Keywords: multibody dynamics, non-holonomic constraints, time-efficient computation, free-floating space robots, real-time simulation, redundant kinematics.

In the near-future on-orbit servicing spaceflight missions, i.e. maintenance and even repair of malfunctioned telecommunications satellites by means of the beneficial use of robotics, will increase the operational lifetime of such satellites. For specific robotics operational purposes during servicing tasks the favoured approach is to switch off the AOCS (attitude and orbit control system) of the servicing satellite. This system then represents a free-floating satellite with a space robot attached to it [1]. From the mechanical viewpoint, free-floating robots in space represent non-holonomic systems, due to the conservation of both linear and angular momentum.

These constraints imply that planning of robotic end effector trajectories and their control is highly complicated. In several studies this problem has already been investigated extensively [2,3], be it more from the kinematics and dynamics point of view or from the control aspect. This complex trajectory planning task is more than ever valid if the manipulator degrees of freedom are increasing beyond the conventional number of six. Such kinematically redundant manipulators are favourably designed because of their flexibility in use and their increased skills. They are more and more intended to be applied in satellite servicing scenarios such as grasping of tumbling or malfunctioned target satellites in order to offer specific maintenance, berthing or even repair services. In these operational cases it is convenient for robotic task accomplishment, for instance in tele-operational and semi-autonomous robotic modes, to switch off the attitude and orbit control system of the chaser satellite where the robot is attached to.

This free-floating satellite-robot compound system, as already stated above, represents a very complex and flexibly moving system since the interaction between the robot motion itself and the satellite base is kinematically and dynamically highly coupled. Given a desired end effector (EE) trajectory of the manipulator in an inertial Cartesian frame for example, the accurate calculation of both the (actively) steered robotic joints and the satellite base passive variables is therefore a prerequisite for precise planning of satellite operational tasks with the robot in the loop.

In this paper we present two different approaches to solve for the compound motion behaviour that consists of degrees of freedom (DOF), with for the redundant manipulator and 6 DOFs for the base. For both approaches the solution of the manipulator inverse kinematics is not as straightforward as in the conventional case with a robot fixed base. In the first approach (IKCO inverse kinematics by constraint optimization), we regard the redundant manipulator with its satellite base, having the additional 6 DOFs as an entire, highly redundant robotic system for which we solve the inverse kinematics (IK) problem by means of a Lagrangian based optimization technique. Here, we have to respect the desired EE trajectory given by its sampled position and orientation values along the prescribed trajectory, which is handled by corresponding constraints in the Lagrangian. Moreover, compared to a redundant robot attached to a fixed base, we now have to respect the conservation law of linear and angular momentum. This is achieved by regarding both laws as two additional constraints within the optimization algorithm.

In the second approach (SBMM superposition of base and manipulator motions), solving for the overall motion dynamics, we subdivide the dynamics into two parts: first, a so-called relative part representing the influence of the manipulator relative to the satellite base (here, the IK problem of the redundant robot has to be solved for a fixed base first), and second, an absolute part representing the influence of the acceleration of the base due to the robot motion.

Simulation results are shown for the entire motion behaviour of the two approaches for a 7 DOF robot attached to a free-floating satellite base. In both approaches, the end effector motion is prescribed. The nonholonomic nature of the complete system is typically shown in the difference between the initial and the final configuration achieved after one closed loop. By observing potential center of mass time drifts as well as time drifts in both, the angular and linear momentum, we can assess the performance of the results obtained. All these quantities should remain zero in time and therefore they represent comfortable measures to check the quality and exactness of the underlying approaches.

1

G. Hirzinger, et al., "DLR's Robotic Technologies for On-Orbit Servicing", J. Advanced Robotics, Special Issue on Service Robots in Space, 18, No. 2, pp. 139-174, 2004. doi:10.1163/156855304322758006

2

R. Longman, R. Lindberg, M. Zedd, "Satellite-Mounted Robot Manipulators - New Kinematics and Reaction Moment Compensation", Intl. J. of Robotics Research, 6, No. 3, pp. 87-103, 1987. doi:10.1177/027836498700600306

3

E. Papadopoulos, K. Nanos, "On Configuration Planning for Free-Floating Space Robots", ROMANSY Conference, Montreal, Canada, 14-18 June 2004.

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