DEVELOPMENT OF A LEGGED ROBOT FOR STUDYING AN EFFICIENT JUMPING MOTION NEAR SINGULAR CONFIGURATIONS

In this paper, we develop a prototype of legged robot to investigate whether its efficient jumping motion is achieved by using singular configurations. The experimental prototype is composed of a legged robot with three revolute joints and a tilting table on which the robot performs its jumping motion. According to the tilt angle of the table, various motions can be performed on the table from vertical jumping to horizontal pushing. The results of trial experiments for horizontal pushing indicate that, when the final posture of the robot is close to the singular configuration, the movement distance of the robot tends to be larger comparing with the case where the final posture is far from the singular configuration. INTRODUCTION In recent years, many efforts have been made to develop various robots that can work for humans. Such a robot is required to perform as many kinds of tasks as possible in unknown environments. According to a task that a robot encounters unexpectedly, the actuators mounted on the robot may be insufficient to achieve it if the robot’s motion is planned in a naive manner. In order to increase the number of achievable tasks, it is necessary to use the actuators in the most effective way in accordance with each task. For dynamic tasks such as lifting heavy objects and jumping over a step, robot’s motions that utilize singular configurations would be advantageous in achieving them with the limited capability of actuators [1-3]. At singular configurations of manipulators, the kinematic relationship between the joint velocity and the end-effector velocity is singular [4]. In motion planning and control of robot manipulators, singular configurations have usually been avoided due to the kinematic singularity [5]. On the other hand, the dynamic aspects of singular configurations have not been paid enough attention to. Despite the possible advantage in dynamic tasks, the dynamic features of singular configurations have not been unveiled yet [6]. We have been tackling the problem of revealing the dynamic features of singular configurations through theoretical analysis, numerical simulations and experiments [7-9]. In [9], we have obtained, through numerical optimization, an optimal jumping motion of a legged robot, where the final posture of the robot is close to its singular configuration. In this paper, we develop a prototype of the legged robot for the purpose of investigating the advantages of singular configuration in jump or push motion from a practical aspect, and present the results of trial experiments for horizontal push motion. The experimental results indicate that the singular configuration of the robot would have an advantage in pushing a springboard strongly to obtain a long movement distance of the robot. EXPERIMENTAL APPARATUS The experimental apparatus is composed of two parts: a legged robot and a tilting table. The legged robot performs a jump or push motion on the tilting table, and the load acting on 205 Proceedings of 2018 ISFA 2018 International Symposium n Flexible Automation Kanazawa, Japan, 15–19 July, 2018 the robot is reduced according to the tilt angle. By using the apparatus, we can perform various experiments from vertical jumping to horizontal pushing. The outline of the two parts will be shown in the following sections. Legged robot Figure 1 shows the skeletal structure of the lower limb of a human and its simplified model. The legged robot imitates the skeletal structure and has the same simplified model with three revolute joints. The four links of the robot are called trunk, Link 1, 2 and 3 as in Fig. 1, and Link 1, 2 and 3 correspond to thigh, lower leg and foot respectively, while Joint 1, 2 and 3 correspond to hip joint, knee joint and ankle joint. The total mass of the legged robot can be increased by putting an additional weight in the trunk. We built a prototype of the legged robot to demonstrate a jump or push motion as shown in Fig. 2. The right picture in this figure shows the joint of the robot. The specification of legged robot is summarized in Table 1. The robot has three servo motors (Dynamixel AX-12A) that are mounted at Joint 1, 2 and 3 as actuators. Figure 3 shows the sketch of motor control system. In the experiments that will be presented later in this paper, desired rotation angles for the three joints are transmitted to the corresponding motors simultaneously from the microcomputer (Vanadium Labs ArbotiX-M Robocontroller) mounted in trunk. Although the motor without load rotates at the speed shown in Table 1, the actual rotational velocity in the experiments depends on the load to each motor. Maximum total length 1080 mm