In this article, we propose an online 3-D planning algorithm for a drone to race competitively against a single adversary drone. The algorithm computes an approximation of the Nash equilibrium in the joint space of trajectories of the two drones at each time step, and proceeds in a receding horizon fashion. The algorithm uses a novel sensitivity term, within an iterative best response computational scheme, to approximate the amount by which the adversary will yield to the ego drone to avoid a collision. This leads to racing trajectories that are more competitive than without the sensitivity term. We prove that the fixed point of this sensitivity enhanced iterative best response satisfies the first-order optimality conditions of a Nash equilibrium. We present results of a simulation study of races with 2-D and 3-D race courses, showing that our game theoretic planner significantly outperforms a model predictive control (MPC) racing algorithm. We also present results of multiple drone racing experiments on a 3-D track in which drones sense each others' relative position with onboard vision. The proposed game theoretic planner again outperforms the MPC opponent in these experiments where drones reach speeds up to 1.25 m/s.

This article proposes an online optimal active perception strategy for differentially flat systems meant to maximize the information collected via the available measurements along the planned trajectory. The goal is to generate online a trajectory that minimizes the maximum state estimation uncertainty provided by the employed observer. To quantify the richness of the acquired information about the current state, the smallest eigenvalue of the constructibility Gramian is adopted as a metric. In this article, we use B-splines for parametrizing the trajectory of the flat outputs and we exploit a constrained gradient descent strategy for optimizing online the location of the B-spline control points in order to actively maximize the information gathered over the whole planning horizon. To show the effectiveness of our method in maximizing the estimation accuracy, we consider two case studies involving a unicycle and a quadrotor that need to estimate their poses while measuring two distances w.r.t. two fixed landmarks. Concurrent estimation of calibration/environment parameters is also considered for illustrating how the proposed method copes with instances of active self-calibration and map building.

This paper deals with the problem of active sensing control for nonlinear differentially flat systems. The objective is to improve the estimation accuracy of an observer by determining the inputs of the system that maximise the amount of information gathered by the outputs over a time horizon. In particular, we use the Observability Gramian (OG) to quantify the richness of the acquired information. First, we define a trajectory for the flat outputs of the system by using B-Spline curves. Then, we exploit an online gradient descent strategy to move the control points of the B-Spline in order to actively maximise the smallest eigenvalue of the OG over the whole planning horizon. While the system travels along its planned (optimized) trajectory, an Extended Kalman Filter (EKF) is used to estimate the system state. In order to keep memory of the past acquired sensory data for online re-planning, the OG is also computed on the past estimated state trajectories. This is then used for an online replanning of the optimal trajectory during the robot motion which is continuously refined by exploiting the state estimation obtained by the EKF. In order to show the effectiveness of our method we consider a simple but significant case of a planar robot with a single range measurement. The simulation results show that, along the optimal path, the EKF converges faster and provides a more accurate estimate than along other possible (non-optimal) paths.

Teleoperating a quadrotor equipped with a monocular camera for exploring a wide area in search of something has become a common practice in many application scenarios (e.g. search and rescue). In order to efficiently plan operations, estimating the 3D pose of a point of interest is as important as detecting it. In this paper we propose a novel bilateral teleoperation architecture where an estimation scheme is exploited for recovering the position of a set of visual features while an operator steers the motion of the quadrotor UAV. The operator acts on a force-feedback master device that produces force cues meant to suggest where to drive the quadrotor for improving the convergence rate of the estimation process. The effectiveness of the proposed teleoperation strategy is validated by means of hardware in the loop simulations.

In this paper, we address the problem of using a camera with limited field of view for controlling the motion of a quadrotor in aggressive flight regimes. We present a minimum time trajectory planning method that guarantees visibility of the image features while allowing the robot to undertake aggressive motions for which the usual near-hovering assumption is violated. We exploit differential flatness and B-Splines to parametrize the system trajectories in terms of a finite number of control points, which can then be optimized by Sequential Quadratic Programming (SQP). The control strategy is similar to a Receding Horizon Control (RHC) approach for modifying online the reference trajectory in order to account for noise, disturbances and any non-modeled effect. The algorithm is validated in a physically realistic simulation environment.

In this paper, we propose a novel decentralized active perception strategy that maximizes the convergence rate in estimating the (unmeasurable) formation scale in the context of bearing-based formation localization for robots evolving in ℝ3× S1. The proposed algorithm does not assume presence of a global reference frame and only requires bearing-rigidity of the formation (for the localization problem to admit a unique solution), and presence of (at least) one pair of robots in mutual visibility. Two different scenarios are considered in which the active scale estimation problem is treated either as a primary task or as a secondary objective with respect to the constraint of attaining a desired bearing formation. The theoretical results are validated by realistic simulations.

The selection of a suitable set of visual features for an optimal performance of closed-loop visual control or Structure from Motion (SfM) schemes is still an open problem in the visual servoing community. For instance, when considering integral region-based features such as image moments, only heuristic, partial, or local results are currently available for guiding the selection of an appropriate moment set. The goal of this paper is to propose a novel learning strategy able to automatically optimize online the shape of a given class of image moments as a function of the observed scene for improving the SfM performance in estimating the scene structure. As case study, the problem of recovering the (unknown) 3D parameters of a planar scene from measured moments and known camera motion is considered. The reported simulation results fully confirm the soundness of the approach and its superior performance over more consolidated solutions in increasing the information gain during the estimation task.

In this paper we experimentally validate and compare three different methods for estimating the 3D parameters of a planar scene from a (possibly time-varying) set of feature points acquired by a moving monocular camera. The first method, based on the classical decomposition of the homography matrix, is meant to serve as a baseline condition classically used in many previous works. The other two methods exploit an active Structure from Motion (SfM) scheme for either extracting the plane from the reconstructed 3D position of all the tracked points, or for directly estimating the plane parameters by considering a set of discrete image moments as visual input. The possible loss/gain of point features during the camera motion is considered in all three methods by, in particular, introducing a suitable weighting strategy for the image moment case. Finally, the results of an experimental validation are presented with a comparative discussion of the pros/cons of the three methods.

Plane detection and estimation from visual data is a classical problem in robotic vision. In this work we propose a novel active strategy in which a monocular camera tries to determine whether a set of observed point features belongs to a common plane, and, if so, what are the associated plane parameters. The active component of the strategy imposes an optimized camera motion (as a function of the observed scene) able to maximize the convergence in estimating the scene structure. Based on this strategy, two methods are then proposed to solve the plane estimation task: a classical solution exploiting the homography constraint (and, thus, almost completely based on image correspondances across distant frames), and an alternative method fully taking advantage of the scene structure estimated incrementally during the camera motion. The two methods are extensively compared in several case studies by discussing the various pros/cons.

In this paper we propose a solution for coupling the execution of a visual servoing task with a recently developed active Structure from Motion strategy able to optimize online the convergence rate in estimating the (unknown) 3D structure of the scene. This is achieved by suitably modifying the robot trajectory in the null-space of the servoing task so as to render the camera motion `more informative' w.r.t. the states to be estimated. As a byproduct, the better 3D structure estimation also improves the evaluation of the servoing interaction matrix which, in turn, results in a better closed-loop convergence of the task itself. The reported experimental results support the theoretical analysis and show the benefits of the method.

Structure estimation from motion (SfM) is a classical and well-studied problem in computer and robot vision, and many solutions have been proposed to treat it as a recursive filtering/estimation task. However, the issue of actively optimizing the transient response of the SfM estimation error has not received a comparable attention. In this paper, we provide an experimental validation of a recently proposed nonlinear active SfM strategy via two concrete applications: 3D structure estimation for a spherical and a cylindrical target. The experimental results fully support the theoretical analysis and clearly show the benefits of the proposed active strategy. Indeed, by suitably acting on the camera motion and estimation gains, it is possible to assign the error transient response and make it equivalent to that of a reference linear second-order system with desired poles.

In this paper, we illustrate the application of a nonlinear active structure estimation from motion (SfM) strategy to three problems, namely 3-D structure estimation for 1) a point, 2) a sphere, and 3) a cylinder. In all three cases, an appropriate parameterization reduces the problem to the estimation of a single quantity. Knowledge of this estimated quantity and of the available measurements allows for then retrieving the full 3-D structure of the observed objects. Furthermore, in the point feature case, two different parameterizations based on either a planar or a spherical projection model are critically compared. Indeed, the two models yield, somehow unexpectedly, to different convergence properties for the SfM estimation task. The reported simulative and experimental results fully support the theoretical analysis and clearly show the benefits of the proposed active estimation strategy, which is in particular able to impose a desired transient response to the estimation error equivalent to that of a reference linear second-order system with assigned poles.

For a quadrotor aircraft, we study the problem of planning a trajectory that connects two arbitrary states while allowing the UAV to grasp a moving target at some intermediate time. To this end, two classes of canonical grasping maneuvers are defined and characterized. A planning strategy relying on differential flatness is then proposed to concatenate one or more grasping maneuvers by means of spline-based subtrajectories, with the additional objective of minimizing the total transfer time. The proposed planning algorithm is not restricted to pure hovering-to-hovering motions and takes into account practical constraints, such as the finite duration of the grasping phase. The effectiveness of the proposed approach is shown by means of physically-based simulations.