Jet-scheduling control for flat systems

The control of cranes and nonholonomic robots has gained increased interest mainly because of the civilian and military industrial need to achieve fast and accurate transport of goods and equipment. Old and new harbors are now venturing into fully automated systems combining automated trolleys and classical cranes. From a theoretical viewpoint these systems are challenging because they are strongly dynamically coupled and offer interesting and useful control problems. Therefore, to take full advantage of their potential, the control design must take into account as much structural information as possible. The structural property that is exploited in the control design proposed in this thesis is the differential flatness property of these systems, that is the existence of particular functions of the states (called flat outputs), the time parametrization of which implies parametrization of all the individual states and inputs. This property is extremely useful for motion planning problems where the system should move quickly from one configuration to another, without inducing too much overshoot or residual oscillations. However, the flatness property is not sufficient to guarantee the design of an efficient controller in the presence of uncertain and unmodeled dynamics. This is especially the case for cranes where the winching mechanism, expressed in terms of the engine and pulleys, has a large amount of unmodeled dry friction. This robustness issue is normally addressed by splitting the control task into a feedforward-like part that handles the dynamical couplings and a feedback term that enforces the tracking of the reference values stemming from the feedforward motion planning algorithm. In contrast, this thesis proposes to combine these two mechanisms, resulting in what will be called the jet-scheduling controller. Classically, the flatness property guarantees the construction of a feedforward input based on a planned motion of the flat outputs by simply combining values of the flat outputs and their time derivatives, i.e. without having to integrate differential equations. Therefore, in the absence of perturbation, this mechanism is sufficient to move the system from one state to another, once a trajectory compatible with the initial and final positions has been designed. However, when the system has some unmodeled dynamics, an additional mechanism must be provided to make sure that the planned trajectory is indeed tracked accurately. The point of view adopted in this thesis is that, instead of specifying a trajectory to be tracked explicitly, a dynamical system called "the jet scheduler" provides the derivatives (the jets) of an ideal stabilizing trajectory. These jets are updated regularly according to measurements so as to react to unknown perturbations. The flat correspondence is used to provide the values of the jets, and a subsidiary controller is designed to ensure that these jets are really matched asymptotically by the true system. Un