Takateru Urakubo

Position and attitude control of a spherical rolling robot equipped with a gyro

This paper deals with the problem of controlling the position and attitude of a spherical rolling robot. The driving torque for the rolling robot is generated by a new type of mechanism equipped with a gyro. We derive two types of models, a kinematic model and a dynamic model, from the equations of motion for the robot. A feedback controller for the kinematic model is designed by using our previous method that is based on Lyapunov control. And then, from the controller, we obtain a feedback controller for the dynamic model by backstepping technique. The effectiveness of both controllers is demonstrated by numerical simulations

Feedback control of a two wheeled mobile robot with obstacle avoidance using potential functions

This paper deals with the feedback stabilization problem for a two-wheeled mobile robot which moves in the presence of obstacles. A state feedback controller is proposed based on Lyapunov control. First, we choose a potential function (Lyapunov function) whose value is minimum at a desired point and maximum on the surfaces of obstacles. And then, we construct a control input by multiplying the gradient vector of the potential function by a matrix composed of a negative definite symmetric one and a skew-symmetric one. It is shown that the system with the controller converges to one of critical points of the potential function. When the potential function has some critical points other than the minimum at the desired point, in order to avoid convergence to those points, the controller is modified. As a result, the controlled system converges to the desired point avoiding collision with obstacles.

Motion control of a two-wheeled mobile robot

The design of the controller of a two-wheeled mobile robot is usually based on a kinematical model. The kinematical model is derived under the assumption that the wheels do not skid or float. However, in the real world, wheels may skid on the ground or float away from the ground due to the rotational motion of the body. This paper analyzes the effects of the skid and the float on the robot with a controller designed based on the kinematical model—by the use of the Lyapunov control method. Numerical simulations are carried out based on the dynamic model including the translational and rotational motion of the body, and then experiments are performed using a hardware model.

Attitude Control of a Spacecraft with Two Reaction Wheels

This paper deals with the attitude control of a rigid spacecraft with two reaction wheels. First, we derive a discontinuous state feedback law based on Lyapunov control. The control input is obtained by multiplying the gradient vector of the Lyapunov function by a matrix that is composed of a symmetric matrix and an asymmetric one. Under this method, when the angular momentum of the system is zero, the desired point is the only stable equilibrium point of the controlled system. Next, we investigate the behavior of the controlled system when the angular momentum of the system is not zero but small. In this case, the system converges to either a limit cycle or an equilibrium point which is not the desired point however, in both cases, the error in attitude remains small.

Optimal placement of a two-link manipulator for door opening

This paper presents a study on the optimal base location and arm motion of a mobile manipulator for door opening task. Numerical simulation results show that the base location where the manipulability of the two-link arm is almost degenerated at the start and end points of door opening is optimal.We show by analysis that the location has an advantage in supplying kinetic energy to the door by using torques at the joints of arm. In order to represent properly the arm motion near a singular point of manipulability, the rotational motion of the door is parameterized by piecewise fifth order polynomials of time, and the parameters of polynomials are optimized to minimize the joint torques.

Hovering control of outdoor blimp robots based on path following

A surveillance system is required to gather information about the stricken area safely and quickly after large-scale disasters. An autonomous blimp is the best option for this purpose. This paper proposes a control design method for automatic hovering of outdoor blimp robots under strong wind by using path following approach. The method consists of inverse optimal path following control in horizontal plane and PID control for altitude and pitching motion of the blimp in longitudinal plane. Some simulations and experiments for an outdoor blimp whose length is 12m are performed to confirm the usefulness of the proposed method.

A motion control of a two-wheeled mobile robot

We discuss the motion control of a two-wheeled mobile robot. In the design of a controller for the system, a kinematic model is usually used; the wheels do not skid at all and the mobile robot is regarded as a 3D 2-input nonholonomic system without drift. Many controllers based on the kinematic model have been proposed. However, in a real world, the wheels may skid on the ground or float away from the ground according to the rolling motion of the body. Therefore, we derive a dynamic model of a two-wheeled mobile robot which implies the translational motion with 3 degrees-of-freedom and the rotational motion with 3 degrees-of-freedom of the body and the rotational motion with one degree-of-freedom of each wheel, and then reduce the dynamic model to the kinematic model under certain assumptions. We design a controller based on the kinematic model by extending the Lyapunov control and analyze whether the designed controller works well in a real world by numerical simulations based on the dynamic model.

Efficient pulling motion of a two-link robot arm near singular configuration

This paper discusses the advantages of singular configurations of a two-link robot arm in achieving tasks of pulling or lifting a heavy object. Optimal base location and arm motion for minimizing the joint torques are examined by numerical simulations, and the base location where the robot arm is near a singular configuration at the start time of task is optimal. It is shown analytically that joint torques can supply energy to the system composed of the robot arm and the object efficiently near singular configurations of the arm. The energy supply rates at two singular configurations are derived based on the equations of motion of the system.

Discontinuous feedback stabilization of a class of nonholonomic systems based on Lyapunov control

This paper deals with the problem of controlling a class of nonholonomic systems, first order systems. The first order systems are systems where the input vector fields and the first level of Lie brackets between them span the tangent space of the state space. We derive a discontinuous state feedback law for the systems by extending Lyapunov control. The input vector is constructed by multiplying the gradient vector of a Lyapunov function by a matrix which is composed of a negative definite symmetric one and a skew-symmetric one. The designed controller makes the desired point the only stable equilibrium point, and the controlled system converges to the desired point from almost all initial points. The proposed controller is applied to two examples of first order systems, a two wheeled vehicle and a spacecraft composed of two rigid bodies.

Experimental study on efficient use of singular configuration in pulling heavy objects with two-link robot arm.

This paper demonstrates that singular configuration of a two-link robot arm is advantageous in doing the task of pulling or lifting up a heavy object with small joint torques. As a result of numerical optimization, the initial configuration that minimizes the joint torques necessary for the task is close to the singular configuration where the arm is stretched out. The singular configuration has the dynamic feature that the joint angle vector can be accelerated in a certain direction almost independently of the mass of the object. Then, the joint torques can generate large kinetic energy efficiently at the singular configuration, and the energy can be utilized to pull or lift up the object. The experimental results show that the dynamic feature is practically useful, even when a feedback control is applied in order to make the object follow a planned trajectory.