Akira Ichikawa

Optimal Impulsive Relative Orbit Transfer Along a Circular Orbit

The relative orbit transfer problem associated with the Hill-Clohessy-Wiltshire equations is considered, and the open-time minimum-fuel problem with impulsive control is formulated. In particular, between two elliptic relative orbits of the in-plane motion, optimal three-impulse controllers are constructed. For the out-of-plane motion, optimal single-impulse strategies are obtained. Based on these results and the null controllability with the vanishing energy of the Hill-Clohessy-Wiltshire equations, a design method of feedback controllers with a total velocity change close to the optimal one is proposed. It is shown by simulation results that asymptotic relative orbit transfer is fulfilled by the proposed feedback controllers.

Output regulation of time-varying systems

In this paper the output regulation problem for linear time-varying systems is considered. Replacing the regulator equation by a regulator differential equation we give a necessary and sufficient condition for the problem to be solvable. As in the time-invariant case we first solve the output regulation problem by state feedback and obtain the required condition. Then with the aid of observers we show that the same condition solves the general problem with measurement feedback. We then consider the classes of almost periodic and periodic systems and refine the main results. A simple example of an almost periodic system and simulation results are given to illustrate the theory.

Null controllability with vanishing energy for discrete-time systems

In this paper null controllability with vanishing energy for discrete-time systems is considered. As in the case of continuous time systems necessary and sufficient conditions in terms of an algebraic Riccati equation are given. Then necessary and sufficient conditions involving the eigenvalues of the state matrix are given. Reachability and controllability with vanishing energy are also considered and necessary and sufficient conditions for them are given. Finally applications to sampled-data systems, systems with impulse control and periodic systems are discussed.

Hysteresis in gait transition induced by changing waist joint stiffness of a quadruped robot driven by nonlinear oscillators with phase resetting

In this paper, we investigated the locomotion of a quadruped robot whose front and rear bodies are connected by a roll joint. The legs of the robot are controlled by nonlinear oscillators with phase resetting. Based on numerical simulations, we showed that the robot produces various gait patterns through dynamical interactions among the robot mechanical system, oscillator control system, and environment and establishes gait transition induced by the change of the roll joint stiffness. In addition, we demonstrated that a hysteresis with respect to gait pattern occurs during the gait transition similarly to humans and animals, and we examined the mechanisms of the hysteresis from a dynamic viewpoint.

Linear Quadratic Differential Games in a Hilbert Space

We consider linear quadratic games in a Hilbert space. The system equation is linear and involves an unbounded operator which generates a strongly continuous evolution operator (or semigroup). We show that the existence of a solution to a Riccati integral equation implies the existence of a saddle point for the closed-loop game, and that the former is guaranteed if there exists a unique open-loop saddle point. We also consider quadratic games on an infinite interval.

Periodic Orbits of Nonlinear Relative Dynamics and Satellite Formation

In this paper, leader―follower formation and reconfiguration problems based on the periodic orbits of the nonlinear relative dynamics along a circular orbit are considered. First, initial conditions of coplanar and noncoplanar relative orbits are characterized by the initial true anomaly, mean motion, semimajor axis, eccentricity, and inclination angle of the followers inertial orbit. Based on the property of null controllability with vanishing energy of the Hill―Clohessy―Wiltshire equations, L 1 suboptimal feedback controllers are designed via the linear quadratic regulator theory. Simulation results for three examples are given. A comparison with the reconfiguration problem based on the periodic orbits of the Hill―Clohessy―Wiltshire equations shows that replacement by nonlinear periodic orbits does not increase the L 1 -norm of the feedback control.

Periodic Orbits of Nonlinear Relative Dynamics Along an Eccentric Orbit

This paper is concerned with formation acquisition and reconfiguration problems with an eccentric reference orbit. As a first step, the characterization problem is considered for all initial conditions that constitute periodic solutions of the nonlinear equations of relative motion. Under the condition that the inertial orbits of the leader and a follower are coplanar, initial conditions of all periodic relative orbits are generated in terms of parameters of their orbits and their initial positions. Then the inertial orbit of the follower is rotated successively around the two axes of its perifocal reference system, and the initial conditions of all noncoplanar relative orbits are derived. Based on these periodic relative orbits, formation acquisition and reconfiguration problems by a feedback controller are formulated. The main performance index of a feedback controller is the total velocity change during the operation. Using the property of null controllability with vanishing energy of the Tschauner-Hempel equations, suboptimal controllers are designed via the differential Riccati equation of the linear regulator theory of periodic systems.

Optimal Pulse Strategies for Relative Orbit Transfer Along a Circular Orbit

This paper is concernedwith a fuel-optimal relative orbit transfer problem forHill–Clohessy–Wiltshire equations. The input is of the pulse type and the performance index is the total velocity change required for a transfer. For the in-plane motion, the existence of optimal three-pulse strategies is shown and the minimum total velocity change is explicitly given under the condition that the difference of orbit size is relatively larger than that of drift velocity. For the out-of-plane motion, the existence of optimal single-pulse strategies is shown. The orbit transfer problem covers formation reconfiguration problem as a special case. Midpoints of the optimal pulses coincide with those points at which the velocity along the radial direction is zero. Using this information and null controllability with vanishing energy of the Hill–Clohessy–Wiltshire equations, suboptimal feedback controllers are designed. Simulation results with optimal open-loop strategies and feedback controls are given for two formation reconfiguration problems.

Attitude control of a helicopter model by robust PID controllers

In this paper, the attitude control, by PID controllers, of a helicopter model with two degrees of freedom is considered. Cross-coupling in the system being neglected, dynamics of elevation and azimuth are independently considered and PID controllers are designed separately. It is then shown that pairs of PID controllers can stabilize the whole system and fulfil the step tracking. Starting a PID controller thus obtained, robust PID controllers are designed iteratively based on the method of Miyamoto. Experimental results show that the final controller stabilizes the whole helicopter model and gives satisfactory performances in step tracking

Output regulation for sampled-data systems with application to marine systems

In this paper the output regulation problem for sampled-data systems with time-varying measurement matrices and constant exogenous signals is considered. Under the assumption that the regulator equation in the continuous-time case has a solution, a discrete-time output feedback controller is designed which fulfills output regulation. As an application, berthing control of a ship is discussed and simulation results are given to show the effectiveness of the controller.