Dynamics Morphing between Standing and Repetitive Hopping ofBiped RobotsHiroshi Atsuta 1 and Tomomichi Sugihara 1Abstract—This paper presents a repetitive hopping controlof biped robots, which has the following properties: 1) It caninitiate or cease hopping at any time, 2) The peak altitudecan be freely altered during hopping, and 3) The impactat touchdown is suppressed. Hopping motions accompanyfrequent changes of contact conditions with the environmentand lead the discontinuity of dynamics they are governed,therefore, it is difficult to achieve the motion in a way withoutrelying any passive mechanisms such as springs and dampers.Three controllers, that is, (I) a regulator to stabilize, (II) acontroller to converge a desired velocity when lifting off theground and (III) a controller to absorb the landing impact areunified by the global scheme to transit each other dependingon a commanded value and the state of the robot.I. I NTRODUCTIONFrom a standpoint of locomotion capability particularlyon complex terrain, legged robots are superior to wheeled ortracked ones since they can step over obstacles and climbstairs. To further enhance the mobility of legged robots,motions including flight phases such as jumping and runningshould be realized. Particularly, stabilization of biped robotswhen they are subjected to external forces may requiresome small hoppings. Since humanoid robots are expected toperform precise positioning as well as dynamic motions, it isundesirable for them to sacrifice controllability through theuse of machine elements to absorb impacts such as springsand dampers more than necessity, thus, it is worth developingcontrol theory to realize such motions.Experimental research on a hopping mechanism may havestarted with Matsuoka [1], who analyzed a two-link modelconsisted with a massless leg and an upper body, andconstructed a one-legged hopping machine constrained tomove on an inclined plane. Raibert [2] and his colleaguespresented stable running motion of a hydraulically actuatedrobot with decoupled control laws. Using modified Raibert’scontroller, Gregorio et al. [3] realized an energy-efficienthopping with electrical actuators and a spring-supportedsystem. Hyon et al. [4] developed a hopping robot imitatingthe structure of a hind limb of a dog. These types ofrobots focused on development of a hopping machine andits control. However, they are not suitable for daily tasksof humanoid robots. Hopping motions themselves can beunderstood as variable constraint systems from a controltheory point of view, that is, mechanical constraints varyas the contact condition changes [5]. Many researchers have1 Hiroshi Atsuta (hiroshi.atsuta@ams.eng.osaka-u.ac.jp)and Tomomichi Sugihara (zhidao@ieee.org) are with Departmentof Adaptive Machine Systems, Graduate School of Engineering, OsakaUniversity, Japantreated the discontinuously changing dynamics of hoppingor running motions with biped robots. Hirano et al. [6]suggested a cyclic jumping control of biped robots usingthe adaptive impedance control. Kajita et al. [7] proposedan offline running pattern planning method. However, thesemethods have some limitations, such as the difficulty ofchanging the robot’s control strategy in real time. Mita etal. [8] proposed a control methodology called a variableconstraint control, which can be applied to underactuatedsystems with some constraints, and demonstrated mono-leg,biped and quadruped running. Nagasaka et al. [9] put forwarda method to plan motion trajectories of the whole bodywhich satisfy dynamical constraints. These two techniquesrequire accurate dynamical model of the robot, therefore,computational cost is high.Online trajectory-based approaches are also proposed bySugihara et al. [10], Tajima et al. [11], Ugurlu et al. [12] andso on. These methods are useful for a sophisticated motiongeneration, however, dynamic motions such as jumping andrunning require robustness against unknown disturbancesrather than preciseness of trajectory tracking. Sugihara [13]–[15] proposed a framework called dynamics morphing, inwhich manipulation of reaction forces and contact conditionswith environment are designed as a comprehensive structureof the dynamical system comprising the robot and the con-troller, and various motions such as standing [13], stepping[14] and longitudinal walking [15] are integrated seamlessly.This transition is realized by a continuous or a discontinuousmorphing of the controller. In this paper, after the idea ofdynamics morphing, we will realize standing and repetitivehopping of biped robots by designing the controller basedon the perspective what structure the whole system shouldhave as the dynamical system. Specifically, we will applya lateral nonlinear oscillation of the center of mass (COM)that was needed for the stepping motion [14] for a cyclicmotion in vertical direction, and propose a control method totransit freely between standing and repetitive hopping. Thisis achieved by the following controllers:(I) a regulator to stabilize a robot at a referential position(II) a controller to converge asymptotically to arbitraryvelocity for reaching a desired peak altitude at themoment of liftoff(III) a controller to absorb the impulsive shock exerted ontouchdown,and we propose a global control scheme to transit thesecontrollers (I)(II)(III) depending on a commanded value andthe state of the robot.2015 IEEE International Conference on Robotics and Automation (ICRA)Washington State Convention CenterSeattle, Washington, May 26-30, 2015978-1-4799-6922-7/15/$31.00 ©2015 IEEE 5704
