Author: Luis Alberto Rodriguez

Publisher:

Published: 2010

Total Pages: 231

ISBN-13: 9781124208787

In disciplines such as robotics and aerospace engineering, there is an increasing demand to find control policies that maximize system performance specified in terms of decreasing effort, reducing fuel consumption, or generating graceful motions to achieve complex tasks. Such objectives can be expressed in terms of a scalar cost function that must be minimized subject to various physical constraints. Due to the importance of solving these optimal control problems, numerous algorithms have been proposed. A common approach employed in many of these algorithms is to discretize the continuous-time problem and obtain a finite-dimensional nonlinear problem that can be solved using a general-purpose nonlinear optimization solver. However, casting the problem in this manner destroys the inherent structure of the optimal control problem and results in large-scale problems that are computationally expensive to solve. Another problem is that the choice of an appropriate discretization to accurately represent the solution is left entirely to the expertise of the user. As a consequence, inefficient discretization schemes are often chosen that either do not provide sufficient control resolution to capture important characteristics such as discontinuities or are too dense, requiring intense computational effort. To address these issues, we propose a Runge-Kutta based algorithm that iteratively solves a sequence of discrete-time optimal control problems (DT-OCP) that consistently approximate the continuous-time optimal control problem. To solve these DT-OCPs efficiently we developed a custom SQP method which we refer to as the Constrained Sequential Linear Quadratic (CSLQ) algorithm. The SQP algorithm handles general inequality path constraints including mixed state-control and state-only constraints, preserves the structure of the optimal control problem and exhibits favorable computational complexities with respect to the problem variables. The efficiency of the CSLQ is derived from the implementation of a Riccati based active-set method for solving general inequality constrained linear quadratic optimal control problems. The associated difficulties in selecting an adequate time discretization grid are alleviated by the implementation of a sensitivity-based adaptive algorithm that efficiently refines the discretization by examining where the largest violations in the optimality conditions occur.