Parameter choices for stable debris-tether-tug systems

The debris-tether-tug (DTT) system is recognized as one of the most promising techniques to remove space debris, especially for large objects like defunct satellites. It is made up by an active tug, a debris and a tether connecting the two bodies. This system shows significant nonlinear characteristics due to the weak connections between debris and tug using soft tethers. Previous studies have revealed that tether tangling, large oscillations, and other unstable phenomena may occur because of the inappropriate inputs, like thrusts, and system parameters, such as tether elasticity, masses of the tug and debris, etc. However, specific ranges or relations is hard to be obtained because the large number of parameters increases the difficulties to determine the desired ranges as one parameter may be affected by others. Thus, it is necessary to reduce the number of parameters using a non-dimensional system dynamics model, and then reveal the specific relationships between non-dimensional parameters and the dynamic behavior of the DTT system, so that general recommendations can be offered to avoid unstable motions when designing the system. In this paper, a non-dimensional model of the DTT system is proposed in which the debris and tug are treated as rigid bodies. The tether is discretized into multiple spring-damper segments, and the tether attachment points on the tug and debris are left arbitrary. Then, the DTT system model is simplified to calculate the analytical solutions. The influences of these nondimensionalized parameters are studied via numerical simulations, and the results are compared with the simplified system models. Finally, reasonable parameter choices are offered for practical cases.