Swinging Up and Stabilization Control of Double Furuta Pendulums by Safe Manual Control Keigo Noguchi, Masaki Izutsu, Norihiro Kamamichi, Tetsuo Shiotsuki, Jun Ishikawa and Katsuhisa Furuta Abstract—In this paper, we propose a control method to swing up and stabilize a double Furuta pendulums (DFP).The DFP is a rotational type inverted pendulum system that has a base-link and two pendulums of different length at the both ends of the base-link. The proposed method consists of three controllers for the DFP, i.e., a swinging up controller for a long pendulum, a controller to keep a long pendulum at the upright position and to swing up a short pendulum simultaneously, and a stabilization controller for both pendulums at the upright position. Since the second controller has two objectives, we use safe manual control[3] proposed by ˚ Astr¨ om and ˚ Akesson. This paper proposes a novel application of the safe manual control. Swinging up and stabilization of the DFP was success- fully achieved by appropriately switching three controllers. The effectiveness of the proposed method was verified by simulation and experiment. I. I NTRODUCTION Inverted pendulums have been widely used as controlled plants to evaluate validities of control theories. The double furuta pendulums (DFP) has a rotational base-link and two pendulums at the both ends of the base-link. The DFP is controlled by a direct drive (DD) motor attached to the base- link. The lengths of the two pendulums are different from each other, and the characteristics of the DFP are changed depending on the lengths of the two pendulums. From this characteristics, the DFP is used as a benchmark to check the abilities of control theories for underactuated mechanical systems[2]. In this paper, we propose a control method to swing up and stabilize the DFP. The designed controller can stabilize both pendulums at the upright position, swinging them up from the pendant position. Dynamics of the DFP are changed fully depending on the states of the both pendulums. In order to achieve the control objective, the proposed method is consisted of three controllers. These controllers are switched by the states of the DFP. The purposes of the controllers respectively are as follows: (1) swinging up a long pendulum, (2) keeping a long pendulum around the upright position and swinging up a short pendulum, and (3) stabilizing both pendulums at the upright position. Then, the first controller is designed by energy control[6] for a long pendulum ignoring the motion of the short pendulum. K. Noguchi, M. Izutsu, N. Kamamichi, T. Shiotuki and J. Ishikawa are with the Department of Robotics and Mechatronics, School of Science and Technology for Future Life, Tokyo Denki University, 2-2, Kanda Nishiki- cho, Chiyoda-ku, Tokyo 101-8457, Japan, phone: +81-3-5280-3915; fax: +81-3-5280-3793; ishikawa@fr.dendai.ac.jp. K. Furuta is with Tokyo Denki University and is a Fellow of IEEE, a Distinguished Member of IEEE Control Systems Society The second controller is needed to control the pendulums so that two different objectives can be simultaneously achieved, i.e., a swing-up control and stabilization control. For this purpose, we use safe manual control proposed by ˚ Astr¨ om, ˚ Akesson. Usually, the safe manual control is used for a combination of manual control and automatic control, but it also can be used for combining two different automatic controls, i.e., a stabilization control of a pendulum and a velocity control of the base-link of the inverted pendulum system. In this paper, we apply the safe manual control, replacing the manual control part with automatic swinging up for a short pendulum. The third controller is designed by common linear control theory because two pendulums can be linearized around the upright position. The effectiveness of the proposed controller is verified by simulation and experiment. II. DOUBLE FURUTA PENDULUM SYSTEM In this section, an equation of motion of the DFP is derived by Euler-Lagrange method. The schematic model of the DFP is shown in Fig. 1. The parameters of the DFP are listed in Table I. The equation of motion of the DFP is given by M (θ) ¨ θ + H(θ, ˙ θ)+ G(θ)= τ (1) where θ =[θ 1 ,θ 2 ,θ 3 ] T and τ =[τ 1 , 0, 0] T , and M (θ) is inertia matrix, H(θ, ˙ θ) is term of coriolis force and friction Long pendulum (Link 2) Short pendulum (Link 3) Base link (Link 1) 1 θ 2 θ 3 θ Fig. 1. Schematic diagram of DFP The 2009 IEEE/RSJ International Conference on Intelligent Robots and Systems October 11-15, 2009 St. Louis, USA 978-1-4244-3804-4/09/$25.00 ©2009 IEEE 4232