Nonlinear optimal feedback law subject to a terminal cost is approximated using quantum mechanical eigenvalue analysis. The optimal feedback law is governed by nonstationary Hamilton-Jacobi equation with a final condition. Numerical time integration in the backward direction must be done along a characteristic curve of the system. Compatibility under such constraints has restricted practical calculations to the system with dimensionality of only 1 or 2. For approximating optimal feedback with a terminal cost, we propose a quantum mechanical algorithm applicable to systems of arbitrary dimensions. The nonlinear optimal control system is represented by a complex-valued linear wave equation, where a time derivative of the system is connected with linear Hamiltonian operator H. We then apply eigenvalue analysis to this operator H. The value function applied to calculation of optimal feedback is approximated using terms, each of which are a product of eigenfunction φK (x) and time exponential function characterized by corresponding eigenvalue EK. The proposed method thus needs no time integration in the backward time direction. Simulation studies are performed for systems with a state variable of either 1 or 2 dimensions. The new algorithm has an advantage over conventional calculations in that we can fully make use of storage and development of eigenvalue analysis tools.
The objective of this work is to investigate the emergent properties of the gaits of the simulated snake-like robot, Snakebot. The gaits are automatically designed through Genetic Programming (GP) to be robust, general, adaptive, and the fastest possible sidewinding, locomotion. Considering the notion of emergent intelligence as the ability of Snakebot to achieve its goals (of moving fast) without the need to be explicitly taught how to do so, we present empirical results demonstrating the emergence of sidewinding locomotion from relatively simple motion patterns of morphological segments of Snakebot. We discuss the emergent properties of the evolved robust high velocity sidewinding locomotion gaits of Snakebot when situated in challenging environments. Then we elaborate on the ability of Snakebot to adapt to partial damage by gradually improving its velocity characteristics, and the emergent properties of obtained adaptive gaits. Verifying the practical implications of the analogy between the emergent properties of the robust and the adaptive sidewinding gaits, this work could be viewed as a step towards building real Snakebots, which are able to perform robustly in challenging environments.
The Monochrome-Projection Color-Analysis (MPCA) technique is proposed in order to measure the three-dimensional shape of an object having a complicated surface color, to shorten the measurement time and to improve measurement accuracy. An optimal color channel is chosen, and a single channel image for intensity calculation is compounded so that the greatest amount of information from an observation image is used and the effect of object color on the measurement is mitigated. By combining MPCA and the Optimal Intensity-Modulation Projection (OIMP) technique, approximately 100 stripes are reliably detectable in a single pattern projection and double image capture.
This paper studies the synchronization of network coupled systems consisting of many identical dynamic subsystems as well as network coupling with interaction time-delay. Based on graph theory and Lyapunov stability theory, the paper gives conditions for the total system synchronization and the boundedness of trajectories with respect to the graph structures of network coupling interaction. According to our study, it is revealed that, different from the systems without time-delay, (1) there will be a case where synchronization will occurs if the interaction strength and the number of the graph edges lie between some upper and lower bounds, (2) in regular graphs, such that complete-, star- and cycle graph, the synchronization conditon will be violated if total number of subsystems increases, (3) for the complex networks such as Small World Network and Scale Free Network, the synchronization conditon is more easier to be satisfied than regular graphs when the total number of subsystems increases.These are verified using numerical simulations.
Damage avoidance of the flexible manipulators in collision with unlooked-for obstacle is a significant problem in industry and space programs. This paper presents a method of control for reducing damage and/or undesirable vibration of the single-link flexible arm due to collision. The detection of the collision is carried out using the detection function which was proposed recently by the author. The controller is designed to have twofold manner : i) to control the position and vibration of the flexible arm; and ii) to suspend the position control and to minimize the deformation and vibration of the arm whenever any collision has been detected. Numerical simulations and experiments are provided.