Abstract
AbstractThis paper presents a joint–coordinate adjoint method for optimal control of multi-rigid-body systems. Initially formulated as a set of differential-algebraic equations, the adjoint system is brought into a minimal form by projecting the original expressions into the joint’s motion and constraint force subspaces. Consequently, cumbersome partial derivatives corresponding to joint-space equations of motion are avoided, and the approach is algorithmically more straightforward. The analogies between the formulation of Hamilton’s equations of motion in a mixed redundant-joint set of coordinates and the necessary conditions arising from the minimization of the cost functional are demonstrated in the text. The observed parallels directly lead to the definition of a joint set of adjoint variables. Through numerical studies, the performance of the proposed approach is investigated for optimal control of a double pendulum on a cart. The results demonstrate a successful application of the joint-coordinate adjoint method. The outcome can be easily generalized to optimal control of more complex systems.
Publisher
Springer Science and Business Media LLC
Subject
Control and Optimization,Computer Science Applications,Mechanical Engineering,Aerospace Engineering,Modeling and Simulation
Cited by
2 articles.
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