System architecture of HALAS—a helicopter slung load stabilisation and positioning system

Abstract

To support helicopter pilots during slung load operations currently a pilot assistance system called Hubschrauber-Außenlast-Assistenzsystem (HALAS) is being developed within a cooperation of the German Aerospace Centre (DLR) and iMAR Navigation GmbH. The objective of this research is the demonstration of an automatic slung load stabilisation and positioning system during the flight test with DLR’s research helicopter Active Control Technology/Flying Helicopter Simulator (ACT/FHS). The automatic slung load control system is being designed to extend the functionalities of the helicopter’s stability, control and augmentation system. The control system will be able to handle the challenges of rescue hoist operations. This means compensation of additional roll, pitch and yaw moments created by a significant distance of the load suspension point to the helicopter’s centre of gravity and the handling of a variable cable length. To measure the slung load motion, an optical-inertial sensor is being developed by iMAR Navigation GmbH. In this paper, the overall system architecture of HALAS as well as the hardware integration into the ACT/FHS is explained. The optical-inertial sensor used for the slung load dynamics measurement and estimation is described in detail. Furthermore, a first system analysis of a simulation model used for the later controller design is presented. The focus of the stability analysis is laid on variations of cable length, load mass and load suspension point position. The control law development process itself is not part of this paper but will be published later.

Appendices

Appendix

In this section, the differential equations of motion for the helicopter with a slung load are derived. The helicopter is modelled as a rigid body with six DOF and the load is modelled as a point mass with three DOF. Helicopter and load motion are coupled by the suspension cable, which is represented by a spring-damper system exerting the cable force as constraining force on helicopter and load (see Fig. 22). The formulation of the equations for the helicopter and the load are set up separately.

Fig. 22

Helicopter coupled with slung load

The general nonlinear equation of motion of the helicopter for the translational motion is

$$\dot{\varvec{V}}_{\text{H,b}} = \left[ {\begin{array}{*{20}c} {\dot{u}} \\ {\dot{v}} \\ {\dot{w}} \\ \end{array} } \right]_{\text{H,b}} = m_{\text{H}}^{ - 1} \mathop \sum \nolimits \varvec{F}_{\text{H,b}} -\varvec{\omega}_{\text{H,b}} \times \varvec{V}_{\text{H,b}}$$

(4)

with the sum of the external forces $\mathop \sum \nolimits \varvec{F}_{\text{H,b}}$, which is composed of the aerodynamic force $\varvec{F}_{\text{H,b}}^{\text{A}}$, gravitational force $\varvec{F}_{\text{H,b}}^{G}$ and cable force $\varvec{F}_{\text{b}}^{\text{C}}$, each of them formulated in the body-fixed frame.

$$\mathop \sum \nolimits \varvec{F}_{\text{H,b}} = \varvec{F}_{\text{H,b}}^{\text{A}} + \varvec{F}_{\text{H,b}}^{\text{G}} + \varvec{F}_{\text{b}}^{\text{C}} = \varvec{T}_{\text{ba}} \varvec{F}_{\text{H,a}}^{\text{A}} + \varvec{T}_{\text{be}} \varvec{F}_{\text{H,e}}^{\text{G}} + \varvec{T}_{\text{be}} \varvec{F}_{\text{e}}^{\text{C}}.$$

(5)

$\varvec{T}_{\text{ba}}$ and $\varvec{T}_{\text{be}}$ are the transformation matrices from the aerodynamic system and from the earth-fixed system to the body-fixed system, respectively. The equation of motion of the rotational motion is derived by

$$\dot{\varvec{\omega }}_{\text{H,b}} = \left[ {\begin{array}{*{20}c} {\dot{p}} \\ {\dot{q}} \\ {\dot{r}} \\ \end{array} } \right]_{\text{H,b}} = \varvec{I}_{\text{H}}^{ - 1} \mathop \sum \nolimits \varvec{M}_{\text{H,b}} - \varvec{I}_{\text{H}}^{ - 1}\varvec{\omega}_{\text{H,b}} \times \left( {\varvec{I}_{\text{H}}\varvec{\omega}_{\text{H,b}} } \right)$$

(6)

where $\varvec{I}_{\text{H}}$ is the helicopter inertia tensor and $\mathop \sum \nolimits \varvec{M}_{\text{H,b}}$ is the sum of the external moments applied at the CG.

$$\mathop \sum \nolimits \varvec{M}_{{{\text{H,}}b}} = \varvec{M}_{\text{H,b}}^{\text{A}} + \varvec{M}_{\text{b}}^{\text{C}} = \varvec{T}_{\text{ba}} \varvec{M}_{\text{H,a}}^{\text{A}} + \varvec{r}_{\text{HSP,b}} \times \varvec{F}_{\text{b}}^{\text{C}}.$$

(7)

$\varvec{M}_{\text{H,a}}^{\text{A}}$ is the aerodynamic moment. If the load is suspended outside of the CG the cable force exerts a moment on the helicopter with the corresponding lever arm $\varvec{r}_{\text{HSP,b}}$—the distance between CG and suspension point.

Equations of motion—load

The load as a point mass has no rotational DOF, which means that the body-fixed frame of the load is aligned with the inertial frame. The differential equations of the load are given by

$$\dot{\varvec{V}}_{\text{L,e}} = \left[ {\begin{array}{*{20}c} {\dot{u}} \\ {\dot{v}} \\ {\dot{w}} \\ \end{array} } \right]_{\text{L,e}} = m_{\text{L}}^{ - 1} \mathop \sum \nolimits \varvec{F}_{\text{L,e}}.$$

(8)

$\mathop \sum \nolimits \varvec{F}_{\text{L,e}}$ is the sum of the external forces. The forces acting on the load are as for the helicopter the aerodynamic force $\varvec{F}_{\text{L,e}}^{\text{A}}$, gravitational force $\varvec{F}_{\text{L,e}}^{\text{G}}$ and the cable force $\varvec{F}_{\text{e}}^{\text{C}}$:

$$\mathop \sum \nolimits \varvec{F}_{\text{L,e}} = \varvec{F}_{\text{L,e}}^{\text{A}} + \varvec{F}_{\text{L,e}}^{\text{G}} + \varvec{F}_{\text{e}}^{\text{C}}.$$

(9)

The aerodynamic force acting on the load is a drag-only force in direction of the local airflow velocity,

$$\varvec{F}_{\text{L,e}}^{\text{A}} = \frac{\rho }{2}\left| {\varvec{V}_{\text{L,e}} } \right|\varvec{V}_{\text{L,e}} S_{\text{L}} c_{\text{D}}$$

(10)

with the density $\rho$, surface $S_{\text{L}}$ and drag coefficient $c_{\text{D}}$.

Calculation of the constraining cable force

In the following, the derivation of the constraining cable force which couples the helicopter and the load motion will be described. The cable is represented by a spring-damper system with the resultant cable force $\varvec{F}_{\text{e}}^{\text{C}}$ (see Fig. 22). For the calculation of the cable force in the earth-fixed frame, the load position relative to the suspension point at the helicopter $\varvec{x}_{\text{C,e}}$ is determined:

$$\varvec{x}_{\text{C,e}} = \varvec{x}_{\text{L,e}} - \varvec{x}_{{{\text{HSP}},{\text{e}}}}$$

(11)

with the load position $\varvec{x}_{\text{L,e}}$ and the suspension point $\varvec{x}_{{{\text{HSP}},{\text{e}}}}$ in the earth-fixed frame. The suspension point can be obtained as follows:

$$\varvec{x}_{{{\text{HSP}},{\text{e}}}} = \varvec{x}_{\text{H,e}} + \varvec{T}_{\text{eb}} \varvec{r}_{{{\text{HSP}},{\text{b}}}} .$$

(12)

$\varvec{T}_{\text{eb}} \varvec{ }$ is the transformation matrix with the Euler angles that performs the transformation from the body-fixed to the earth-fixed frame. The actual cable length $L$ is the absolute value of the relative load position:

$$L = \left| {\varvec{x}_{\text{C,e}} } \right|.$$

(13)

The cable force is the sum of the spring and damping force

$$\varvec{F}_{\text{e}}^{\text{C}} = (F_{\text{spring}} + F_{\text{damp}} )\frac{{\varvec{x}_{\text{C,e}} }}{L}$$

(14)

where the spring force is proportional to the elongation,

$$F_{\text{spring}} = c_{\text{cable}} {\text{d}}L$$

(15)

with the spring constant $c_{\text{cable}}$ and the elongation

$${\text{d}}L = L - L_{0}$$

(16)

where $L_{0}$ is the unstretched cable length.

The damping force is determined by the elongation rate ${\text{d}}\dot{L}$:

$$F_{\text{damp}} = d_{\text{cable}} {\text{d}}\dot{L} = \left( {\dot{\varvec{x}}_{\text{L,e}} - \dot{\varvec{x}}_{{{\text{HSP}},{\text{e}}}} } \right)\frac{{\varvec{x}_{\text{C,e}} }}{L}$$

(17)

where $d_{\text{cable}}$ is the damping coefficient,

$$d_{\text{cable}} = 2D\sqrt {c_{\text{cable}} m_{\text{L}} } .$$

(18)

Further, the velocity of the suspension point is calculated by:

$$\dot{\varvec{x}}_{{{\text{HSP}},{\text{e}}}} = \varvec{T}_{\text{eb}} \left( {\varvec{V}_{\text{H,b}} +\varvec{\omega}_{\text{H,b}} \times \varvec{r}_{{{\text{HSP}},{\text{b}}}} } \right).$$

(19)

It is assumed that the cable exerts only a tension force. In case of a loose cable, the cable force is set to zero, leading to the following distinction:

$$\varvec{F}_{\text{e}}^{\text{C}} = \left\{ {\begin{array}{*{20}c} {\varvec{F}_{\text{e}}^{\text{C}} , \quad {\text{d}}L > 0} \\ {0, \quad {\text{d}}L \le 0} \\ \end{array} } \right..$$

(20)

Calculation of the cable angles and rates

The modelling of the load system with an elastic suspension cable and a point mass as the load leads to a formulation of the differential equations of motions, where the cable or pendulum angles and rates do not appear explicitly. For this reason, they have to be determined by the relative position of the load in respect to the helicopter (see Eq. 11). In the next step, the relative load position is transformed to the coordinate system that is aligned with the helicopter heading $\psi$

$$\varvec{x}_{{{\text{C,e}}\psi }} = \left[ {\begin{array}{*{20}c} {x_{\text{C}} } \\ {y_{\text{C}} } \\ {z_{\text{C}} } \\ \end{array} } \right]_{{{\text{e}}\psi }} = \varvec{T}_{\psi } \varvec{x}_{\text{C,e}} = \left[ {\begin{array}{*{20}c} {\cos \psi } & {\sin \psi } & 0 \\ { - \sin \psi } & {\cos \psi } & 0 \\ 0 & 0 & 1 \\ \end{array} } \right]\varvec{x}_{\text{C,e}} .$$

(21)

The transformation ensures that the longitudinal and lateral cable angle are related to the corresponding helicopter axis, i.e. the longitudinal cable angle describes the aft and fore swinging of the load and the lateral cable angle describes the lateral load swinging motion, seen from the pilot’s view. The longitudinal and lateral cable angles are calculated by:

$$\vartheta_{\text{C}} = { \arctan }\left( {\frac{{x_{{{\text{C,e}}\psi }} }}{{z_{{{\text{C,e}}\psi }} }}} \right)$$

(22)

and

$$\varphi_{\text{C}} = - { \arctan }\left( {\frac{{y_{{{\text{C}},{\text{e}}\psi }} }}{{z_{{{\text{C,e}}\psi }} }}} \right).$$

(23)

The rates are obtained by time derivation of the corresponding angles:

$$\dot{\vartheta }_{\text{C}} = \frac{\text{d}}{{{\text{d}}t}}\vartheta_{\text{C}}$$

(24)

and

$$\dot{\varphi }_{\text{C}} = \frac{\text{d}}{{{\text{d}}t}}\varphi_{\text{C}} .$$

(25)