Optimal control with adaptive internal dynamics models

Optimal feedback control has been proposed as an attractive movement generation strategy in goal reaching tasks for anthropomorphic manipulator systems. The optimal feedback control law for systems with non-linear dynamics and non-quadratic costs can be found by iterative methods, such as the iterative Linear Quadratic Gaussian (iLQG) algorithm. So far this framework relied on an analytic form of the system dynamics, which may often be unknown, difficult to estimate for more realistic control systems or may be subject to frequent systematic changes. In this paper, we present a novel combination of learning a forward dynamics model within the iLQG framework. Utilising such adaptive internal models can compensate for complex dynamic perturbations of the controlled system in an online fashion. The specific adaptive framework introduced lends itself to a computationally more efficient implementation of the iLQG optimisation without sacrificing control accuracy – allowing the method to scale to large DoF systems

Comparative evaluation of approaches in T.4.1-4.3 and working definition of adaptive module

The goal of this deliverable is two-fold: (1) to present and compare different approaches towards learning and encoding movements us- ing dynamical systems that have been developed by the AMARSi partners (in the past during the first 6 months of the project), and (2) to analyze their suitability to be used as adaptive modules, i.e. as building blocks for the complete architecture that will be devel- oped in the project. The document presents a total of eight approaches, in two groups: modules for discrete movements (i.e. with a clear goal where the movement stops) and for rhythmic movements (i.e. which exhibit periodicity). The basic formulation of each approach is presented together with some illustrative simulation results. Key character- istics such as the type of dynamical behavior, learning algorithm, generalization properties, stability analysis are then discussed for each approach. We then make a comparative analysis of the different approaches by comparing these characteristics and discussing their suitability for the AMARSi project