This research develops a new automatic path following control method for a car model based on just-in-time modeling. The purpose is that a lot of basic driving data for various situations are accumulated into a database, and we realize automatic path following for unknown roads by using only data in the database. Especially, just-in-time modeling is repeatedly utilized in order to follow the desired points on the given road. From the results of a numerical simulation, it turns out that the proposed new method can make the car follow the desired points on the given road with small error, and it shows high computational efficiency.

This paper develops a design method and theoretical analysis for piecewise nonlinear oscillators that have desired circular limit cycles. Especially, the mathematical proof on existence, uniqueness, and stability of the limit cycle is shown for the piecewise nonlinear oscillator. In addition, the relationship between parameters in the oscillator and rotational directions and periods of the limit cycle trajectories is investigated. Then, some numerical simulations show that the piecewise nonlinear oscillator has a unique and stable limit cycle and the properties on rotational directions and periods hold.

In this paper, we consider a stabilization problem for the cart-pendulum system based on discrete mechanics, which is known as a good discretizing method for mechanical systems and has not been really applied to control theory. First, the continuous and discrete cart-pendulum systems are explained. We next propose a transformation method that converts a discrete-time input derived from the discrete-time optimal regulator theory into a continuous-time zero-order hold input, and carry out some simulations on stabilization of the cart-pendulum system by the transformation method. Then, we apply not only our proposed method but also existing methods to an experimental laboratory of the cart-pendulum system and perform some experiments in order to verify the availability of the proposed method.

This letter presents integrating algorithms for affine constraints defined on a manifold. We first explain definition and geometric representation of affine constraints. Next, we derive integrating algorithms to calculate independent first integrals of affine constraints for the two cases where the they are completely integrable and partially nonintegrable. Moreover, we prove the existence of inverse functions in the algorithms. Some examples are also shown to verify our results.

This paper considers the discrete model of the cart-pendulum system modeled by discrete mechanics, which is known as a good discretizing method for mechanical systems and has not been really applied to control theory. We first sum up basic concepts on discrete mechanics and discuss the explicitness of the linear approximation of the discrete Euler-Lagrange Equations. Next, the discrete cart-pendulum system is derived and analyzed from the viewpoint of solvability of implicit nonlinear control systems. We then show a control algorithm to stabilize the discrete cart-pendulum based on the discrete-time optimal regulator theory. Finally, some simulations are shown to demonstrate the effectiveness of the proposed algorithm.

This letter is devoted to derivation of a transformation law which converts a class of nonlinear affine control systems with n-states and 2-iputs into simpler systems with chained structure. First, we give a problem formulation that we consider throughout this letter. We next introduce a transformation law and gives its mathematical certification. Then, we apply the transformation method to an example and consider control design based on chained structure for the example in order to confirm the effectiveness of our approach.

This study develops a new automatic hovering control method based on just-in-time modeling for a multicopter. Especially, the main aim is to compute gains of a feedback control law such that the multicopter hovers at a desired height and at a desired time without overshoot/undershoot. First, a database that contains various hovering data is constructed, and then the proposed method computes gains for a query input from the database. From simulation results, it turns out that the multicopter achieves control purposes, and hence the new method is effective.