IROS2019国际学术会议论文集0559

Development of an adaptive hexapod robot based on Follow-the-contact-point gait control and Timekeeper control Yuki Murata1, Shinkichi Inagaki1and Tatsuya Suzuki1 AbstractIn this paper, a new control method for a hexapod robot walking on irregular terrain based on a human operators foot-placement navigation is proposed and evaluated. The control method is based on the Follow-the-contact-point (FCP) gait control that operates on the principle that each leg follows the contact point of its foreleg. Hence, planning the contact points for all the legs are summarized to one of the front legs. To dedicate the FCP gait control to a hexapod robot, three control architectures are added. First, new constraints in the transition from a stance phase to a swing phase are added to maintain static stability when a leg leaves the ground. Second, a real-time posture control system for contacting legs is added. The third is an adaptive control to adjust the time elapsed in each control mode, by which specifi cations of deadlock-free and static stability are satisfi ed. The proposed control architecture is installed to a small hexapod robot, and its performance is evaluated through experiments wherein the robot walks on uneven terrain. I. INTRODUCTION Mobile robots are often required to traverse irregular terrains during exploratory activities in disaster-like sites and uncharted territories. In particular, hexapod robots are expected to have not only high stabilities but also diverse ranges of walking motions due to their redundant number of legs and the mechanisms that control them. Such hexapod robots are designed to be capable of navigating many dif- ferent environments and performing many tasks. One major consideration of such robots is the management of all six legs to allow the robot to keep walking even on irregular environments. One method, called Free gait, is based on the optimization of all the legs movements 1-5. The behaviors of the legs are planned by considering their contact points and the desired body posture simultaneously. However, since the computational burden of this method is high, due to the many degrees of freedom involved, real-time control by this method is diffi cult for small onboard computers. Another approach relies on the particular mechanism of the legs. RHex 6 is a multi-legged robot whose legs have high elasticities and only one joint. This robot shows great traversability on complex irregular terrains while maintaining a low computational burden. Unfortunately, the robot is not able to maintain its body in one desired posture because of the low degrees of freedom. Tasks such as carrying an object are therefore diffi cult for this robot. 1Yuki Murata,ShinkichiInagaki,andTatsuyaSuzuki,are withtheDepartmentofMechanicalSystemEngineering, NagoyaUniversity,Furo-cho,Chikusa-ku,Nagoya,Aichi,Japan. y murata,inagaki,t suzukinuem.nagoya-u.ac.jp Another approach to deal with the issue of high com- putational burden is a decentralized calculation. A model called the central pattern generator (CPG), which comprises a network of neurons in the central nervous system, is used to control the locomotion of legged robots7-10. CPG- based robots are capable of adaptively walking on moderate irregular terrains using sensory feedback. An event-driven decentralized walking control called “Follow-the-contact-point (FCP) gait control” proposed by Inagaki et al. 11 was inspired by the earlier “Follow-the- leader gait control” 12. Both methods are based on the principle that each leg lands on the same contact point that the preceding foreleg has already contacted. FCP gait control achieves this using a decentralized control architecture. The advantage of this principle is that the overall planning of all the legs is centralized on just one of the front legs. FCP gait control is easy to install on a small onboard computer, thanks to its decentralized calculating and its concentrated foot placement planning. However, the original FCP gait control does not consider posture control, because it has been proposed for a centipede- like robot. In this study, a hexapod robot was used. Because a hexapod robot has more legs than biped and quadruped robots, it is easier for a hexapod robot to keep stable walk- ing. However, it has also shown that even hexapod robots often fall down, especially on complex irregular terrains. Therefore, a hexapod robot also requires adaptive control for tumble stability. In addition, this type of robot needs another type of adaptive control to suitably adjust the movement rhythms of legs that are disturbed by the fi rst adaptive control. In this paper, the former problem is solved with an improved FCP control. The latter issue is solved using a “Timekeeper control.” In order to solve the fi rst issue, three points are added to the FCP gait control: the fi rst one consists of the constraints which are added to the condition when a standing leg transitions into a swing phase; The second is real-time balance control, which is added to the legs in the stance phase; The third, in order to guarantee the robot a statically stable walk, is a new adaptive control architecture weve called “Timekeeper control.” This new method adjusts the timing to transition the control mode in the FCP gait control, so as to guarantee a deadlock- free statically stable walk. Finally, the effectiveness of the proposed control method is demonstrated by a small hexapod robot with a human-in-the-loop control navigation interface. The remaining sections of this paper are organized as follows: the hexapod robot used in this paper is discussed in section II, the improved FCP gait control for the hexapod 2019 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS) Macau, China, November 4-8, 2019 978-1-7281-4003-2/19/$31.00 2019 IEEE3321 Fig. 1.Hexapod robot Fig. 2.Each mode and transition condition in control automaton robot is explained in section III, the Timekeeper control is introduced in section IV, the experimental specifi es of the hexapod robot and the human-in-the-loop navigation interface are introduced in section V, the experimental results are shown in section VI, and this paper is fi nally concluded in section VII. II. MECHANISM OF THE HEXAPOD ROBOT The hexapod robot used in this study is shown in Fig. 1. The robot consists of a body and six legs, which are located radially. Each leg has three links: Link1, 2, and 3, and three motors. The two legs in the moving direction are defi ned as left and right front legs. The right legs are labeled as Legi (i = 1,2,3) from front to back, and the left legs are similarly designated as Legi (i = 4,5,6). The leg which is located laterally opposite to Legi corresponds to Leg(i + 2) mod 6+1. A coordinate system B is fi xed on the body, with its origin on the center of the body. The y-axis of B is defi ned as the front direction, and the z-axis as the upper one. The reachable area of Legi is defi ned as iand the boundary of i is defi ned as i. Note that the legs are located so that the reachable areas of neighboring legs overlap.In addition, Link1 is tilted by 45 against the body, so that each leg can exchange its contact points with its adjacent legs without the links colliding one another. III. FCPGAIT CONTROL MODIFIED FOR STATIC STABILITY A. FCP gait control for a hexapod robot In this section, the FCP gait control for a hexapod robot is introduced. In this control, each leg has a control automaton and is controlled according to the control modes in the automaton. The control modes transition in the order of mode 1 2 3 4 1 (Fig. 2). The control modes and the transition conditions are detailed as follows: 1) Control mode 1: The leg tip raises from the ground and approaches an intermediate point P1at a speed of v1. When the leg tip reaches P1, the control mode transitions to mode 2. 2) Control mode 2: The speed of the leg tip is set to v2= 0, and the leg tip stays at the intermediate point P1. For the leading front legs, Legi (i = 1,4), when a new contact point is identifi ed in the reachable areas 1and 4, respectively, the control mode transitions to mode 3. The new contact points are given by the human operator in this study. For trailing legs, Legi (i = 2,3,5,6), when the leg tips of the forelegs enter the reachable area i, the control mode transitions to mode 3. 3) Control mode 3: The leg tip moves to the next target point P3at a speed of v3. When a trailing leg exchanges its contact point with a foreleg, P3is set to a point slightly apart from the contact point. For the front legs, Legi (i = 1,4), P3is the new contact point. Thus, target point P3moves with the robots progression, from the point of view of the robot. Therefore, the new contact point is tracked using an image sensor. The trailing legs, Legi (i = 2,3,5,6), always take over the former positions of the foreleg tips. When each leg tip arrives at P3, the control mode transits to mode 4. 4) Control mode 4: This control mode corresponds to the stance phase. The legs in control mode 4 propel the body with a speed of v4. The derivation of the target point P4 of the leg tip is introduced in section III-B. The transition condition from control mode 4 to 1 is explained in section III-C. B. Posture control of the body using a posture sensor In FCP gait control, the supporting legs are supposed to contact the points which the front legs have previously contacted. However, in practice, the leg tips slip and the robot occasionally falls down. In this section, posture control using a posture sensor equipped on the body is introduced, and the target point P4of control mode 4 is derived based on posture control. At fi rst, the order in which the legs contact the ground is recorded. The contacting order includes the next new contact point of the front legs. At least three legs are ensured to contact the ground by the transition condition from control modes 4-1, as explained in the next section and by the Timekeeper control introduced in section IV. From this, it is possible to make a triangle whose vertices are the last three contacting points (Fig. 3), or two last contact points and one new contact point (Fig. 4). The coordinates of the vertices of 3322 the triangle are defi ned as Ca,Cb, and Ccin the coordinate system B. A rotating matrix R(,g ,g ) from the global coordinates to the body coordinate system B is calculated in every control step. gand gare the pitch and yaw angles in the global coordinate system, respectively, and are measured dynamically by a posture sensor equipped on the body (Fig. 1). , , and , are the target values of yaw, pitch, and roll, angles, respectively, and are given by the human operator. Next, the coordinates of the target positions of the body P in the coordinate system Bare calculated as follows: P = Ca+Cb+Cc 3 +R1(,g,g)(0,0,h)T(1) where h is the target height of the body, also given by the operator. The fi rst term on the right side is the center of the triangle in Figs. 3 and-4. The second term is the vertical vector of length h, which is converted into B. A sub-target P of the body is calculated as follows: P = P |P|v4t |P| , (0,0,0)Totherwise (2) where |P| is the norm of vector P, t is the control step, and is the threshold distance to stop moving the body. Finally, the coordinates of the target point P4i of Legi in control mode 4 are calculated as follows: P4i R1(,g,g)(P4iP)(3) where signifi es updating the value in the next control step. (P4iP) is the current target position of Legi tip in order to propel the center of body by P. A rotational matrix R1is then multiplied to it in order to make the current posture angles g,gfollow , . C. Transition condition from control mode 4 to 1 The original FCP gait control 11 was proposed for a centipede robot with over ten legs. In this case, there was no need to consider violating static stability, due to the many supporting legs. On the other hand, in the case of a hexapod robot, the combination of supporting legs must be considered in order to maintain the static walk. In consideration of this, the transition conditions from control mode 4 to 1 for Legi are defi ned as follows: Condition 1 For i = 1,2,4,5, the rear leg Legi + 1 has already contacted the contact point of Legi, and the opposite side leg Leg(i + 2) mod 6 + 1 is in control mode 4. As for the rearmost legs Leg3 and Leg6, the condition is that the opposite side leg Leg6 and Leg3 both in control mode 4. Condition 2 All three legs Leg2n1+i mod 2,n 1,2,3 are in control mode 4. Condition 3 A point projected vertically downward onto the walking surface from the center point of the robot body walls within a triangle defi ned by the three Fig. 3.The three last contact points and the target position of the body: the target point of the leg tip of Legi in control mode m is expressed as Pmi. Fig. 4.The two last contact points, the next new contact point, and the target position of the body Fig. 5.The projected center of the body and the margined triangle made from three contact points points of Leg2n 1 + i mod 2, n 1,2,3, with a margin (Fig. 5). IV. TIMEKEEPER CONTROL The improved FCP gait control proposed in the previous sections has no guarantee to avoid deadlock, because added conditions may confl ict with one other. Therefore, an addi- tional control architecture to adjust transition timing of each control mode is considered in this section. First, a timed automaton is used to express the behavior of legs controlled by the FCP gait control, based on previous works 13, 14. This automaton expresses not only the control modes of the FCP gait control, but also the position of the leg. The details to derive this automaton have been skipped in this paper-for the sake of brevity. The term ti m is defi ned as the time elapsed in each control mode 3323 Supporting leg (d)All legs are supporting. (c)Only Legi is not supporting. (a)Odd or even numbered legs are supporting. Legi Legi Another leg (b)Legi 2) real-time posture control; 3) “Timekeeper control” to control time elapsed in each control mode. Finally, an experiment consisting of a small hexapod robot walking on uneven terrain with navigation dictated by a human operator was performed in order to validate the method. Development of a new robot more suitable for the proposed FCP gait control is one future direction for this work, which we are already undertaking. ACKNOWLEDGEMENT This research is subsidized by Grant-in-Aid for Scientifi c Research (16K06181). REFERENCES 1 Peter Fankhauser, Marko Bjelonic, C. 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