Satoshi Satoh

On passivity based control of stochastic port-Hamiltonian systems

This paper introduces stochastic port-Hamiltonian systems and clarifies some of their properties. Stochastic port-Hamiltonian systems are extension of port-Hamiltonian systems which are used to express various deterministic passive systems. Some properties such as passivity of port-Hamiltonian systems do not generally hold for the stochastic port-Hamiltonian systems. Firstly, we show a necessary and sufficient condition to preserve the stochastic Hamiltonian structure of the original system under time-invariant coordinate transformations. Secondly, we derive a condition to maintain stochastic passivity of the system. Finally, we introduce stochastic generalized canonical transformations and propose a stabilization method based on stochastic passivity.

Gait Generation for Passive Running via Iterative Learning Control

This paper proposes a novel framework to generate optimal passive gait trajectories for a planar one-legged hopping robot via iterative learning control. The proposed method utilizes variational symmetry of the plant model in executing the steepest decent method in the learning algorithm. This allows one to obtain solutions of a class of optimal control problems without using precise knowledge of the plant model. Furthermore, its application to a hopping robot produces a passive running gait trajectory with zero input. Some numerical examples demonstrate the effectiveness of the proposed method

Biped gait generation via iterative learning control including discrete state transitions

Abstract This paper is concerned with a gait generation for legged robots via iterative learning control (ILC) including discrete state transitions. This method allows one to obtain solutions of a class of optimal control problems without using precise knowledge of the plant model by iteration of laboratory experiments. Generally in walking motion, there are discrete state transitions caused by landing. The proposed framework can also deal with such state transitions without using the parameters of the transition model by combining ILC method and the least-squares. It is applied to the compass gait biped to generate optimal gait on the level ground. Furthermore, some numerical examples demonstrate the effectiveness of the proposed method.

A framework for optimal gait generation via learning optimal control using virtual constraint

This paper proposes an optimal gait generation framework using virtual constraint and learning optimal control. In this method, firstly, we add a constraint by a virtual potential energy to prevent the robot from falling. Secondly, we execute iterative learning control (ILC) to generate an optimal feedforward input. Thirdly, we execute iterative feedback tuning (IFT) to mitigate the strength of the virtual constraint automatically according to the progress of learning control. Consequently, it is expected to generate an optimal gait without constraint eventually. Although existing ILC frameworks require a lot of experimental data under the same initial condition, the proposed method does not need to repeat experiments under the same initial condition because the virtual constraint restricts the motion of the robot to a symmetric trajectory. Furthermore, it does not require the precise knowledge of the plant system. Finally, some numerical simulations demonstrate the effectiveness of the proposed method.

Gait Generation for a Hopping Robot Via Iterative Learning Control Based on Variational Symmetry

This paper proposes a novel framework to generate optimal gait trajectories for a one-legged hopping robot via iterative learning control. This method generates gait trajectories which are solutions of a class of optimal control problems without using precise knowledge of the plant model. It is expected to produce natural gait movements such as that of a passive walker. Some numerical examples demonstrate the effectiveness of the proposed method.

Bounded stabilisation of stochastic port-Hamiltonian systems

This paper proposes a stochastic bounded stabilisation method for a class of stochastic port-Hamiltonian systems. Both full-actuated and underactuated mechanical systems in the presence of noise are considered in this class. The proposed method gives conditions for the controller gain and design parameters under which the state remains bounded in probability. The bounded region and achieving probability are both assignable, and a stochastic Lyapunov function is explicitly provided based on a Hamiltonian structure. Although many conventional stabilisation methods assume that the noise vanishes at the origin, the proposed method is applicable to systems under persistent disturbances.

Gait generation via unified learning optimal control of Hamiltonian systems

This paper proposes a repetitive control type optimal gait generation framework by executing learning control and parameter tuning. We propose a learning optimal control method of Hamiltonian systems unifying iterative learning control (ILC) and iterative feedback tuning (IFT). It allows one to simultaneously obtain an optimal feedforward input and tuning parameter for a plant system, which minimizes a given cost function. In the proposed method, a virtual constraint by a potential energy prevents a biped robot from falling. The strength of the constraint is automatically mitigated by the IFT part of the proposed method, according to the progress of trajectory learning by the ILC part.

An Iterative Method for Nonlinear Stochastic Optimal Control Based on Path Integrals

This paper proposes a new iterative solution method for nonlinear stochastic optimal control problems based on path integral analysis. First, we provide an iteration law for solving a stochastic Hamilton-Jacobi-Bellman (SHJB) equation associated to this problem, which is a nonlinear partial differential equation (PDE) of second order. Each iteration procedure of the proposed method is represented by a Cauchy problem for a linear parabolic PDE, and its explicit solution is given by the Feynman-Kac formula. Second, we derive a suboptimal feedback controller at each iteration by using the path integral analysis. Third, the convergence property of the proposed method is investigated. Here, some conditions are provided so that the sequence of solutions for the proposed iteration converges, and the SHJB equation is satisfied. Finally, numerical simulations demonstrate the effectiveness of the proposed method.

Stabilization of Time-varying Stochastic Port-Hamiltonian Systems Based on Stochastic Passivity

Abstract The authors have introduced stochastic port-Hamiltonian systems and have clarified some of their properties. Stochastic port-Hamiltonian systems are extension of deterministic port-Hamiltonian systems, which are used to express various deterministic passive systems. However, since only time-invariant case has been considered in our previous results, the aim of this paper is to extend them to time-varying case. Finally, we propose a stabilization method based on passivity and the stochastic generalized canonical transformation, which is a pair of coordinate and feedback transformations preserving the stochastic Hamiltonian structure.

Stability analysis of feedback systems with dead-zone nonlinearities by circle and Popov criteria

A method of global stability analysis is proposed for a feedback system with dead-zone nonlinearities. Using a global property that the output of a saturation function is bounded, the bound on the input to the saturation function is estimated using the L ∞ norm of a linear subsystem. The feedback system can be treated as a feedback system with a narrower sector bound using this method, and a sharper global stability condition is obtained by applying the circle or Popov criterion to the system.