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A new approach to the solution of optimal control problems for mechanical systems is proposed. It is based on a direct discretization of the Lagrange-d’Alembert principle for the system (as opposed to using, for example, collocation or multiple shooting to enforce the equations of motion as constraints). The resulting forced discrete Euler-Lagrange… (More)

The optimal control of a mechanical system is of crucial importance in many realms. Typical examples are the determination of a time-minimal path in vehicle dynamics, a minimal energy trajectory in space mission design, or optimal motion sequences in robotics and biomechanics. In most cases, some sort of discretization of the original, infinite-dimensional… (More)

- Sina Ober-Blöbaum, Nils Saake
- Adv. Comput. Math.
- 2015

1Aeronautics and Control and Dynamical Systems, California Institute of Technology, 1200 E. California Boulevard, Mail Code 107-81, Pasadena, CA 91125, U.S.A. 2Control and Dynamical Systems, California Institute of Technology, 1200 E. California Boulevard, Mail Code 205-45, Pasadena, CA 91125, U.S.A. 3Aeronautics and Mechanical Engineering, California… (More)

- Jerrold E. Marsden, Michael Dellnitz, +22 authors Steve Wig
- 2005

The title of this paper is inspired by the work of Poincaré [1890, 1892], who introduced many key dynamical systems methods during his research on celestial mechanics and especially the three body problem. Since then, many researchers have contributed to his legacy by developing and applying these methods to problems in celestial mechanics and, more… (More)

In this paper we present a new approach to determine trajectories for changing the state of the double pendulum on a cart from one equilibrium to another and show the experimental realization on a test bench. The control of these transitions is accomplished by a two-degrees-of-freedom control scheme. For the design of the feedforward and feedback control of… (More)

The equations of motion of a controlled mechanical system subject to holonomic constraints may be formulated in terms of the states and controls by applying a constrained version of the Lagrange-d’Alembert principle. This paper derives a structure preserving scheme for the optimal control of such systems using, as one of the key ingredients, a discrete… (More)

- Weizhong Zhang, Tamer Inanc, Sina Ober-Blöbaum, Jerrold E. Marsden
- 2008 IEEE International Conference on Robotics…
- 2008

The problem of showing that Lagrangian Coherent Structures (LCS) are useful in determining near optimal trajectories for autonomous underwater vehicles (AUVs) known as gliders is investigated. This paper extends our preliminary results in couple ways. First, the ocean current flows are modeled by 3D B-spline functions in which the input variables are… (More)

We employ a recently developed new technique for the numerical treatment of optimal control problems for mechanical systems in order to compute optimal open loop control laws for the reconfiguration of a group of formation flying satellites. The method is based on a direct discretization of a variational formulation of the dynamical constraints. We extend… (More)

This paper introduces a hierarchical, decentralized, and parallelizable method for dealing with optimization problems with many agents. It is theoretically based on a hierarchical optimization theorem that establishes the equivalence of two forms of the problem, and this idea is implemented using DMOC (Discrete Mechanics and Optimal Control). The result is… (More)