Pedro O. Pereira

Lyapunov-based generic controller design for thrust-propelled underactuated systems

We present a controller for an underactuated system which is driven by a one dimensional linear acceleration/thrust along a direction vector, by a time-varying gravity, and by the angular acceleration of the direction vector. We propose state and time-dependent control laws for the linear and angular accelerations that guarantee that the position of the system is steered to the origin. The proposed control law depends on (i) a bounded control law for a double integrator system; and (ii) on a Lyapunov function that guarantees asymptotic stability of the origin for the double integrator system when controlled with the previous bounded control law. As such, the control law forms a family of control laws depending on (i) and (ii). The complete state space of the system, under the proposed control laws, has two equilibria, and by proper control design, a trajectory of the system is guaranteed to converge to only one of those. The overall design provides a common framework for controlling different systems, such as quadrotors and slung load transportation systems.

Slung load transportation with a single aerial vehicle and disturbance removal

We present a trajectory tracking controller for a quadrotor-load system, composed of a single load and a single unmanned aerial vehicle connected by a cable or rope. The load is modeled as a point mass while the aerial vehicle is assumed to be fully actuated, with thrust and attitude of the quadrotor as inputs to the system quadrotor-load. We assume there is a constant input disturbance at the thrust input, and a disturbance estimator is presented that guarantees that asymptotic tracking is guaranteed in the presence of such a disturbance. The load and the aerial vehicle are connected by a cable of fixed length that behaves as a rigid link under tensile forces, and as a non-rigid link when under compressive forces. The proposed controller guarantees that the cable is always under tensile forces, provided that the position trajectory to be tracked satisfies some mild conditions. The system quadrotor-load can be transformed into a form that resembles that of systems describing underactuated aerial vehicles, and for which a variety of control strategies have been proposed. In particular, we propose a controller based on a backstepping procedure in conjunction with a bounded double integrator controller. We present simulations validating the proposed control algorithm, and some preliminary experimental results are also presented.

Family of controllers for attitude synchronization in S2

In this paper we study a family of controllers that guarantees attitude synchronization for a network of elements in the unit sphere domain, i.e., S2. We propose distributed continuous controllers for elements whose dynamics are controllable (i.e., control with torque as command), and which can be implemented by each individual agent without the need of a common global orientation frame among the network, i.e., it requires only local information that can be measured by each individual agent from its own orientation frame. The controllers are specified according to arbitrary distance functions in S2, and we provide conditions on those distance functions that guarantee that i) a synchronized network of agents is locally asymptotically stable for an arbitrary connected network topology; ii) a synchronized network can be achieved for almost all initial conditions in a tree graph network. We also study the equilibria configurations that come with specific types of network graphs. The proposed strategies can be used in attitude synchronization of swarms of fully actuated rigid bodies, such as satellites.

Family of controllers for attitude synchronization on the sphere

In this paper we study a family of controllers that guarantees attitude synchronization for a network of elements in the unit sphere domain, i.e.

Stability of load lifting by a quadrotor under attitude control delay

\mathcal{S}^2

Decoupled design of controllers for aerial manipulation with quadrotors

. We propose distributed continuous controllers for elements whose dynamics are controllable (i.e. control with torque as command), and which can be implemented by each individual agent without the need of a common global orientation frame among the network, i.e. it requires only local information that can be measured by each individual agent from its own orientation frame. The controllers are specified according to arbitrary distance functions in

Leader following trajectory planning

\mathcal{S}^2

Collaborative transportation of a bar by two aerial vehicles with attitude inner loop and experimental validation

, and we provide conditions on those distance functions that guarantee that i) a synchronized network of agents is locally asymptotically stable for an arbitrary network graph; ii) a synchronized network can be achieved for almost all initial conditions in a tree graph network. We also study the equilibria configurations that come with specific types of network graphs. The proposed strategies can be used in attitude synchronization of swarms of fully actuated rigid bodies, such as satellites.

Control framework for slung load transportation with two aerial vehicles

We propose a control law for stabilization of a quadrotor-load system, and provide conditions on the control laws gains that guarantee exponential stability of the equilibrium. The system is composed of a load and an unmanned aerial vehicle (UAV) attached to each other by a cable of fixed length, which behaves as a rigid link under tensile forces; and the control input is composed of a three dimensional force requested to the UAV, which the UAV provides with or without delay. Given the proposed control law, we analyze the stability of the equilibrium in two separate parts. In the first, the system is modeled assuming that the UAV provides the requested control input without delay, and we verify that the equilibrium is exponentially stable. In the second part, the UAV is modeled as possessing an attitude inner loop, and we provide a lower bound on the attitude gain for which exponential stability of the equilibrium is preserved. An integral action term is also included in the control law, which compensates for battery drainage or model mismatches, such as an unknown load mass. We present experiments for different scenarios that demonstrate and validate the robustness of the proposed control law.

Nonlinear pose tracking controller for bar tethered to two aerial vehicles with bounded linear and angular accelerations

In this paper, we model an aerial vehicle, specifically a quadrotor, and a load attached to each other by a rigid link. We assume a torque input at the joint between the aerial vehicle and the rigid link is available. After modeling, we decouple the system dynamics in two separate subsystems, one concerning the position of the center of mass, which we control independently from the chosen torque input; and a second subsystem, concerning the attitude of the rigid link, which we control by appropriately designing a torque control law. Differential flatness is used to show that controlling these two separate systems is equivalent to controlling the complete system. We design control laws for the quadrotor thrust, the quadrotor angular velocity and the torque input, and provide convergence proofs that guarantee that the quadrotor follows asymptotically a desired position trajectory while the manipulator follows a desired orientation. Simulation and experimental works are presented which validate the proposed algorithms.