This paper deals with the problem of trajectory planning and tracking of a quadcopter system based on the property of differential flatness. First, B-spline characterisations of the flat output allow for optimal trajectory generation subject to waypoint constraints, thrust and angle constraints while minimising the trajectory length. Second, the proposed tracking control strategy combines feedback linearisation and nested saturation control via flatness. The control strategy provides bounded inputs (thrust, roll and pitch angles) while ensuring the overall stability of the tracking error dynamics. The control parameters are chosen based on the information of the a priori given reference trajectory. Moreover, conditions for the existence of these parameters are presented. The effectiveness of the trajectory planning and the tracking control design is analysed and validated through simulation and experimental results over a real nano-quadcopter platform, the Crazyflie 2.0.

We propose two different nonlinear model predictive control (NMPC) schemes (with and without terminal cost and constraints) for stabilizing the translational dynamics of thrust-propelled vehicles. Both approaches make use of an elaborated nonlinear feedback linearization controller and its associated ellipsoidal invariant set under restrictive input constraints, hence guaranteeing the closed-loop asymptotic stability. The terminal constraint set of the corresponding NMPC design is easy to tune due to its clear formulation expressed directly in terms of the tuning variables, while for the NMPC scheme without terminal constraint, the design allows to stabilize the system with a significantly shorter prediction horizon in comparison with the existing method in the literature. Simulation and experimental tests over a nano-drone platform validate the proposed approaches.

We propose a 2D path planning algorithm in a non-convex workspace defined as a sequence of connected convex polytopes. The reference path is parameterized as a B-spline curve, which is guaranteed to entirely remain within the workspace by exploiting the local convexity property and by formulating linear constraints on the control points of the B-spline. The novelties of the paper lie in the use of the equivalent Bézier representation of the B-spline curve, which significantly reduces the conservatism in the local convexity bound and in the integration of these constraints into a convex quadratic optimization problem, which minimizes the curve length. The algorithm is successfully validated in both simulations and experiments, by providing obstacle-free reference paths on real occupancy grid maps obtained from the laser scan data of a mobile robot platform.

To deal with the problem of optimal path planning in 2D space, this paper introduces a new toolbox named “Navigation with Polytopes” and explains the algorithms behind it. The toolbox allows one to create a polytopic map from a standard grid map, search for an optimal corridor, and plan a safe B-spline reference path used for mobile robot navigation. Specifically, the B-spline path is converted into its equivalent Bézier representation via a novel calculation method in order to reduce the conservativeness of the constrained path planning problem. The conversion can handle the differences between the curve intervals and allows for efficient computation. Furthermore, two different constraint formulations used for enforcing a B-spline path to stay within the sequence of connected polytopes are proposed, one with a guaranteed solution. The toolbox was extensively validated through simulations and experiments.

This paper proposes a two-layer hierarchical control scheme for trajectory tracking of a multicopter system using attitude quaternion. We first present the differential flatness properties of the system and then, exploit them to design the feedback linearization laws for the position controller at the high control level. Next, the computed-torque control method is employed for stabilizing the attitude quaternion. The whole control scheme is illustrated through simulations while the position controller is further tested under experiments over a nano-drone quadcopter platform.