Global stabilization of multiple integrators by a bounded feedback with constraints on its successive derivatives

In this paper, we address the global stabilization of chains of integrators by means of a bounded static feedback law whose p first time derivatives are bounded. Our construction is based on the technique of nested saturations introduced by Teel. We show that the control amplitude and the maximum value of its p first derivatives can be imposed below any prescribed values. Our results are illustrated by the stabilization of the third order integrator on the feedback and its first two derivatives

Nonlinear control of a nano-hexacopter carrying a manipulator arm

International audienceThis paper proposes a simple solution for stabilization of a nano-hexacopter carrying a manipulator arm in order to increase the type of missions achievable by these types of systems. The manipulator arm is attached to the lower part of the hexacopter. The motion of the arm induces a change of the center of mass of the whole body, which induces torques which can produce the loss of stability. The present work deals with the stabilization of the whole system-that is hexacopter and arm-by means of a set of nonlinear control laws. First, an attitude control, stabilizes the hexacopter to a desired attitude taking into account the movement of the arm. Then, a suitable virtual control and the translational dynamics allow the formulation of a nonlinear controller, which drives the aerial vehicle to a desired position. Both controls consist in saturation functions. Experimental results validate the proposed control strategy and compares the results when the motion of the arm is taken into account or not

Control and Model-Aided Inertial Navigation of a Nonholonomic Vehicle

International audienceThe present work deals with the control and localization problem of wheeled-mobile robots with nonholonomic constraints. In the proposed method a simple nonlinear control law, composed of a position and heading direction controller, is designed to asymptotically stabilize the position error. The control law takes into account the constraints on the control signals in order to avoid saturation of the actuators. Furthermore, this paper considers a method of using the dynamic vehicle model and vehicle's nonholonomic constraints in order to aid position and attitude estimates provided by an Inertial Navigation System (INS). It is shown that dynamic model and vehicle's nonholonomic constraints can reduce the error growth in robot position estimates. Simulations are included to confirm the effectiveness of the proposed scheme

Bounded Coordination Control of Second-order Dynamic Agents

This paper presents a constructive design of distributed and bounded coordination controllers that force mobile agents with second-order dynamics to track desired trajectories and to avoid collision between them. The control design is based on the new bounded control design technique for second-order systems, and new pairwise collision avoidance functions. The pair wise collision functions are functions of both the relative position and velocity of the agents instead of only the relative position as in the literature. Desired features of the proposed control design include:1) Boundedness of the control inputs by a predefined bound despite collision avoidance between the agentsconsidered,2) No collision between any agents,3) Asymptotical stability of desired equilibrium set, and4) Instability of all other undesired critical sets of the closed loop system. The proposed control design is then applied to design a coordination control system for a group of vertical take-off and landing (VTOL) aircraft

Coordination Control of Quadrotor VTOL Aircraft in Three-Dimensional Space

This paper presents a constructive design of distributed coordination controllers for a group of N quadrotor vertical take-off and landing (VTOL) aircraft in three-dimensional space. A combination of Euler angles and unit-quaternion for the attitude representation of the aircraft is used to result in an effective control design, and to reduce singularities in the aircraft’s dynamics. The coordination control design is based on a new bounded control design technique for second-order systems and new pairwise collision avoidance functions. The pairwise collision functions are functions of both relative positions and relative velocities between the aircraft instead of only their relative positions as in the literature. To overcome the inherent underactuation of the aircraft, the roll and pitch angles of the aircraft are considered as immediate controls. Simulations illustrate the results