Mitsuji Sampei

Throwing motion control of the springed Pendubot via unstable zero dynamics

This paper describes a control strategy for throwing motion of the springed Pendubot based on the concept of unstable zero dynamics. An underactuated two-link planar robot called the Pendubot is investigated to realize dexterous actions of the superior limb in human throwing motion. A torsion spring is mounted on the passive joint of the Pendubot representing the flexibility of the cubital joint. In the proposed control strategy, the zero dynamics is intentionally destabilized when the end-effector of the springed Pendubot is constrained on a geometric path via output zeroing control for the deviation between the end-effector and the geometric path. The unstable zero dynamics drives the end-effector along the geometric path to achieve a fast and accurate throw in a desired direction when the input is devoted to constrain the end-effector on the geometric path. The unstable zero dynamics is analytically derived to guarantee the divergence of the end-effector along the geometric path. Numerical simulations confirm the effectiveness of the proposed control strategy.

Throwing Motion Control of the Springed Pendubot

This brief describes a control strategy for the throwing motion of an underactuated two-link planar robot called the Pendubot. The springed Pendubot is built based on the concept of unstable zero dynamics, and our investigation uses it as a dynamic model of superior limbs to imitate human throwing motion. In the proposed control strategy, the zero dynamics is intentionally destabilized when a ball held by the end-effector is constrained on a geometric path in a vertical plane, using output zeroing control for the deviation between the ball and geometric path. The unstable zero dynamics drives the ball along the geometric path to achieve fast and accurate throw in a desired direction. The unstable zero dynamics is analytically derived to guarantee the dynamic acceleration of the ball along the geometric path. Numerical simulations and experimental results confirm the effectiveness of the proposed control strategy.

Nonlinear Control and Model Analysis of Trirotor UAV Model

Abstract This paper reveals the minimal number of inputs for hovering control from the perspective of nonlinear control system theory. Then, a nonlinear controller is designed to obtain meaningful motion for an underactuated UAV with the consideration of the limitation acknowledged through the model analysis. Throughout this paper, a particular UAV model having three rotors is considered as a controlled object. First, nonlinear state equations are computed with valid assumptions. Next, the model analysis reveals that hovering control is impossible for not only the proposed model but also a generic three-inputs model through the argument of Locally Asymptotically Stabilizability(LAS). Finally, numerical simulation confirms that position control is realizable via Output Zeroing Control along with preferable attitude.

Exact linearization by time scale transformation based on relative degree structure of single-input nonlinear systems

The problem of exact linearization of single-input nonlinear systems by time scale transformation (TST) is considered in this paper. The aim of this paper is to derive method of computing time scale function based on relative degree structure of nonlinear systems. The method using two independent functions which have the largest relative degree of the system is proposed. Because of no requirement of the solution of the nonlinear PDE, the time scale function can be computed easily. An example of the Acrobot is also given. The Acrobot can not be linearized by feedback transformation and state feedback, but this paper shows that the Acrobot is linearizable exactly by applying time scale transformation.

Structural optimization of hexrotors based on dynamic manipulability and the maximum translational acceleration

This paper investigates a structural optimization problem of hexrotors. As structural evaluation indices, we introduce the maximum translational acceleration, in addition to general 6-DOF dynamic manipulability, taking account of payload flying against the gravity force. We next consider a special class of structure where 6-DOF dynamic manipulability can be approximated by the simple product of translational and rotational manipulability. Then, we consider the optimization problem and solve it by a nonlinear optimization technique. As a result, it is shown that the optimized structure has symmetric properties. We finally evaluate the optimality via simulations with simple feedback control.

Control of bipedal running by the angular-momentum-based synchronization structure

This paper investigates the running control problem for the 7-link, 6-actuator planar bipedal robot including ankle joints. The control strategy is based on the “synchronization structure” with the angular momentum of the pivot point. The synchronization not only follows the simplified joint angle dynamics of human running but also generates the uniform running speed from wide range of initial speed, which claims that the controller is robust for the error of initial speed. Moreover, it successfully verifies the acceleration of running speed from 0.1[m/s], which is almost zero speed, to a uniform running speed “without” switching controllers. Finally, the controller is applied for the running on an uneven terrain, and it successfully achieves running with the maximum slope angle 6[deg], which is highly steep terrain in the real situation.

Visual feedback pose tracking control of two-wheeled vehicles with target vehicle motion models

This paper studies a visual feedback pose estimation/control problem in the situation that a two-wheeled vehicle equipped with a camera tracks a vehicle equipped with a target object. Then, we handle this problem under the assumption that the velocity of the object vehicle is expressed by a fourier series expansion. First, we propose the problem statement of visual feedback pose tracking control. We next prove the convergence of the estimation of the rotation part. Then, the convergence of the translation part is shown via stability analysis of perturbed systems. Moreover, we analyze the convergence of relative attitude of both vehicles. Finally, we demonstrate the validity of the proposed method through a simulation.

Change of controller based on partial feedback linearization with time-varying function

This paper considers the problem to transfer the state from one zero dynamics submanifold to another one in finite time, for a time-invariant nonlinear system. The usage of time-varying zero dynamics submanifold is proposed to accomplish the transfer. The feature of this paper is facus on keeping the state on zero dynamics submanifold during the transfer. Main contribution is to develop the condition for doing this for the case that the two zero dynamcis submanifolds have the same dimension. The validity of the controller that is designed to satisfy the condition is demonstrated via a numerical simulation of mono-rotor unmanned aerial vehicle (UAV) system.

Experimental study of stabilization of the inverted pendulum with horizontal and vertical movement via exact linearization based on the dynamic extension

This paper discuss about the problem of the stabilization of the inverted pendulum on the cart which moves not only in the horizontal direction but also in the vertical direction. This stabilizing problem is addressed by the exact linearization via dynamic extension. The conditions for the system to be the exact linearizable via dynamic extension is derived by restricting the form of the extension and the input transformation which converts the system to satisfy the conditions is derived. After applying the input transformation, the system is extended and applied a feedback transformation. Then the linear controllable system associated with the inverted pendulum system is derived. The validity of this linearization is shown by the several numerical simulations and experiments. In the experiments, the inverted pendulum system is realized by means of the 3-link manipulator.

3D inverted pendulum stabilization on a quadrotor via bilinear system approximations

This paper tackles a 3D inverted pendulum stabilization problem, where the pendulum is attached on a quadrotor. We first derive the mathematical model of the quadrotor-pendulum system based on the Euler-Lagrange equation. Then, with hope for better control performance than traditional linear quadratic optimal control by efficiently using the vertical input, the bilinear approximation model is built by the second order Taylor expansion. We then propose an inverse optimal stabilization law for the bilinear system, conduct the convergence analysis and give the interpretation of the optimality. Finally, the validity of the present approach is demonstrated via simulations, where we explicitly show the effectiveness of the vertical input by comparing with the linear quadratic control case.