These are some notes on the paper “Free-floating space manipulator impacting a floating object: Modeling and output SDRE controller design” by Nekoo et al.

Abstract

This work investigates the dynamics modeling, control, and impact resolution between a floating object and a free-floating space manipulator (FFSM). The controller design is carried out by using an output- and state-dependent Riccati equation (OSDRE) approach. In a collision between an object and a mechanism, the computation of the generalized velocities and the impact force or impulse, which are interrelated, is a challenging problem. Taking into account the free-floating conditions of the space environment, the conservation of linear and angular momentum equations, combined with the conservation of kinetic energy under the elastic impact assumption, are used to find the unknown variables of the impact problem. The control problem addressed for the FFSM is to regulate its end-effector in a point-to-point motion scenario, this while the space manipulator suffers an unintended impact with a floating object, such as a damaged satellite or space debris. By proposing a safety pause starting with the occurrence of impact and for a short duration thereafter, the proposed OSDRE design succeeds in achieving the end-effector regulation control. Although the FFSM can reach the target point, it is shown that maintaining the end-effector regulation at the target is not feasible due to the momentum imparted to the FFSM as a result of the collision. To this end, we employ a simple thruster control on the space manipulator base to complete the regulation task. The theoretical development and controller design are demonstrated through a simulation case study of a spacecraft equipped with a three-link manipulator colliding with an object.

Introduction

The ideal scenario in such a situation would be the completion of a control task by the space manip- ulator, even though it suffered a collision.

Modeling: Mathematical Representation of Dynamics

Dynamics Model of the Floating Object

Dynamics Model of FFSM

Impact Modeling

Reduced-order Dynamics for Controller Design

Output Feedback SDRE Control

Case Study: FFSM with a Three-DoF Manipulator

System Definition

Simulation: Baseline Scenario

Simulation: FFSM Response to Impact Without Post-impact Actuation

Free-flying in Safety Pause: Compensating for Impact Momentum

Asymptotic Convergence, Velocity of the End-effector

Conclusions

Concluding Remarks

Future Studies: Penetration, Pushing, and Passing Through the Object