Inverted pendulum

Abstract: During the Chilean earthquakes of May, 1960, a number of tall, slender structures survived the ground shaking whereas more stable appearing structures were severely damaged. An analysis is made of the rocking motion of structures of inverted pendulum type. It is shown that there is a scale effect which makes tall slender structures more stable against overturning than might have been expected, and, therefore, the survival of such structures during earthquakes is not surprising.

Abstract: It is known that for a large magnitude push a human or a humanoid robot must take a step to avoid a fall. Despite some scattered results, a principled approach towards "when and where to take a step" has not yet emerged. Towards this goal, we present methods for computing capture points and the capture region, the region on the ground where a humanoid must step to in order to come to a complete stop. The intersection between the capture region and the base of support determines which strategy the robot should adopt to successfully stop in a given situation. Computing the capture region for a humanoid, in general, is very difficult. However, with simple models of walking, computation of the capture region is simplified. We extend the well-known linear inverted pendulum model to include a flywheel body and show how to compute exact solutions of the capture region for this model. Adding rotational inertia enables the humanoid to control its centroidal angular momentum, much like the way human beings do, significantly enlarging the capture region. We present simulations of a simple planar biped that can recover balance after a push by stepping to the capture region and using internal angular momentum. Ongoing work involves applying the solution from the simple model as an approximate solution to more complex simulations of bipedal walking, including a 3D biped with distributed mass.

Abstract: For 3D walking control of a biped robot we analyze the dynamics of a 3D inverted pendulum in which motion is constrained to move along an arbitrarily defined plane. This analysis yields a simple linear dynamics, the 3D linear inverted pendulum mode (3D-LIPM). Geometric nature of trajectories under the 3D-LIPM and a method for walking pattern generation are discussed. A simulation result of a walking control using a 12-DOF biped robot model is also shown.

Abstract: While neural network control has been successfully applied in various practical applications, many important issues, such as stability, robustness, and performance, have not been extensively researched for neural adaptive systems. Motivated by the need for systematic neural control strategies for nonlinear systems, Stable Adaptive Neural Network Control offers an in-depth study of stable adaptive control designs using approximation-based techniques, and presents rigorous analysis for system stability and control performance. Both linearly parameterized and multi-layer neural networks (NN) are discussed and employed in the design of adaptive NN control systems for completeness. Stable adaptive NN control has been thoroughly investigated for several classes of nonlinear systems, including nonlinear systems in Brunovsky form, nonlinear systems in strict-feedback and pure-feedback forms, nonaffine nonlinear systems, and a class of MIMO nonlinear systems. In addition, the developed design methodologies are not only applied to typical example systems, but also to real application-oriented systems, such as the variable length pendulum system, the underactuated inverted pendulum system and nonaffine nonlinear chemical processes (CSTR).