Keigo Kobayashi

Nonholonomic control of 3 link planar manipulator with a free joint

This paper is concerned with point-to point control of a 3 link planar manipulator where the first two joints are actuated and the third revoluted joint is unactuated. This system is a special case of under-actuated manipulators, which have nonholonomic constraints. The main result of this paper is to show that this system is feedback equivalent to the chained form which is composed of twice differential equations. In addition, we propose a controller that stabilizes the system from any initial position to any desired position.

Controllability of Under-Actuated Planar Manipulators with One Unactuated Joint

This paper is concerned with analysis on controllability for a class of nonholonomic systems. We discuss controllability of underactuated planar manipulators with one unactuated joint. We show that if the first joint (in the base side) is actuated, these systems are completely controllable, namely, there exists an admissible trajectory from any given initial point to any given final point. In order to prove this, we use global stabilizing feedback control law to converge the state to a manifold, where the system is locally controllable. By this controller, we have two trajectories, one starting at the given initial position and the other starting at the given final position. Then we connect them using a kind of bi-directional approach to show the existence of the whole admissible trajectory. Finally, we give some simulation results to discuss controllability of more general cases, the first joint being actuated and all other joints being unactuated.

Controllability of under-actuated planar manipulators with one unactuated joint

This paper is concerned with the analysis of controllability for a class of nonholonomic systems. We discuss the controllability of under-actuated planar manipulators with one unactuated joint. We show that these systems are completely controllable if the first joint (in the base side) is actuated. In order to prove this, we use a kind of bi-directional approach.

Motion planning for humanoid robots using timed Petri net and modular state net

We propose a supervisory control system for motion planning of humanoid robots. The proposed system is hierarchically structured into two levels. The lower level controls and monitors the robots using modular state nets. The upper level generates an optimal sequence of motion for users requirements using timed Petri nets.

Design of a desirable trajectory and convergent control for 3-DOF manipulator with a nonholonomic constraint

This paper deals with the control of a 3-link planar underactuated manipulator whose most distal joint is unactuated. This system is known as a second order nonholonomic system. In a previous paper (1996), we proposed a control law that guarantees the convergence of its state to a given desirable trajectory and to any desired final point, and we also gave a design method of the desirable trajectory. However, this method has a limitation on the location of the initial state. In this paper, we propose a design method of a desirable trajectory that starts from any given initial point, converges to any given desired final point, and on the way passes through any given desired passing point that can be specified rather freely. By this new design method, one can derive a desirable trajectory that satisfies given requirements much better than the previous method.

Exponential stabilization problem of nonholonomic chained systems with specified transient response

In this paper, we propose a control method for nonholonomic systems expressed by the chained form, where the exponential convergence to the desired final state is guaranteed and the desired transient response is achieved simultaneously. Next, we propose a trajectory generation method for the chained system, which gives a systematic procedure to find a reference trajectory that passes several given points at each specified time and exponentially converges to the origin. Finally, our method is applied to control of a 4-wheeled car. In this case, to express all the state of the 4-wheeled car by the chained form, the above method is extended to the case where several coordinate frames are needed.

LLP supervisory control with timed Petri net models in mobile robots

This paper deals with the high level control of robot systems. We abstract the robot system as timed Petri net and give a high level controller which consists of a limited lookahead policy (LLP) supervisor. A simple application of the control system to a mobile robot system is given.

An application of LLP supervisory control with Petri net models in mobile robots

This paper is concerned with high level control of robot systems. We abstract the robot system as a discrete event system and present a high level controller which consists of a limited lookahead policy (LLP) supervisor and a Petri nets model. We show its simple application to a mobile robot system.