Position and inclination control of a passive disk based on cyclic motion generation

Aoyama et al. Robomech J Position and inclination control of a passive disk based on cyclic motion generation Tadayoshi Aoyama ‑u.ac.jp 0 2 Qingyi Gu 1 Takeshi Takaki 0 2 Idaku Ishii 0 2 0 Department of System Cybernetics, Hiroshima University , 1‐4‐1, Kagamiyama, Higashi‐Hiroshima 739‐8527 , Japan 1 Research Center of Precision Sensing and Control Institute of Automation, Chinese Academy of Sciences , 95 Zhongguancun East Road, Beijing 100190 , China 2 Department of System Cybernetics, Hiroshima University , 1‐4‐1, Kagamiy‐ ama, Higashi‐Hiroshima 739‐8527 , Japan We propose a position and inclination controlling method for a passive object using an active plate. Previously, we proposed a novel manipulation scheme that can control a passive object's orientation using an active plate. In the work, stable plate cyclic motion is designed and inclination control of the object is realized. However, the object's position is not considered, so there is a possibility that the object could move. Using our plate trajectory design we can control not only the passive object's inclination but also its position. We verify that the designed plate motion can control both the object's inclination and its position through dynamics simulation. A stability analysis around a fixed point is conducted using a Poincaré return map, demonstrating that fixed points are asymptotically stable. Cyclic motion; Nonlinear discrete system; Manipulation - Rhythmic motion control has been an important research topic studied for many years in robotics and mechatronics [1–18]. Legged locomotion is one type of rhythmic motion that requires cyclic stability. A simple hopping robot using a leg composed of a double-acting air cylinder was built, and completely dynamic, stable hopping locomotion was realized [1]. The designed controller can handle hopping motion, forward speed, and body upright attitude. Koditschek et al. theoretically analyzed the motion of Raibert’s hopping robot [1] by using simplified models of the hopping robot [2]; it has been confirmed that the modeled properties match those of Raibert’s physical data. A three-dimensional (3-D) biped walking controller that ensures cyclic stability based on passive dynamic autonomous control (PDAC) [19] was proposed, and 3-D biped walking using an actual robot was realized [3]. Moreover, the adaptability of the cyclic motion to terrain has been analyzed, and 3-D biped walking on nonflat terrain was realized experimentally [4]. Juggling is also a task that requires cyclic stability with dynamic dexterity. Koditschek’s group has been studying robotic juggling for many years [5–8]. Bühler et  al. proposed a mirror algorithm from their successful experiments that can determine the trajectory of a robot paddle as mirrored [5]. A robot that can juggle up to two pucks was realized by using the feedback strategy of the mirror law. In addition, the proposed algorithm was developed further and juggling and catching of two objects has been experimentally realized [6]. The mirror law was modified for spatial two-object juggling and the algorithm was verified through experiment using a three-degrees-offreedom robotic arm along with a real-time stereo camera system [7]. Some research groups have proposed nongrasping manipulation schemes using an active plate, which also require cyclic stability [9–17]. Senforless positioning and orientation adjustment have been realized using a flexible vibrating plate [9]. The vibrating plate is able to create a two-dimensional programmable force field and generated sequences of force fields. A vibratory transport mechanism using an active plate was proposed by Umbanhowar and Lynch, and the transportation behavior was verified through experiments using a vibrating plate [10]. Vose et al. analyzed the bang-bang motion of a rigid plate and derived the generation of nodal lines; the analysis results were verified through comparison between numerical simulation results and experimental results obtained © The Author(s) 2017. This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. from an experimental active plate system with six degrees of freedom [11]. In addition, a mechanism to predict the relationship between the small-amplitude cyclic motion of a six-degrees-of-freedom rigid plate and its velocity field, called asymptotic velocity theory, has been developed [12]. The importance of the asymptotic velocity for characterizing plate motion was verified through simulations and experiments. Ronsse et al. proposed and experimentally verified sensorless stabilization of bounce juggling based on a stabilization analysis in rhythmic tasks using (...truncated)