A unified computational framework for real-time optimal control

The dynamics of each agent of a multi-agent controlled dynamical system can be formulated in several possible ways: differential inclusion, flatness parameterization, higher-order inclusions and so on. A plethora of techniques have been proposed for each of these formulations but they are typically not portable across equivalent mathematical formulations. Further complications arise as a result of path constraints such as those imposed by obstacle avoidance or control saturation. In this paper, we present a unified computational framework based on pseudospectral methods to handle the optimal control of dynamical systems where the description of the governing equations or that of the path constraint is not a limitation. We illustrate our ideas by way of multiple formulations of a flexible link manipulator problem that includes a differentially flat formulation subject to control saturation. A comparison of our approach to a recent method reveals that we get an almost 30% improvement in the cost. Our results also show that equivalent mathematical formulations can yield varying run times leading to some surprising questions on flatness parameterization for real-time computation.