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We propose a new dynamic extension of the thrust variable in the quadcopter dynamics that preserves the positive sign of the thrust. This extension not only eliminates the positive sign constraint on the thrust variable, but also leads to global chartwise feedback linearization of the quadcopter dynamics. For the latter, an atlas is first constructed on the entire state space of the quadcopter and then the dynamically extended quadcopter system is transformed to a 14-dimensional linear controllable system on each chart in the atlas. Based on the chartwise dynamic feedback linearization, a global tracking strategy is proposed for the quadcopter and its excellent performance is demonstrated with a simulation. [ABSTRACT FROM AUTHOR]

We present necessary and sufficient optimality conditions for finite-time optimal control problems for a class of hybrid systems described by linear complementarity models. Although these optimal control problems are difficult in general due to the presence of complementarity constraints, we provide a set of structural assumptions ensuring that the tangent cone of the constraints possesses geometric regularity properties. These imply that the classical Karush–Kuhn–Tucker conditions of nonlinear programming theory are both necessary and sufficient for local optimality, which is not the case for general mathematical programs with complementarity constraints. We also present sufficient conditions for global optimality. We proceed to show that the dynamics of every continuous piecewise affine (PWA) system can be written as the optimizer of a mathematical program, which results in a linear complementarity model satisfying our structural assumptions. Hence, our stationarity results apply to a large class of hybrid systems with PWA dynamics. We present simulation results showing the substantial benefits possible from using a nonlinear programming approach to the optimal control problem with complementarity constraints instead of a more traditional mixed-integer formulation. [ABSTRACT FROM AUTHOR]

Swarms, flocks, and other group formations can be found in nature in many organisms ranging from simple bacteria to mammals. Such collective and coordinated behavior is effective for avoiding predators and/or for increasing the chances of finding food (foraging). In this technical note we develop a mathematical model for analyzing the benefits of social foraging in a noisy environment. We identify conditions on the nutrient profile ensuring that local agent actions will lead to cohesive foraging. For convex, smooth nutrient profiles, we formalize the way in which swarming for social foraging is better at handling the effects of noise when compared to the average of individual foraging strategies. Under a swarming discipline, observational noise realizations that induce trajectories differing too much from the group average are likely to be discarded because of each individual's need to maintain cohesion. As a result, the group trajectories are less affected by noise. Simulation experiments indicate our theoretical results are robust to inter-agent communication constraints and non-convex nutrient profiles. These results suggest that swarming-like approaches for the control of networked agents may provide an additional level of robustness. [ABSTRACT FROM AUTHOR]

This technical note addresses a tradeoff in the tree based trajectory optimization algorithms for open-loop optimal control problem of rigid body system. In this technical note, linear prediction based uniform state sampling method (LPUSS), which relaxes the tradeoff between solutions' quality and computational efficiency, is proposed on the basis of the local linearity of motion equations. LPUSS has a lower calculation order than randomized kinodynamic planning (RKP) and rapid semi-optimal motion planning (RASMO). In the validation using multi degree-of-freedom (DOF) under actuated manipulator models, the solutions' quality and the computational efficiency of LPUSS were better than those of RKP and RASMO. LPUSS finished the optimization for the 6 DOF model within 40 minutes. This was the world's first success of the optimization of the swing up motion of a 6 DOF under actuated manipulator model. [ABSTRACT FROM PUBLISHER]

This paper deals with the observer problem for dynamical systems in a behavioral context. We are given a dynamical system together with a partition of the system variables into a set of known or measured variables and a set of unknown, to be estimated variables. The observer problem is to find a system that produces an estimate of the unknown variables on the basis of the known or measured variables. For a given plant and partition, we establish a characterization of all error behaviors that can be achieved by interconnecting the plant with some observer. The main result of this paper is a very general, behavioral formulation of an internal model principle for observers. We will show that a nonintrusive observer achieves a stable error behavior if and only if, in addition to a detectability condition on the observer, the observer behavior contains the anti-stabilizable part of the plant behavior. [ABSTRACT FROM AUTHOR]