Regularized Hierarchical Differential Dynamic Programming

TL;DR: This paper properly defines the problem of regularizing the task cost functions in the presence of a hierarchy and proposes an algorithm to compute an approximate solution, validating the interest of the hierarchy in OC and empirical demonstrating the importance of regularization to generate feasible behaviors.

Abstract: This paper presents a new algorithm for optimal control (OC) of nonlinear dynamical systems. The main feature of this algorithm is that it allows the specification of the control objectives as a hierarchy of tasks, each task representing an action that the robot should perform. Each task is described by a cost function that the algorithm tries to minimize, while not affecting the tasks of higher priority. The concept of strict priority allows for an easier and more robust specification of the control objectives, without hand tuning of task weights. The hierarchy also makes it possible to properly regularize the behavior of each task independently. For the first time, we properly define the problem of regularizing the task cost functions in the presence of a hierarchy and propose an algorithm to compute an approximate solution. Several simulated scenarios with different robots compare our solution with other state-of-the-art methods, validating the interest of the hierarchy in OC and empirically demonstrating the importance of regularization to generate feasible behaviors.