In this paper, an original method about heavy vehicles rollover risk prediction is presented and validated experimentally. It is based on the calculation of the LTR (load transfer ratio) which depends on the estimated vertical forces using high order sliding mode observers. The validation tests were carried out on an instrumented truck rolling on the road at various speeds and lane-change manoeuvres. Many scenarios have been experienced: driving on straight line, curve line and zigzag to emphasize the rollover phenomenon and its prediction to set off an alarm to the driver.

This paper presents the design of a backstepping controller using sliding mode estimation technique which aims to simplify the control procedure. This approach, applied to a quadrotor unmanned aerial vehicle, differs from standard backstepping in that the virtual control inputs are designed based on estimates of the previous virtual control inputs. This eliminates the need to take derivatives of the system dynamics, which simplifies the control law. The estimation design is based on the exact second-order sliding mode differentiator. The controller objective is to achieve good tracking of desired positions and yaw angle while keeping the stability of the pitch and roll angles. The design methodology is based on the Lyapunov stability. Simulation results demonstrate the effectiveness of the proposed approach.

This paper presents a nonlinear dynamic model for a quadrotor helicopter in a form suited for backstepping control design. Due to the under-actuated property of quadrotor helicopter, the controller can set the helicopter track three Cartesian positions (x,y,z) and the yaw angle to their desired values and stabilize the pitch and roll angles. The system has been presented into three interconnected subsystems. The first one representing the under-actuated subsystem, gives the dynamic relation of the horizontal positions (x,y) with the pitch and roll angles. The second fully-actuated subsystem gives the dynamics of the vertical position z and the yaw angle. The last subsystem gives the dynamics of the propeller forces. A backstepping control is presented to stabilize the whole system. The design methodology is based on the Lyapunov stability theory. Various simulations of the model show that the control law stabilizes a quadrotor with good tracking