Avoiding dynamic singularities in Cartesian motions of free-floating manipulators

Abstract

Free-floating manipulators are subject to dynamic singularities that complicate their Cartesian motions and restrict their workspace. In this work, the Cartesian trajectory planning of free-floating manipulators is studied. A methodology is developed in which, for given end-effector trajectories, appropriate initial system configurations are found that result in singularity avoidance during end-effector motion. The method applies to both planar and spatial systems, with and without initial angular momentum, and to any desired end-effector position and attitude trajectories.

On the Dynamics and Control of Free-floating Space Manipulator Systems in the Presence of Angular Momentum

“…In case the GJM for some path taken becomes singular, the system manipulator becomes singular (Papadopoulos and Dubowsky, 1993) and the end-effector cannot follow the desired path (see Section "Constraints"). However, in Nanos and Papadopoulos (2015), a methodology to avoid such singularities, by carefully choosing the FFSMS initial configuration, has been developed. Thus, Eq.…”

“…Note that the additional terms C h and g h , caused by the presence of initial angular momentum, are functions of the spacecraft attitude described by the Euler parameters ε, n. Thus, in the spatial case, the system's reduced equations of motion depend on the spacecraft's attitude. The spacecraft attitude can be computed using the equations (Nanos and Papadopoulos, 2015):…”

“…Thus, to avoid any failure of the TJC-AMC, the end-effector must be in the PIW during its motion. Else, the initial spacecraft attitude and manipulator configuration should be selected to avoid DS (Nanos and Papadopoulos, 2015). The abovementioned constraints must be considered regardless of the existence of NZAM (Papadopoulos and Dubowsky, 1991a).…”

“…As mentioned in Section "Discussion, " DS avoidance, which results in a successful endeffector approach to point C, depends on the initial spacecraft attitude. A method to compute the appropriate initial spacecraft attitudes to avoid a DS can be found in Nanos and Papadopoulos (2015). In case the spacecraft initial attitude is θ 0,in = 270°, the FIGURE 7 | (A) The response of the manipulator configuration, (B) the required joint torques result by the application of the PD control law, given by Eq.…”

“…The same authors have proposed a methodology to avoid the path-dependent dynamic singularities (DS), defined in Papadopoulos and Dubowsky (1993), by carefully choosing the FFSMS initial configuration (Nanos and Papadopoulos, 2012). More recently, they extended this methodology to FFSMS with NZAM (Nanos and Papadopoulos, 2015).…”