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Dynamics over graph are large-scale systems in which the dynamic coupling among subsystems is modeled by a graph. Examples arise in spatially distributed systems (as discretized PDEs), multi-agent control systems or social dynamics. In this paper, we propose a cloud-assisted distributed algorithm to solve optimal control problems for nonlinear dynamics over graph. Inspired by the centralized Hauser’s projection operator approach for optimal control, our main contribution is the design of a descent method in which at each step agents of a network compute a local descent direction, and then obtain a new system trajectory through a distributed feedback controller. Such a controller, iteratively designed by a cloud, allows agents of the network to use only information from neighboring agents, thus resulting into a distributed projection operator over graph. The main advantages of our globally convergent algorithm are dynamic feasibility at each iteration and numerical robustness (thanks to the closed-loop updates) even for unstable dynamics. In order to show the effectiveness of our strategy, we present numerical computations on a discretized model of the Burgers’ nonlinear partial differential equation.

In this paper, we present a novel strategy to compute minimum-time trajectories for quadrotors in constrained environments. In particular, we consider the motion in a given flying region with obstacles and take into account the physical limitations of the vehicle. Instead of approaching the optimization problem in its standard time-parameterized formulation, the proposed strategy is based on an appealing re-formulation. Transverse coordinates, expressing the distance from a frame path, are used to parameterise the vehicle position and a spatial parameter is used as independent variable. This re-formulation allows us to (i) obtain a fixed horizon problem and (ii) easily formulate (fairly complex) position constraints. The effectiveness of the proposed strategy is proven by numerical computations on two different illustrative scenarios. Moreover, the optimal trajectory generated in the second scenario is experimentally executed with a real nano-quadrotor in order to show its feasibility., arXiv admin note: text overlap with arXiv:1702.04275

In this paper we study the problem of designing periodic orbits for a special class of hybrid systems, namely mechanical systems with underactuated continuous dynamics and impulse events. We approach the problem by means of optimal control. Specifically, we design an optimal control based strategy that combines trajectory optimization, dynamics embedding, optimal control relaxation and root finding techniques. The proposed strategy allows us to design, in a numerically stable manner, trajectories that optimize a desired cost and satisfy boundary state constraints consistent with a periodic orbit. To show the effectiveness of the proposed strategy, we perform numerical computations on a compass biped model with torso.

In this paper we design a nonlinear controller for aggressive maneuvering of a quadrotor. We take a maneuver regulation perspective. Differently from the classical trajectory tracking approach, maneuver regulation does not require following a timed reference state, but a geometric “path” with a velocity (and possibly orientation) profile assigned on it. The proposed controller relies on three main ideas. Given a desired maneuver, i.e., a set of state trajectories equivalent under time translations, the system dynamics is decomposed into dynamics longitudinal and transverse to the maneuver. A space-dependent version of the transverse dynamics is derived, by using the longitudinal state, i.e., the arc-length of the path, as an independent variable. Then the controller is obtained as a function of the arc-length consisting of two terms: a feed forward term, being the nominal input to apply when on the path at the current arc-length, and a feedback term exponentially stabilizing the state-dependent transverse dynamics. Numerical computations are presented to prove the effectiveness of the proposed strategy. The controller performances are tested in presence of uncertainty of the model parameters and input noise and saturations. The controller is also tested in a realistic simulation environment validated against an experimental test-bed.