Abstract
In recent years, there has been a growing interest in servicing orbiting satellites. In most cases, in-orbit servicing relies on the use of spacecraft-mounted robotic manipulators to carry out complicated mission objectives. Dual quaternions, a mathematical tool to conveniently represent pose, has recently been adopted within the space industry to tackle complex control problems during the stages of proximity operations and rendezvous, as well as for the dynamic modeling of robotic arms mounted on a spacecraft. The objective of this paper is to bridge the gap in the use of dual quaternions that exists between the fields of spacecraft control and fixed-base robotic manipulation. In particular, we will cast commonly used tools in the field of robotics as dual quaternion expressions, such as the Denavit-Hartenberg parameterization, or the product of exponentials formula. Additionally, we provide, via examples, a study of the kinematics of different serial manipulator configurations, building up to the case of a completely free-floating robotic system. We provide expressions for the dual velocities of the different types of joints that commonly arise in industrial robots, and we end by providing a collection of results that cast convex constraints commonly encountered by space robots during proximity operations in terms of dual quaternions.
Highlights
Robots are increasingly present in our daily lives, with their many uses ranging from simple vacuuming devices to complex manufacturing robotic arms
Quaternions are the representation of choice when it comes to attitude parameterization for spacecraft control and estimation, while SE(2)/SE(3) and the Spatial Vector Algebra [5] are the dominant tools of choice in the fixed-base robotic community
With the recent advent of dual quaternions, it is only natural to explore the use of a pose representation tool for spacecraft control and estimation in order to study robotic systems mounted on a spacecraft
Summary
Robots are increasingly present in our daily lives, with their many uses ranging from simple vacuuming devices to complex manufacturing robotic arms. Özgür and Mezouar [20] make use of said representation of dual velocity, commonly given by an expression of the form ω = ω + ev, to perform kinematic control on a robotic arm, yielding a clever representation of the Jacobian matrix that uses dual quaternion screws Their approach, has a fixed base and requires the use of base-frame coordinates—as opposed to body-frame coordinates, which are commonly used in the study of spacecraft motion—to describe the Plücker lines associated to the different joints of the system. We provide some important well-known results, such as the derivation of the famous quaternion kinematic law, and the aforementioned dual quaternion equivalent, as well as a collection of results that capture convex constraints using dual quaternions While the latter expressions have been used in the field of Entry, Descent, and Landing (EDL), their incorporation in robotic manipulation for in-orbit servicing missions is extremely beneficial in order to ensure safety and robustness. Addressing these constraints in a numerically efficient manner (e.g., casting them as convex constraints) leads to safe and elegant solutions of the in-orbit servicing problem
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