Control of Nonholonomic Systems Under the Gravity Field

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In this research, we investigate the following systems for nonholonomic system under the gravity field.1. Continuous Hopping Motion Control of One Linear Actuator RobotThis robot has mechanics to be able to realize continuous hopping motion on vertical plane by one linear actuator : We showed that continuous hopping is possible to build servo system by regarding one linear actuator robot as a discrete system. Also we constructed the hopping robot which has a pneumatic cylinder and a small air tank, and succeeded 14 times hopping by this robot.2. Enduring Rotary Motion Control of Devil StickWe showed that enduring rotary motion of devil stick is realized by zeroing output functions which are obtained through observation of human operations. Also we constructed experimental devil stick system by using a industrial manipulator in substitution for a human arm, and succeeded 15 times rotary motion of the stick.3. Swing Up Control on the Horizontal Bar with ComplianceWe proposed the model of an acrobot on the horizontal bar with compliance, and derived the control strategy to swing up the acrobot more rapidly by efficient use of that compliance. Also we developed experimental system which uses linear springs to simulate the compliance, and confirmed effective swing up motion is achieved.4. Nonlinear Control of Inverted Pendulum System with Up-down MotionWe analyzed the performance of the stabilization of a inverted pendulum by using not only horizontal motion but also vertical motion. By expressing the inverted pendulum model which moves on vertical plane freely as bilinear system, we derived the nonlinear H infinity control law so as to make use of vertical motion appropriately.