rover is explained. It is needed to increase M_os by inclining forward a rover to prevent a fall of it. In the proposed walking method, M_os is increased using the feature, which is caused by giving vibration to the loose ground. The particles of the ground are moved by giving vibration to the ground as shown in Fig. 2. The shear strength of the ground is decreased by moving the particles. The amount of leg subsidence is increased by decreasing the shear strength. Therefore, a rover inclines forward by giving vibration to the ground.

Fig. 2. Movement particles of the ground when vibration is given to the ground.

Details of the proposed walking method are explained. The proposed walking method is used for the six-legged rover. The reason is that the six-legged rovers can walk in static walking without moving the center of gravity. The proposed walking method is shown in Fig. 3. First, the front legs and the middle legs vibrate (Fig. 3(a)). The rover inclines forward by this motion. Then, the rover moves legs forward one by one (Figs. 3(b)-(d)). This motion is based on wave gait. Fig. 4 shows the movement of each leg and the timing to vibrate the leg. First, the leg raises and moves forward (Fig. 4(a)). Second, the leg moves down to the ground. Then, the leg is vibrating when the leg touches the ground (Fig. 4(b)). Moreover, the leg sinks into the ground. Finally, vibration stops when the leg finishes sinking into the ground (Fig. 4(c)). In the previous study, our study group proposed this motion as the walking method that the legged rover can prevent slipping on the loose ground [16]. This motion indicates that density of the ground and earth pressure are increased. Therefore, the traction force of the legged rover is increased by increasing earth pressure. The effectiveness of this motion was confirmed. Finally, the body of the rover moves forward (Fig. 3(e)). Moreover, one cycle of this gait is finished.

Fig. 3. Sequence of proposed walking.

Fig. 4. Vibration timing when walking.

A.METHOD OF A PENETRATION EXPERIMENT

First, the experimental machine is explained. The experimental machine is shown in Fig. 5. It consists of the soil tank part, the leg part, and the actuator part. The size of the soil tank is H 300 mm × W 354 mm × L 609 mm. Fig. 6 shows the structure and the size of the rod. The vibration motor is mounted in the rod. Fig. 7 shows the movement of this machine. The leg part is penetrated in the soil tank part by the actuator part. The leg part consists of the force sensor and the rod. The resistance force from the ground when penetrating the rod is measured by the force sensor.

Fig. 5. Overview of penetration testing machine.

Fig. 6. Overview of rod.

Fig. 7. Movement of penetration testing machine.

Then, the flow of the experimental method is explained. The flow of this experiment is shown in Fig. 8. The leg part is set on the ground (Fig. 8(a)). The ground consists of Silica No. 5. Then, the leg part is penetrated into the soil tank (Fig. 8(b)). The speed of moving the leg part is 0.55 mm/s. The vibrations are three kinds. These kinds of vibrations are prepared by changing the voltage that is supplied to the vibration motor. Table I shows these vibrations. The force sensor receives the value of the resistance force from the ground. The number of trials is 10 times. Table II shows the condition of this experiment.

Fig. 8. Flow of penetration experiment.

TABLE I. Parameters of Table of Vibration

TABLE II. Condition for Penetration Experiment

B.RESULTS AND DISCUSSION OF A PENETRATION EXPERIMENT

Figs. 9–12 show the graphs about the distance of subsidence vs resistance force from the ground in each kind of vibration. In Fig. 9, the resistance force was shown as a curve and increased in the experiment without vibration. From Fig. 9, these shapes of the graphs were hardly different in all trials. This minor difference in graph shapes is seemingly caused by the irregularity of the loose ground. As shown from Figs. 10 to 12, graph shapes in the experiment with vibration were different in comparison with that in the experiment without vibration. In the experimental results with vibration, the resistance force was low at the beginning of these graphs. In the same experimental condition, these shapes of the graphs were similar, but they have variations. The stronger the vibration was, the larger these variations were. These variations are seemingly caused by vibration given to the ground. The particles of the ground are moved by giving vibration to the ground. This movement of particles is irregular. Therefore, these variations are seemingly caused by moving the particles. In Fig. 13, the resistance forces are compared in each experimental condition of vibration. In Fig. 13, the data of median values are chosen because the resistance forces that were obtained in the same experimental conditions were hardly different in all trials. Fig. 14 shows the difference between the result in the case of using vibration and one in the case of not using vibration. At the beginning of this graph, the resistance forces in the case of using vibration were smaller than one in the case of not using vibration. In this result, the rod was easy to sink to the ground by giving vibration. Therefore, it is possible that the rover inclines forward by giving vibration to the ground. Moreover, the larger the vibratory force was, the smaller the resistance force was (Fig. 13). In this result, it is considered that the larger the vibratory force is, the more effective the proposed walking is. Finally, the resistance forces in the case of using vibration were increased rapidly and fit one in the case of not using vibration. The reason is considered that the higher the subsidence of the rod is, the larger the earth pressure is. The situation in each amount of subsidence is shown in Fig. 15. The amplitude of vibration is decreased by increasing the earth's pressure. Therefore, it is considered that the resistance force in the case of using vibration is matched with one in the case of not using vibration when the earth pressure is higher than the vibratory force.

Fig. 9. Resistance force vs penetration distance using no vibration (vibratory force: 0.00 N and frequency: 0 Hz).

Fig. 10. Resistance force vs penetration distance using weak vibration (vibratory force: 0.27 N and frequency: 70 Hz).

Fig. 11. Resistance force vs penetration distance using middle vibration (vibratory force: 1.32 N and frequency: 153 Hz).

Fig. 12. Resistance force vs penetration distance using strong vibration (vibratory force: 3.04 N and frequency: 231 Hz).

Fig. 13. Comparison of resistance force in each vibration.

Fig. 14. Overview of difference between resistance force in the case of using vibration and one in the case of not using vibration.

Fig. 15. Situation in each amount of sinkage.

A.METHOD OF A SLOPE WALKING EXPERIMENT

First, the experimental method is explained. In this experiment, the testbed walks on the loose ground with a slope. The experimental environment is shown in Fig. 16. The ground consists of Silica No. 5. Two kinds of walking methods are used. There are the proposed walking and the walking without vibration. The proposed walking and the walking without vibration are wave gait. The entire walking motion is shown in Fig. 3. However, the motion that is shown in Fig. 3(a) is not conducted in the walking without vibration. Moreover, the details of these walking methods are shown in Fig. 17. In the proposed walking, the leg vibrates and sinks 30 mm to the ground after it touches the ground (Fig. 17(b)). In walking without vibration, this motion is not conducted after the leg touches the ground. Strong vibration is used in the proposed walking (Table I). The detail of the walking is shown in Table III. The slope of the ground changes by 5° between 0° and 20°. The movement of the testbed is measured by motion capture system (OptiTrack Prime 13). The number of walking steps is five steps. The number of trials is five times in each experimental condition. Table IV shows the condition of this experiment.

Fig. 16. Overview of slope walking experiment on the loose ground using testbed.

Fig. 17. Details of walking methods.

TABLE III. Specifications of Walking Methods

TABLE IV. Condition for Slope Walking Experiment

Then, the testbed is explained. Table V shows the specifications of the testbed. The overview and the structure of the testbed are shown in Fig. 18. The leg of the testbed consists of three joints. The vibration motor is mounted in the leg. Judging the contact between the ground and the legs and measuring the posture of the testbed are conducted to evaluate the walking methods. The force sensor (FSR400) is used to judge the contact between the ground and the legs. These force sensors are attached to the toes, as shown in Fig. 19(a). The acceleration sensor (ADXL345) is used to measure the posture of the testbed. Fig. 19(b) shows the measuring direction about the posture of the testbed. The sampling frequency of these sensors is 2 Hz.

Fig. 18. Overview and structure of legged testbed.

Fig. 19. Sensing system of legged testbed.

TABLE V. Specifications of Testbed

B.EVALUATION OF WALKING METHODS

In this experiment, M_os is calculated to evaluate the walking methods. In this section, calculation of M_os is explained. The term M_os is the moment around the touching point between the ground and the legs (Fig. 20). In this experiment, the force and the moment for the acceleration and the deceleration of the testbed are very small because the testbed walks static. Therefore, gravity is the primary force that the testbed is received. The term M_os is calculated from gravity that the testbed is received. The testbed consists of six legs and a body. The legs have three joints. Therefore, the testbed consists of 19 links. Each link is called L_ij (Fig. 21). The term i is a leg’s number and j is a joint’s number. In each link, the mass, the size, and the coordinate of the center of gravity were already measured. The gravity of each link in the coordinate of testbed is calculated from (4)

Fig. 20. Conceptual diagram of testbed on the slope.

Fig. 21. Overview of links in the testbed.

where R is the rotation matrix of the x-, y-, and z-directions, θ_Yaw, θ_Pitch, and θ_Roll are the posture angle of the testbed on a slope, and the x-, y-, and z-directions are shown in Fig. 20. The term θ_Yaw is approximately 0 because the testbed walks straight. The directions of θ_Pitch and θ_Roll are shown in Fig. 19(b). The term m_ij is the mass of the link, which is ith of the leg and jth of the joint, and g is the gravitational acceleration. Then, the moment around the touching point between the ground and the leg is calculated. For example, M_k that is the moment around the touching point between the ground and the leg of kth is calculated from (5)

Fig. 22. Overview of position vectors in testbed.

where R is the rotation matrix and expressed in (8), θ_ij is the angle of the link, which is ith of the leg and jth of the joint (Fig. 22), and θ_ij consists of the angles in yaw, pitch, and roll directions

Fig. 23. Overview of position vectors in the link.

Their points are that the leg is touched the ground. The terms k and n are leg’s numbers. Calculation of M_os is divided into three cases because points touching the ground and the legs are changed in walking. The cases of calculating M_os are shown in (10) and Fig. 24

Fig. 24. Calculation cases of Mos.

When the 3rd leg is the free leg, M_os is M₆₂. When the 6th leg is the free leg, M_os is M₅₃. In other cases, M_os is M₆₃. The larger the value of M_os is, the more difficult the testbed is to fall down. Table VI shows the symbols used for calculating M_os.

Moreover, the posture of the body in roll direction and the amount of movement by walking are measured to confirm the effectiveness of the proposed method. The amount of movement is measured by the motion capture system.

TABLE VI. List of Symbols That Used Calculating Moment on a Slope

C.RESULTS AND DISCUSSION OF A SLOPE WALKING EXPERIMENT

Table VI shows the result of the slope walking experiment. In Table VII, success means that the testbed could walk without falling down in all trials. Fall means that the testbed fell down in all trials. The testbed fell down on the loose ground with a lean of 15° and 20° when it used the walking without vibration. The testbed could walk using the proposed walking on all slopes without falling down. In this result, the proposed walking prevented a fall of the testbed. Moreover, the angle of a slope that the testbed can walk became large by using the proposed walking.

TABLE 7. Result of Slope Walking Experiment

From Figs. 25 to 29, there are the graphs of time vs M_os in walking. In these graphs, the data of one trial are chosen because M_os, which was obtained in the same experimental conditions, was hardly different in all trials. Fig. 30 shows the change of M_os in one cycle of the walking. The term M_os was decreased at the beginning of this graph because the testbed raised the rear legs (Fig. 30). The term M_os was increased in the ending of this graph because the body of the testbed moved forward. From Figs. 25 to 27, time is expressed in percentage because the walking times are different in each walking method. These values of M_os were not different on a slope with 0° (Fig. 25). In Figs. 26 and 27, M_os in the proposed walking was larger than one in the walking without vibration on a slope with 5° and 10°. In this result, the testbed was difficult to fall down when it used the proposed walking. In Figs. 28 and 29, only M_os in the proposed walking is shown because the testbed fell down using the walking without vibration. In Figs. 28 and 29, M_os in the proposed walking is not decreased in each walking cycle. In these graphs, the larger the slope angle was, the smaller the M_os was. However, the testbed could walk using the proposed walking on all slopes without falling down. The reason for this result is considered that the resistance forces that prevent a fall of the testbed are caused. The friction force between the leg and the ground and the earth pressure is caused by sinking the legs in the ground (Fig. 31). Therefore, it is considered that the actual M_os is larger than the calculated M_os. In this result, falling down of the testbed was seemingly prevented by not only the effect of gravity but also other effects.

Fig. 25. Moment vs time on a slope with 0°.

Fig. 26. Moment vs time on a slope with 5°.

Fig. 27. Moment vs time on a slope with 10°.

Fig. 28. Moment vs time on a slope with 15°.

Fig. 29. Moment vs time on a slope with 20°.

Fig. 30. Change of Mos in 1 walking cycle.

Fig. 31. Overview of resistance forces by subsidence.

From Figs. 32 to 36, there are the graphs of time vs testbed’s posture. In these graphs, the data of one trial are chosen because the posture of the testbed, which was obtained in the same experimental conditions, was hardly different in all trials. In these graphs, the posture of the testbed is the angle in roll direction (Fig. 19(b)). Their values of the testbed’s postures were not different on a slope with 0° (Fig. 32). In Figs. 33 and 34, the posture of the testbed in the proposed walking was smaller than one in the walking without vibration on slopes with 5° and 10°. In Fig. 35, the posture of the testbed in the proposed walking was not increased. However, the posture of the testbed in the proposed walking was increased in Fig. 36. Therefore, the proposed walking method has the feature that the posture angle of the testbed is decreased. However, the larger the angle of a slope is, the less effective this feature is.

Fig. 32. Posture of testbed vs time on a slope with 0°.

Fig. 33. Posture of testbed vs time on a slope with 5°.

Fig. 34. Posture of testbed vs time on a slope with 10°.

Fig. 35. Posture of testbed vs time on a slope with 15°.

Fig. 36. Posture of testbed vs time on a slope with 20°.

Fig. 37 shows the graph comparing the amounts of movement. The amount of movement in the proposed walking is larger than one in the walking without vibration. The testbed slipped and did not move forward in a slope of 10° when it walked using the walking without vibration. In this result, the running performance was improved by using the proposed walking.

Fig. 37. Amount of movement in each walking.

Finally, we discuss the advantage and weaknesses of the proposed walking. On the advantage, a legged rover is difficult to fall down because the posture angle of a legged rover is decreased by using the proposed walking. Moreover, the amount that a legged rover walks becomes large by using the proposed walking. On the weakness, the time during one cycle of walking motion in the proposed walking is longer than one in the walking without vibration. The reason is that the time of vibrating legs is added in the proposed walking. In this study, shortening of vibrating time is not addressed yet. This weakness will be solved when the relationship between vibrating time and running performance is confirmed in the future study.