IROS2019国际学术会议论文集2326

Evaluation of Hopping Robot Performance with Novel Foot Pad Design on Natural Terrain for Hopper Development Kosuke Sakamoto1, Masatsugu Otsuki2, Takao Maeda3, Kent Yoshikawa4, and Takashi Kubota2 AbstractThis paper presents the hopping performance evaluation on 3 types of terrains and novel foot pad designs for effi cient traverse of hopping rovers. Hopping rovers, called Hopper, are expected to explore scientifi c richness areas where wheeled vehicles are hard to traverse. In order to succeed in the robotic planetary exploration, optimization and effi cient designs of rovers are essential. Almost planetary surface are covered with sand, called regolith, which make hopping effi ciency bad. In this paper, we discover the hopping performance on three kinds of terrains. Moreover, we also propose the method of increasing hopping performance on soft soil. Inspired by the conventional wheeled vehicle design, treads, called grouser, are installed on the bottom of the foot pad. While grousers are eff ective on hard ground and soft soil, they are ineff ective on bilayer terrain. Bilayer means that hard ground is covered with thin regolith. And the other novel grouser shape is designed based on the soil interaction model using a multi- objective evolutionary algorithm. The proposed design improve the hopping performance on soft soil in comparison with the straight grouser. I. Introduction How to expand planetary exploration area? Planetary sur- face exploration has been conducted using wheeled vehicle robots, called rover. Lunokhod 1 and 2 1, and ChangE- 3 and -4 2 had been developed to explore the Moon and succeeded in their missions. The Martian surfaces had been explored by Sojourner 3, Spirit and Opportunity 4, and has been being explored by Curiosity 5. Recently, various environments, such as a Recurring Slope Lineae (RSL)6, are expected to research by robots. However, such environments are often hard to traverse using wheeled rovers. Hopping rovers, called hopper, are one of the solutions to perform on challenging terrains. In practice, a few hoppers have been designed to traverse diffi cult terrains in high- level gravity environments 7, 8, 9. The eff ectiveness of hopper has been shown by a few missions for low- or ultra- low gravity celestial bodies: MASCOT developed by DLR and MINERVA-II in the Hayabusa-2 mission 10 succeeded their exploration on the Ryugu asteroid. As other hoppers, there are the MINERVA 11 in the Hayabusa mission and the PrOP-F 12 in the USSR Phobos-2 mission. 1K. Sakamoto is with Department of Electrical Engineering and Infor- mation Systems, The University of Tokyo, 7-3-1 Hongo, Bunkyo, Tokyo, Japan.k_sakamotoac.jaxa.jp 2M. Otsuki and T. Kubota are with Institute of Space and Aeronautical Science, Japan Aerospace Exploration Agency, Sagamihara, Kanagawa 252- 5210, Japan. 3T. Maeda is with Faculty of Electrical, Electronic, and Communication Engineering, Chuo University, Bunkyo, Tokyo 112-8551, Japan. 3K. Yoshikawa is with Research and Development Directorate, Japan Aerospace Exploration Agency, Sagamihara, Kanagawa 252-5210, Japan. Planetary surfaces are almost covered with granular media, called regolith. Although rovers have to traverse on such terrains, they have faced various diffi culties by locomotion on soft soil. In fact, Spirit got involved in trouble when Spirit was moving on sandy terrain. The trouble is that Spirit got stuck in sand, and could not escape from the embedding in sand. The locomotion mechanics of wheel on soft soil has been studied in the fi eld of terramechanics 13, 14. However, the hopping has been scarcely investigated, mainly because of a dynamics of granular media which are diffi cult to explain by conventional models 15. In order to improve locomotion effi ciency of rovers on natural terrains, there are mainly two methods: an adaptive motion control depending on environments, and a hardware design which improve traversability. In this paper, we focus on hardware design because hardware designs greatly aff ects motion control. Hoppers have not been used for actual plan- etary exploration so far, because there are a lot of challenges to tackled, especially related of hardware design. The contribution of this paper is the discoveries about hopping performance on natural terrains. This paper presents the two main results : To evaluate the hopping performance with foot pads on three types of terrains. To design the grousers shapes to improve the hopping performance on soft soil. One of the main factors causing a decrease of locomotion performance is slip on the soil surface. The proposed designs can reduce slip. Studies exist about the effi ciency of wheeled locomotion on soft soils 16, 17, 18, 19. However, to the best of our knowledge, there are few hopping platform designs suited for the locomotion on sandy soil. A design of foot pads is an important task to improve traversability. Locomotions on sandy soil often leads to slip because of the deformation of the granular media. In order to prevent slip, the key technique is to get enough resistive force from soil. Some treads, called grousers, are attached to the foot pad to generate an additional resistive force by embedding in sand. The eff ectiveness of grousers has been validated for conventional wheeled rovers20, 21. This paper shows the eff ectiveness of grousers through hopping experiments and proposes novel grouser shapes. In addition, one of the shapes is designed based on the soil interaction model by using a multi-objective evolutionary algorithm. Section II reviews related works on this topic. Section III presents the proposed designs of the foot pads for eff ective hopping locomotion on granular media. Section IV describes the evaluation method IEEE Robotics and Automation Letters (RAL) paper presented at the 2019 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS) Macau, China, November 4-8, 2019 Copyright 2019 IEEE of the eff ectiveness of the proposed foot pads, and Section V validates the proposed design through hopping experiments. Finally, Section VI summaries this paper. II. Related Works The performance of locomotion on granular media is lower than on hard ground, because it is harder to get friction than on hard ground. Thus, mobile robots require additional equipment in order to improve their locomotion performance on such terrain. The Martian rovers have rigid wheels with low grousers. One of the examples is the wheel of Curiosity 22, which is 50 cm in diameter and 40 cm wide. The grousers on these wheels intrude into soil, and generate traction force by raking granular media. In addition, grousers can help rovers to climb over obstacles by hooking on the surface. Axel rover showed the eff ectiveness of grousers by using simple physical analysis 16. Axel has two wheels with paddles and can climb up/down steep slopes using tether from mother ship rover. This design is often applied to small rovers which are not equipped with large suspension system, such as the rocker-bogie system 17, 18. Coyote II is a wheel-leg combination platform 19. These legged-wheels sink in the soil shallower than conventional wheels, which can prevent them to be stuck in the sand. Yeomans et al. designed foot pads which were mounted on the tip of the legs 23. They studied the thrust force vs sinkage depth of four kinds of shapes and the prediction of the drag force. Although there are several conventional works which focus on the wheel-based platforms, there are few studies about other type of platforms. In addition, these works are based on empirical designs. One of the reasons is the lack of knowledge about the interaction with granular media. In particular, the dynamic interaction, such as hopping, is so complex that we dont have enough knowledge about the physical properties of granular media. This study also employs the empirical model presented in 24, and evaluates the eff ectiveness of the proposed design through experiments. One of the examples using this interaction model is the foot pad of lander for celestial bodies 25. This paper presents the eff ectiveness of RFT-based model to design landing-gear foot pads. III. Foot Pad Designs This section presents proposed foot pad designs for effi - cient hopping locomotion on soft soil. The hopper used in this study consists of two main parts: the hopper body and the contact part with the ground, called foot pad. In one of our our previous work26, we observed that the hopping performance decreases on soft soil mainly due to slipping. In order to prevent slipping, some grousers are attached to the bottom of the foot pad. The eff ectiveness of grousers have been demonstrated by various studies of wheeled rovers described in section II. In the following sections, the foot pad without grousers is called “fl at pad”, and the foot pad with grousers is called “grouser pad”. This paper presents (a) The fl at pad.(b) The straight grouser pad. (c) The V grouser pad(d) The SIB grouser pad. Fig. 1: The CAD image of the proposed foot pads. three kinds of grousers: straight, V, and Soil interaction based (SIB) shape. A. Flat Pad The CAD image of the fl at pad is shown in Fig.1a. The size of a foot pad is 6 cm width, 8 cm length, and 0.3 cm thickness. All foot pads have two attachment parts on top to connect with the hopper body. This fl at pad is also used for the other foot pads as a base frame. B. Straight Grouser The CAD image of the straight grouser pad is shown in Fig. 1b. This simple shape is based on the conventional wheels grouser. Three grousers, 1 cm high and 0.2 cm thickness , are attached to the plate. The longitudinal direc- tion of the grousers were the same as the initial attitude angle (injection angle) of the hopper. The reason for this is to make the extracting resistance as low as possible. The number of grousers is three. These designs of grousers (number and size) have been decided as follows: All grousers can sink into the soil. If the size of grousers is large or the number of grousers is big, grousers cannot sink enough into the soil. In addition, resistance force while extracting is proportional to these parameters. This is why that these values are employed. C. V Grouser The CAD image of the V shape grouser pad is shown in Fig. 1c. This pad is the same size as the straight grouser pad. The grouser of this pad is bended as “V” Shape. The valley side faces opposite to hopping direction in order to get enough resistive force from soil. The angle of this valley is 2tan12 126.9 deg. This angle is decided based on the foot pad side and number of grousers. D. Soil Interaction Based Grouser RFT 24 is one of the effi cient empirical interaction models. The model is expressed as follow: Fx,z= x,z(,)zdA(1) Fig. 2: The problem design. Fig. 3: The calculated design of the SIB grouser shape. where, Fx,z, , x,z, z, and A denote the resistive force from soil, the soil parameter called scaling facter, the stress per unit depth, the sinkage depth, and the interaction area, respectively. RFT assumes that the resistive force acts on the micro plate which move in granular media with the attack angle and the moving direction , and then, calculates by integrating the resistive force along the interaction area. The details of x,zare described in 24. RFT can be applied to various mobility platforms, and RFT-based interaction model is also eff ective for hopping 15. This paper presents the SIB grouser shape as the solution of a multi-objective optimization problem (MOP) based on RFT. The objective functions are the hopping distance and the hopping height, because one of the most important challenges is to improve hopping performance. The hopping distance and height are simulated by calculating the resistive force using RFT. The MOP decides the grouser shapes which are maximizing these objective functions. The constraint is the grouser height to (a) Hopping on hard ground.(b) Hopping on soft soil. Fig. 4: The dynamic model of hopping; (a): Hopping on hard ground without slip; (b): Hopping on soft soil. v denotes the initial velocity of the bodies, denotes the hopping angle, and d1and d2denote hopping distance on hard ground and on soft soil respectively. be 1 cm. The shape of the grouser is decided as follows: set 11 points per 1 mm between 010mm in the vertical direction (z-axis), then connect all points by drawing straight lines. These points can take any values between 010 mm in the horizontal direction (x-axis). These points are design variables. This problem design is illustrated in Fig.2. To solve this MOP, “NSGAII” is used , which is one of the multi- objective evolutionary algorithms (MOEAs). The reason is that NAGAII performs well to solve two objective functions with few constraint 27. The “PlatEMO” 28 is used to solve this MOP. In this optimization, populations size is 300, and the number of evaluation is 20,000. These numbers are decided empirically. The obtained shape is shown in Fig.3 and the SIB pad is shown in Fig.1d. Actually, the SIB grouser is designed so that one side is the optimized shape and the other side is parallel with the initial hopping angle. In order to minimize the resistance when the grousers are drawn out from the soil. The shape can be divided into two part; the upper part and the lower part. It is thought that the upper part increases the vertical resistive force in order to improve the hopping height and the lower part prevents slip in order to increase hopping distance. IV. Evaluation Method This section describes the evaluation method of hopping performance. A dynamic model of parabolic hopping is considered and illustrated in Fig.4. In this model, hopping is caused by a spring which follows the Hookes law. In general, hopping performance depends on the conditions of the terrain. Hence, we evaluate hopping by the following parameters on each terrain: distance, angle, and energy effi ciency. A. Distance The “Distance” is one of the most important performance of the hopper. Therefore, this paper evaluate hopping dis- tances on each terrain by comparing with ideal condition, i.e., hard ground with large enough friction to prevent slip. B. Angle Knowing hopping angle is essential for accurate hop, because the hopping distance and height are determined by the hopping angle and the kinetic energy. The larger the gap between an injection angle (setup angle) and an actual hopping is, the lower the accuracy of hopping is. Hopping is high speed motion, and hence a hopping angle control is diffi cult while hopping. We can discuss controllability of hopping angle by studying the gap between angles on various of terrains. Hopping angle is defi ned by: = tan1 ( vz vx ) (2) where vxand vzare the initial velocity of horizontal and vertical direction of a hopper, respectively. In this paper, the hopping motion is assumed to follow a parabolic trajectory. These velocities are obtained as vx= gd/2vz, vz= 2gh. Where d and h are the hopping distance and height of the hopper respectively. Therefore, an actual hopping angle is calculated by: = tan1 ( 4h d ) (3) This paper uses the following hopping angle range: 45deg, because of actual missions requirements. In ideal conditions, the maximum hopping distance is at = 45 deg and the maximum hopping height is at = 90 deg. C. Energy Evaluating the energy effi ciency is important to design mobile robots. Here, “effi ciency” means the amount of the kinetic energy loss. In general, it is diffi cult to estimate or to calculate the energy dissipation on natural terrain. However, in the case of hopping motions using springs, it is easy to calculate energy balance by assuming Hookes law. The total energy in this system is described by: Etotal= 1 2 kx2(4) where k and x denote the spring constant and the initial sinkage. The elastic energy 1 2kx 2 is converted immediately before hopping as follows: 1 2 kx2= 1 2mv 2 0 + Eloss+ Edis(5) where m, v0, Eloss, Edisdenote the mass of the body, the velocity in the hopping direction, the mechanical energy loss including damping, and the energy dissipation to the soil, respectively. In the case of hopping on hard ground without slip, i.e., Edis= 0 is assumed. It is also assumed that the body stops exactly on the landing point when the body touches the ground. The following relation between the hopping distance, d, and the velocity, v0, is obtained: d = v2 0 g sin(2)(6) TABLE I: Parameters used in simulations and experiments. TermsSymbolValueUnit Gravitational accelerationg9.81m/s2 Mass of bodyM0.090kg Mass of foot padm0.020kg Spring coeffi cientk1225N/m Damping coeffi cientc5.42Ns/m Mechanical lossEloss0.65J Initial sinkage of springd0.037m Initial positionz00m Width of foot padw0.08m Length of foot padh00.06m Thickness of foot padb0.003m where g and denote the gravitational acceleration and the hopping angle respectively. The initial kinetic energy of the body is calculated by Eq.(7): 1 2mv 2 0 = mgd 2sin(2) (7) With d1 defi ned as the hopping distance on ideal surface and d2 defi ned as the hopping distance on real surface, Edis is expressed by: Edis= mg(d1 d2) 2sin(2) (8) This equation implies that part of the kinetic energy is dissipated in the soil. As consequence the diff erence of hopping distances is proportional to a diff erence of kinetic energy, i.e. Energy dissipation by the soil. V. Experimental Study This section describes the experimental evaluation of hopping with the proposed foot pads on each terrains. The experimental terrains are shown in Fig.5. This experiments were tested on three types of terrain: hard ground, bilayer ground, and soft soil. A wood-board is used as a hard ground. Bilayer ground represents the terrain which is hard ground covered with thinly sand or regolith. In this experiments, the constant weight of sa