4,021 research outputs found
Normal forms for underactuated mechanical systems with symmetry
We introduce cascade normal forms for underactuated mechanical systems that are convenient for control design. These normal forms include three classes of cascade systems, namely, nonlinear systems in strict feedback form, feedforward form, and nontriangular quadratic form (to be defined). In each case, the transformation to cascade systems is provided in closed-form. We apply our results to the Acrobot, the rotating pendulum, and the cart-pole system
Optimal Control of Underactuated Mechanical Systems: A Geometric Approach
In this paper, we consider a geometric formalism for optimal control of
underactuated mechanical systems. Our techniques are an adaptation of the
classical Skinner and Rusk approach for the case of Lagrangian dynamics with
higher-order constraints. We study a regular case where it is possible to
establish a symplectic framework and, as a consequence, to obtain a unique
vector field determining the dynamics of the optimal control problem. These
developments will allow us to develop a new class of geometric integrators
based on discrete variational calculus.Comment: 20 pages, 2 figure
Quasivelocities and Optimal Control for Underactuated Mechanical Systems
This paper is concerned with the application of the theory of quasivelocities
for optimal control for underactuated mechanical systems. Using this theory, we
convert the original problem in a variational second-order lagrangian system
subjected to constraints. The equations of motion are geometrically derived
using an adaptation of the classical Skinner and Rusk formalism.Comment: 8 page
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