This paper first presents a novel control strategy for periodic motion control based on a Hamiltonian system. According to the strategy, hybrid symmetric orbits (ideal walking gaits) are explored using reversal symmetry of the Hamiltonian system. Then, an invariance controller, a Symmetric Walking Controller, is derived systematically to distribute the symmetric orbits densely throughout the entire phase space. Finally, a new robust walking speed controller is formulated based on the passivity of the controlled system. Consequently, solutions starting from any point globally converge to a stable limit cycle having a desired energy level. The controller has strong passivity and robustness, thereby rendering it capable of using external disturbances as energy for walking propulsion. It requires no model parameters and can be implemented in a very small program size. Furthermore, it is applicable to any biped robot without major modification. In this report, the effectiveness of this controller is proved mathematically, validated numerically, and confirmed experimentally.

In this paper, we extend the running controller of a passive one-legged hopper to a planar biped robot with torso, and evaluate the controller on simulations. The controller is derived based on an energy-preserving strategy and it actually preserves mechanical energy at touchdown. Interestingly, zero dynamics of decoupling controller (dynamics about a pair of controlled legs) is found to be stable. Combining the simple attitude controller at stance phase generates stable periodic running gaits of arbitral period. The control performance is shown to be better than a simple PD-feedback control of leg placement.

In this paper, we report on passive running of planar one-legged, biped, and quadruped robots. The topic includes the analysis of passive running gaits and their orbital stabilization. For one-legged robot, two stabilizing controllers that asymptotically stabilize periodic passive gaits are derived. In particular, the second controller is based on energy-preserving principle and its original form generates interesting quasi-periodic running gaits, which can be seen in Hamiltonian system. The controller is extend to a planar biped robot with torso, which does not have any passive running gaits. Combining simple attitude controller at stance phase generates stable periodic running gaits. For a planar quadruped robot, with an advanced gait searching algorithm, some fundamental properties of the passive running gaits, such as stability or symmetry, are observed.

This paper reports on a gymnastic robot, which are developed for various floor exercises such as jumping, somersault and back handspring. The robot is a planar and serially connected four-link robot, whose joints are fully actuated by electric servomotors. In this paper, the modeling and the controller for back handspring are addressed. The controller is derived from task-specific target dynamics and its model matching. The use of global physical quantities such as center of mass, or angular momentum allows even simple target dynamics to generate complex gymnastic motions of multi-body system. The effectiveness of the controller is confirmed via simulations and experiments.

A new 3D biped prototype with small DOF, SKIPPER, was developed. As an important component of a running controller for this robot, an aerial posture controller is presented. This is the extended version of planar running controller, which was previously developed for a passive one-legged hopping robot, and plays important roll for orbital stabilization at the lowest control layer. The controller stabilizes three output functions defined as lateral leveling, holonomic constraint of pitch dynamics, and linearization of swing leg dynamics. Simulation results show that the robot achieves desired posture control for wide sets of initial conditions, naturally utilizing its compensator around yaw axis. In this paper, after describing the 3D biped model and its basic running control strategy, the details of the aerial posture controller are presented, as well as the simulation results.

In this paper, we present a novel controller for a passive one-legged hopping robot. First, based on the dynamics of this nonlinear hybrid system, we derive a simple control law to ensure the total energy preservation and continuation. Simulation results show that the robot can hop from the wide set of initial conditions. The generated hopping gaits are found to be quasi-periodic orbits, which can be seen in some Hamiltonian systems. Next, we propose a simple parameter adaptation law to asymptotically stabilize the quasi-periodic gaits to the periodic gaits of arbitrary period, and spring stiffness adaptation law to minimize control inputs. Simulation results show that the robot eventually hops without any control inputs, especially for 1-periodic gait. We believe that the controllers we invented have much potential for energy-efficient control of legged running robot.

Walking robots are useful for uneven terrain where wheels or crawlers are unsuitable. The biped robot is a kind of walking robot that we can use under human-live environments. There are many research works on biped robots. The biped robots need ability to adapt itself to uneven or non-horizontal plane if we want to use them in our environment although the robots walked on flat horizontal plane or fixed inclined plane in most of these works. In this paper, we propose a control method for walking of biped robots on undulating ground. This method contains grade estimation of ground using stereo vision and walk of robot on slope. Experimental results that indicate ability of this method are also shown.