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Robotic Gripper for Payload Capture in Low Earth Orbit

  • Genta Giancarlo
  • Dolci MarcoEmail author
Original Paper
  • 64 Downloads

Abstract

The consensus to a study phase for an Intermediate eXperimental Vehicle (IXV) successor, a preoperational vehicle called Space Reusable Integrated Demonstrator for European Return (SPACE RIDER), has been recently enlarged, as approved during last EU Ministerial Council. One of the main project tasks consists in developing SPACE RIDER to conduct on orbit servicing activity with no docking. SPACE RIDER would be provided with a robotic manipulator system (arm and gripper) able to transfer cargos, such as scientific payloads, from low Earth orbiting platforms to the SPACE RIDER cargo bay. The platform is a part of a space tug designed to move small satellites and other payloads from Low Earth Orbit to Geosynchronous Equatorial Orbit and vice versa. A study on this robotic technology is here presented. This research is carried out by Politecnico di Torino and Thales Alenia Space Italy. The system configuration of the robotic manipulator is first described in terms of volumes and masses. The considered housing cargo bay requirements in terms of volume (< 100 l) and mass (< 50 kg) combined with the required overall arm dimensions (4 m length), and mass of the cargo (5–30 kg) force to developing an innovative robotic manipulator with the task-oriented end-effector. It results in a 7df arm to ensure a high degree of dexterity and a dedicated end-effector designed to grasp the cargo interface. The gripper concept here developed consists in a multi-finger hand able to lock both translational and rotational cargo degrees of freedom through an innovative under-actuation strategy to limit its mass and volume. A configuration study on the cargo handle interface has also been performed together with some computer-aided design models and multibody analysis of the whole system to prove its feasibility. Finally, the concept of system control architecture is defined.

Keywords

On-orbit servicing Space robotic manipulator Grasping orbiting payload 

List of symbols

l0

Linear actuator motion variable

l1

Medial beam length

l2

L-shape beam length

s1

Medial beam arc length

s2

L-shape beam arc length

ϑ1

Medial beam angle variation

ϑ2

L-shape beam angle variation

ϑor

Out-of-plane rotation error

ϑir

In-plane rotation error

ϑn

Nominal camera field of view

\( \vartheta_{n}^{\prime } \)

Modified nominal camera field of view

x0

State vector camera position

σ

State vector camera position errors

\( \phi_{x} \)

Attitude angle related to the x-axis

\( \phi_{y} \)

Attitude angle related to the y-axis

\( \phi_{z} \)

Attitude angle related to the z-axis

pb

Operational space vector linear velocities

ωb

Operational space vector angular velocities

xb

State vector of the base

q

Joint vector of the arm

Hb

Inertia matrix of the base body

Hm

Inertia matrix of the manipulator arm

Hbm

Matrix that takes in account the coupling between base and arm

cb

Non-linear velocity dependent term of the base body

cm

Non-linear velocity dependent term of the arm

Fb

External forces/moments acting on the base

Fh

External forces/moments acting on the end-effector of the arm

τ

Joint torque vector on the arm

Jb

Jacobian matrix dependent on the base body motion

Jm

Jacobian matrix dependent on the arm motion

Abbreviations

ADCS

Attitude determination and control system

BLDC

Brushless direct current motor

CCD

Charge-coupled device

CSA

Canada Space Agency

ESA

European Space Agency

EVA

Extra vehicular activity

GEO

Geosynchronous Equatorial orbit

IXV

Intermediate eXperimental Vehicle

JEMRMS

Japanese Experiment Module Remote Manipulator System

LEO

Low Earth Orbit

NASA

National Aeronautics and Space Administration

P/L

Payload

RV

Rendezvous

RV&D

Rendezvous and Docking

SAPERE

Space advanced project excellence in research and enterprise

SARAH

Self adaptive robotic auxiliary hand

SFA

Small fine arm

SPACE RIDER

Space rider reusable integrated demonstrator for European return

SRMS

Space shuttle remote manipulator system

STRONG

System technology and research national global operations

TRL

Technology readiness level

1 Introduction

1.1 SAPERE—STRONG Projects

Under the SAPERE project, there is the STRONG project, related to the theme of space exploration, servicing in orbit and access to space. STRONG is related to the theme of space exploration and access to space having the objective of increasing the operability national space in this area by expanding the capacity industry in the creation of a Space Tug, an essential element in any space exploration scenario and enable, starting from intermediate orbits as those of the space station, launching tools and platforms with considerable savings in weight, and a strong optimization of the ratio between payload and platform itself. The IXV evolution system, developed by ESA, is a reusable demonstration of a return vehicle intended to the development of European technologies as equipment for aerodynamic and aerothermodynamics, heat protection, and navigation control system. This vehicle is designated by ESA to be the intermediate element in the European roadmap for the technological development with a view to future operative vehicles. The first step was the demonstrator IXV launched by ESA on 11 February 2015 [1]. Differently from its precursor, this demonstrator executes a landing on the runway and not a splash down as last step of the re-entry phase. However, in this case, SPACE RIDER is in charge of bringing back to the ground a P/L from the platform attached to the Space Tug. Achieving this goal is essential to develop a specific robotic system that allows the approach and the grasping of the selected P/L and his placement in the cargo bay of the vehicle. The P/L object of this service could be experiments related to the material science, advanced propulsion, or radiation protection.

This work is devoted to the description of the grasping manipulator design and mechanical aspect of this robotic system architecture. To get this goal, some assumptions and trade-off, described in the successive sections, have been considered to identify the best arrangement of the system.

1.2 Past, Present, and Future Scenarios

This paper focuses on the design study of a gripper for capturing payload in LEO. Grasping devices have evolved to help humans in manipulation for handling objects of different sizes, materials, and conditions. Grasping has been always considered as an essential part of manipulation and only recently a specific attention has been addressed to grasping devices as independent mechanical/mechatronic designs with theory, practice, and application. Grasping can be brought also into space activities and being customized for specific applications.

The first robotic manipulator arm used in the orbital environment was the SRMS [2]. This success opened a new era of orbital robotics and inspired numerous mission concepts. A long-term goal that has been discussed extensively since the early 1980s is the application of a robotic free-flyer or free-flying space robot to the rescue and servicing of malfunctioning spacecrafts. As other orbital space robots, there are Space Shuttle Remote Manipulator System, International Space Station Mounted Robot Manipulator Systems, Rotex [3] and Rokviss [4, 5], and Orbital Express [6] and ETS-VII [7]. At present, the existing grippers developed for space applications are the already cited Space Station Remote Manipulator System developed by CSA [8, 9, 10], the end-effector of European Robotic Arm developed by ESA [11, 12, 13, 14], and a Canadian under-actuated end-effector named by SARAH [15]. Particular attention has been given to the Robonaut [16, 17]. Robonaut is a dexterous humanoid robot designed and built at NASA’s Johnson Space Center in the United States. Robonaut’s future upgrade could enable it to move outside to help astronauts with EVA tasks or perform repairs on the exterior of the station. Combined with a surface mobility system like legs or wheels, Robonaut could perform as a human-like manipulation system for future exploration missions on the Moon or Mars. Orbital space robots will be able to assist humans in space by constructing and maintaining space modules and structures. Robotic manipulators have played essential roles in orbital operations. Moreover, satellite servicing missions are crucial to prevent the increase of space debris. More technological developments are expected to realize free-flying robots for servicing, rescuing, or capture-and-removal missions of the existing spacecraft in orbit.

In this paper, a new gripper concept for on-orbit servicing is presented in terms of:
  • numbers of actuators;

  • under-actuated working strategy;

  • mass and size minimization.

1.3 Paper Aim

This paper describes an innovative orbital robotic gripper mechanical system in terms of concepts of operation, elements, and baseline process. Considering the different masses, forces, sizes, and lengths as starting points for this concept of the SFA baseline configuration [7], a baseline configuration for this particular system is produced. A literature research is performed for what concerns the grasping tool [18, 19] and trade-offs are conducted. An under-actuation strategy is finally selected [20, 21, 22, 23, 24]. It minimizes the number of actuators, and the grasping tool mass at the cost of a certain mechanical and software complexity. Some assumptions and trade-offs, described in the successive sections, have been considered to identify the best arrangement of the system to reach this goal.

2 Robotic System Constraints and Mission Profile

2.1 Mission Scenario

This mission scenario depicts a standard satellite platform carrying a payload of interest (i.e., scientific or military). This satellite is docked to a Space Tug, capable of bringing it in low orbit and then releasing it in a known destination. To complete the processing of the payload, it has to be brought back to the ground at the end of its operating cycle using a re-entry vehicle with a small cargo bay, housing the robotic system. This robotic system has to operate in synergy with the Space Tug to capture the payload from the standard platform. A schematic view of this scenario is shown in Fig. 1.
Fig. 1

Mission scenario elements. Left: a general platform architecture is attached to the Space Tug. On the platform, there is the payload to be brought to the ground. Right: re-entry vehicle attached to the VEGA upper stage (AVUM). In the cargo bay of the re-entry vehicle, a robotic manipulator is located. This work is devoted to define its requirements and its preliminary design

2.2 System Requirements and Constraints

The requirements and constraints imposed by considering a realistic VEGA (European launcher [25]) payload are difficult to satisfy in terms of dimensions and weight:
  • Cargo Bay Main dimensions are about 550 × 240 × 1250 mm.

  • Maximum storable mass: 50 kg.

  • Maximum available volume: 100 l.

It is clear that the robotic system design is very challenging; moreover, considering that the robotic arm should be stowed in the bay long at least 4 m (to ensure the required safety during its operations, having a margin distance to exploit in an emergency case or in any case that required a moving away of robotic arm from the target) equipped with appropriate grasping tool and cameras, a battery for its elements power supply, a computer with its dedicate control system, and all interfaces with the bay and payload, once performed the capture. In addition, the robotic manipulator shall be able to withstand all the mechanical, thermal, and electromagnetic environments which occur during the launch, orbital, and re-entry phase.

2.3 System Configuration Trade-Off

As shown in Fig. 1, the elements taken into account are the Target, composed by the Space Tug and a standard platform carrying the payload, and the Chaser, composed by the orbiting vehicle and the VEGA upper stage, AVUM. Space Tug and AVUM are the unique elements equipped with an attitude control to perform the cooperative RV&D. Although most of the studies in the literature focus on active–passive (non-cooperative) RV, there are also works considering active–active (cooperative) RV [26]. The system under study does not belong to any of these two classes. In this case, for cooperative RV, it is meant that a spacecraft (re-entry vehicle) is performing active RV through a reaction control system, while the other one presents a stable control and attitude behavior without actively cooperating during the RV phase. This is stated as a semi-cooperative Rendezvous. The robotic system shall ensure both a robust contact, allowing a firm hooking of the payload, and a soft contact to guarantee a certain degree of compliance. There is not a rigid connection between the two spacecrafts during the grasping operations. The two vehicles will maintain themselves placed side by side without a physical docking. An arm-grasping mechanism is realized to carry out the payload. These results are to be the most suitable system configuration despite its higher software complexity. Mass and volume minimizations are considered more relevant with respect to the system complexity due to the stricter cargo bay requirements.

3 Robotic Arm Preliminary Design

3.1 Design Assumptions

To proceed with the preliminary design of the robotic arm, some assumptions have been made, in particular, the following:
  • The payload that has to be moved inside the cargo bay has a mass of 30 kg.

  • The limbs are assumed to be aluminum cylindrical tubes with an external diameter 50 and 2 mm thick.

  • The actuator sizing process has been based on the calculation of the worst-case payload acceleration \( \alpha_{\hbox{max} } \) [27].

This latter one has been calculated considering the main available data from the Japanese SFA [7] of the JEMRMS completely extended with the maximum tip force applied to the payload orthogonally with respect to the arm (starting still and reaching the maximum velocity). This results in 0.05 rad/s2. From this value of acceleration, the inertial resistance torques required to each actuator have been calculated, considering that:
  • The actuators are activated one by one (while the others are still).

  • The ith actuator has to be able to rotate the subsequent chain of actuators + links + payload of 30 kg with the angular acceleration previously calculated.

  • This subsequent chain is seen as a completely rigid body. Its mass is the sum of all actuators, links, end-effector, and payload that follow the ith actuator/joint. The chain has also a geometric configuration that maximizes its inertia matrix with respect to rotation axis of the ith actuator.

3.2 Design Description

The robotic arm has 7df/joints, to have more dexterity in its operations: 3df in the shoulder, 1df in the elbow, and 3df in the wrist, linked by two 2 m limbs. The manipulator has to be stowed inside a cargo bay whose length is about 1.25 m; this constraint forces to fold each limb in half (for a total of four cylindrical tubes) with the aid of two dedicated actuators, adding 2df during the deployment of the arm itself (once deployed, the two limbs will remain completely extended). The following factors are considered for the motor choice: application, environment, thermal, efficiency, weight, volume, life, complexity, torque, speed, torque ripple, power source, envelope, duty cycle, and controllability. The choice has fallen on BLDC because of their long life, high torque, high efficiency, and low heat dissipation, while, concerning the gears, planetary gears seem to be the preferable choice in terms of mass savings. Summarizing, the chosen concept is an actuator composed by a BLDC motor (with electronic drive + encoder + brake) and a planetary gear.

4 Robotic Manipulator Design

4.1 Gripper Requirement Identification

To perform a first choice of the gripper configuration parameters, it is important to describe the existing prehension methods and their advantages and disadvantages both from the gripper side and from the grasped object points of view. Following [21], there are four possible configurations for prehension scenarios:
  • Impactive the retention force provided by these tools is based on the physical effects of Newtonian mechanics, mainly associated with mass points and forces, and requiring more or less extensive mechanisms.

  • Ingressive gripping methods which permeate a material surface to some given depth.

  • Astrictive providing a continuous holding force without the application of compressive stress.

  • Contigutive prehension techniques which rely on direct contact–contiguity between gripper and object surfaces.

The adopted trade-off criteria are the following.
  • Power required to grasp and hold the payload.

  • TRL are a type of measurement system used to assess the maturity level of a particular technology. Each technology project is evaluated against the parameters for each technology level and is then assigned a TRL rating based on the projects progress. There are nine technology readiness levels. TRL 1 is the lowest and TRL 9 is the highest [28].

  • No rigid impact damping systems in the gripper.

  • Error tolerance, i.e., how the gripper helps to recover positioning (± 30 mm) and attitude (± 6°) errors.

  • Volume occupied by the integrated system interface and end-effector (design driven).

  • Gripper force to grasp and to hold the payload.

  • Payload degrees of freedom blocked by the gripper.

After a trade-off study, an impactive–ingressive gripper scenario has been chosen. This trade-off study is reported in Table 1. The selected scenario is constituted by a multi-finger hand and a handle. In the second column, the weights are present; they go from 1 (inappropriate) to 5 (optimum). Once the prehension scenario is selected, it is fundamental to focus on a preliminary multi-finger hand-handle configuration study. Without having any knowledge about the nature of the payload, it is characterized considering the following features:
Table 1

Trade-off study to select the prehension scenario

Prehension scenarios

Weight (1–5)

Scenario 1 impactive–ingressive

Scenario 2a ingressive

Scenario 2b ingressive

Trade-off parameters

Multi-finger hand and handle

Fitter and conical fitting

Conical fitting and fitter

Supplied power

5

4

4

4

Heritage

5

3

3

1

No rigid impact possibility

4

4

3

3

Error tolerance

4

4

3

3

Occupied volume

3

4

4

4

Prehended force

2

5

5

5

Impeded P/L dofs

4

5

5

5

Total

 

109

97

91

In the upper right part of the table, the possible scenarios are reported, while, in the left part of the table, the trade-off parameters are present. The impactive–ingressive scenario is selected due to its higher total score

  • payload mass range (5–30) kg;

  • payload volume 16 l (200 × 200 × 600 mm);

  • single-element payload considered.

One fundamental aspect to design a robotic grasping system is to determine the position and attitude errors present in the whole system.

The overall systems’ error is ± 30 mm for the relative position misalignment and ± 6° for 3-axis relative attitude. Following the System Requirements expressed in Sect. 2 for the whole robotic system, the Functional Requirements related to this scenario are derived. Together with the trade-off criteria, they become necessary for a first-design evaluation.
  • Due to the mission profile, there is the assumption that the system operates in an environment with temperature range [− 150 °C, +150 °C].

  • Volume (< 16 l) and mass (< 3 kg) occupied by the gripper-handle system.

  • Minimizing system degrees of freedom and, consequently, system control complexity.

  • Determining a grasping activity that could accommodate possible errors in positions (± 30 mm) and attitude (± 6°). These limits are imposed by the ADCS of a realistic orbiting vehicle-platform and by the grasping strategy;

  • Minimizing applied force per finger.

  • Guarantee blocking of payload degrees of freedom. Three different modes have been identified: Grasping. Holding, and Releasing. In this system, only a prehension activity is requested. Neither anthropomorphism nor high-level dexterity is required.

The desired capabilities must be translated into technical requirements that result in a trade-off between system complexity, capabilities, reliability, volume, weight, and cost. Moreover, a camera sensor is placed inside the gripper palm to help the grasping phase. It has to be:
  • No rolling shutter camera.

  • No constant focal length.

  • In-camera shade condition: 4 white-light led lights are present symmetrically around the camera to illuminate the marker in shadow conditions.

  • In-camera sun ray condition: tracking algorithm software has to stop grasping action if saturation is present due to direct or reflected sun light.

In this work, a 1 M Pixel Radiation Hard CMOS Image Sensor (square size, 30 × 30 mm) is considered. A preliminary characterization of the camera is presented. To size it, the worst possible cases are taken into considerations. Camera position has an uncertainty of ± 30 mm with respect to the marker tracker, see Fig. 2. ± 6° errors are considered in attitude for \( \phi_{x} \) and \( \phi_{y} \) (angles, respectively, related to the x- and y-axes). These are in plane rotation errors (ϑir). Then, due to \( \phi_{z} \), an apparent enlargement of the marker tracker is present. The worst case is where the nominal side has to be multiplied by a factor of \( \sqrt 2 \) (square diagonal factor). This effect produces an out-of-plane rotation error (ϑor). At the end, the new modified camera nominal field of view (\( \vartheta_{\text{n}}^{\prime } \)) is 98.5°.
Fig. 2

Camera-marker scheme to infer position and attitude possible errors. This is fundamental to get a first evaluation of the camera main features

For what concerns the error in z-direction, at a certain distance from the marker tracker (50 mm), the control system works using the instantaneous marker tracker angular diameter. Once it is 56° (at 40 mm distance), the gripper will start the grasping phase. At that point, the only errors present will be those related to the marker tracker-camera system (± 2.5 mm and ± 2.8°). These errors have been included in the sizing of the new modified camera field of view (61.8°). The camera system has to work with a lens-marker tracker (working) distance varying from 50 mm (start working distance of the camera) to 15 mm (stop working distance of the camera) and with a camera lens–CCD distance of 15 mm (palm depth). A requirement about the focal length interval is so necessary. It has to vary according to the different working distances with a focus/zoom mechanism. Obviously, the camera needs to have a very high sampling frequency (higher than the control system one). As mentioned above, due to structural constraints, a maximum thickness of 15 mm is utilized. In this space, the whole system has to be accommodated. It consists of the optical system (lens) and the CCD sensor that will transmit signals to the central electronic board. Moreover, to ensure a higher redundancy level, it is possible doubling the CCD sensors. Another CCD sensor is added using the same optical system illustrated before. About that, it is feasible to take into consideration the use of beam splitter structures (prismatic or planar). More technical details about the camera model selection and the tracking algorithms (machine vision) are not object of this current work, and they will be dealt with in a future more detailed approach, during the realization of this project. More information can be found in the Open Source Computer Vision library [29]. Before starting to determine gripper requirements, it is essential to indicate and to preliminary describe what the gripper is going to grasp. As handle requirements, the following ones are considered:
  • blocked degrees of freedom (translational and rotational ones);

  • wedge-in handle profile;

  • maximum grasping in all possible handle positions;

  • possibility to host a 30 mm-side marker on the palm of the gripper;

  • perimeter-area ratio as figure of merit of profile configurations.

  • volume minimization.

As possible handle profile configurations, circular, triangular, and rectangular profiles are selected. Taking into account all the above requirements, a triangular configuration profile is the first choice. This allows to block all the degrees of freedom and to host in the middle of the palm a 30 mm-side marker (90 mm-handle side length). Moreover, this profile maximizes the figure-of-merit perimeter/area, having in this way a larger perimeter to allow the grasping and a smaller area to reduce the occupied volume. This handle presents a triangle basis of 80 mm side (to host the marker and to allow the complete closure of the fingers), 30 mm depth (to minimize the occupied payload volume), and 25° extrusion angle (to minimize the payload attached area min base area and maximize the grasped area). The handle marker has to be: 30 mm-side square, asymmetric pattern, low reflectivity material (no metallic) to avoid in-camera reflections, and black and white pattern to increase contrast [30]. Obviously, the size of the sensor will affect the size of the handle. More technical details about the maker selection and the tracking algorithms (machine vision) are not an object of this current work and they will be dealt with in a future more detailed approach, during the realization of this project.

4.2 Gripper Possible Configuration Identification and Trade-Off Executions

In Sect. 3, the possible grasping configurations, strategies, and methods are presented. Before executing the grasping features trade-offs, the gripper configuration parameters to design the tool [21, 22] are reported:
  • actuation architectures and actuation placement;

  • number of dependent/independent fingers;

  • number of actuators;

  • number of phalanxes per finger;

  • thumb presence.

4.2.1 Gripper Configuration Results

After a configuration study, the robotic hand system will be characterized by the following:
  • Three-contact-independent-finger under-actuated (2df per finger, single actuator) hand:

  • Finger and phalanxes adjustment to compensate for misalignment;

  • The distal phalanx closes before the proximal one, allowing to grasp the handle side and limiting the handle length and volume;

  • Two-phalanx fingers.

  • No thumb.

  • Remote (palm located) actuator, with possibilities to implement also redundancies.

  • Double-acting actuator.

4.2.2 Under-Actuation Strategy

Under-actuation is a widely used and a relatively old concept in robotics. Basically, it expresses the property of a system to have an input vector of smaller dimension than the output vector. Practically, in robotics, it means having fewer actuators than degrees of freedom. Applying this concept to robotic grasping arises from a simple fact: it is better to be able to grasp objects using a simple control rather than having to command and coordinate several actions. The idea behind under-actuation in grasping is to use an ingenious mechanical system that can adapt to the shape of the object automatically. This mechanical intelligence, embedded in the hand, is based on the principle of differential systems. The latter devices automatically distribute one input to several outputs, the ratio between the different outputs being determined by the design parameters and the output states themselves [31]. While in the literature in usual actuation architectures [20, 21, 22, 32, 33], under-actuated systems have been realized where the first (proximal) phalanx closure led afterwards to the closure of the second (distal) one using the loading of a torsional springs and mechanical linkages, in this application, a new under-actuation strategy is developed. In this case, the distal phalanx closes before the proximal one, allowing to grasp the handle side and limiting the handle length and volume. This concept will allow the distal phalanx to move independently from the proximal one. A rigid tendon architecture is adopted to move the distal phalanx and a torsional spring (4 N mm/°) to hold the movement of the proximal one. This concept is innovative with respect to the usual ones, because the kinematics works in the opposite way. As first proof of concept, a very simple model dynamic simulation is runs. The three plots in Fig. 3 depict the three phases of the finger actuation mechanism. The finger stays open, allowing to capture the handle with ± 30 mm and ± 6° uncertainties. After that, the distal phalanx is closed. The proximal phalanx does not move thanks to a torsional spring that holds it in place. This happens until the mechanism hits a stop located on the proximal phalanx. In doing that, the whole finger rotates around the point that connects the proximal phalanx to the gripper palm and the whole finger rotates capturing the handle side.
Fig. 3

Finger mechanism actuation phases. The finger stays open, to guarantee the handle capturing requirement with ± 30 mm and ± 6° uncertainties. After that, the distal phalanx is closed. The proximal phalanx does not move thanks to a torsional spring that holds it in place. This happens until the mechanism hits a stop located on the proximal phalanx. In doing that, the whole finger rotates around the point that connects the proximal phalanx to the gripper palm and the whole finger rotates capturing the handle side

Figure 4 shows that the movement of the proximal phalanx (phalanx 1—solid line) holds, while the distal one moves (phalanx 2—dotted line), angular velocities are reported. When the second phalanx is open, the whole finger will rotate at the same angular velocity (after 1 s).
Fig. 4

Phalanx kinematics plot using SolidWorks. Phalanx angular velocity as a function of time for the proximal phalanx and the distal phalanx. It is worth noting that, while the mechanism is working, the first phalanx holds, while the second moves. The same behavior is observed for angular velocities. When the second phalanx is open, the whole finger will rotate at the same angular velocity. As expected, after 1 s, the absolute angular displacement of the phalanxes is the same. The noise affecting the phalanxes in the angular displacement plot is due to the handle-interaction disturbances

5 Robotic Manipulator Baseline Configuration

5.1 Geometrical Models

Here, the geometric models of the handle, the single finger and the gripper are described and discussed.

5.1.1 Handle

Starting from the handle requirements in Sect. 3, in Fig. 4, an image of the re-entry vehicle grasping handle technical drawing is reported. This tool is attached to the payload external surface. Figure 5 shows the technical drawings of the payload with the attached handle. Although the exact place of this attachment is not specified in this work, obviously, it will be placed on a surface that can be reached from the robotic arm. More details on this specific point will be the object of a future more detailed study performed, during the realization phase of this project.
Fig. 5

Schematic drawing of the re-entry vehicle grasping handle. This tool is attached to the payload external surface. The dimensions are reported in mm

The handle dimensions are determined to comply with all the requirements stated previously. The handle hole width (20 mm) (place where the phalanxes realize an ingressive grasping) favors a better grasping control, taking into account that the error on the gripper positioning will be ± 2.5 mm in the final grasping phase. The full handle width (45 mm) guarantees a better grasping control and minimizes the payload volume occupied. The handle side length (90 mm) allows the position of the 30 mm-square marker tracker and the perfect closing of the fingers to stabilize the grasping (see Fig. 6).
Fig. 6

Re-entry vehicle payload and preliminary handle positioning. This tool is attached to the payload external surface. The dimensions are reported in mm

5.1.2 Single-Finger Grasping Tool

For what concerns the grasping tool, once the geometric model of a single finger is defined, then three fingers are assembled together to a palm to realize the gripper. The main constraint in designing the finger is the proximity constraint. It deals with not touching the handle and the payload before the final grasping closure phase happens. For this reason, the second phalanx should be longer than the first one. Moreover, at the same time, assuring an adequate length of the first phalanx is needed to respect the requirements in terms of error recovery. This grasping closure interval takes into consideration the camera-marker tracker system errors. A numerical analysis (using a specific Matlab program) is run about the finger grasping closure operation to study the possible lengths. It allows defining the two-phalanx finger lengths: the first one (proximal) is 35 mm, while the second one (distal) is 40 mm. The next step is to size the vertical beam lengths. In Fig. 7, the basic finger kinematics is depicted to size the two vertical beams constituting the chain. When the chain moves (Eq. 1), the two arcs cover the same path lengths (Eq. 2):
Fig. 7

Single-finger grasping basic kinematics. Right: second phalanx open; Left: second phalanx closed

$$ s_{1} = 2\pi l_{1} \frac{{\vartheta_{1} }}{360^\circ }\;{\text{and}}\;s_{2} = 2\pi l_{2} \frac{{\vartheta_{2} }}{360^\circ }. $$
(1)
Considering that
$$ s_{1} = s_{2} . $$
(2)
Equation 3 brings to
$$ \frac{{l_{1} }}{{l_{2} }} = \frac{{\vartheta_{2} }}{{\vartheta_{1} }}. $$
(3)
Assuming that \( \vartheta_{2} = 45^\circ \), \( \vartheta_{1} = 30^\circ \), and l1 = 30 mm. It is found that l2 = 20 mm. The results of these preliminary analyses are later confirmed by the correct behavior of the multibody simulation results using MSC Adams. The single-finger grasping tool technical drawing is shown in Fig. 8. The thickness of all these components is 7.5 mm. This value has been confirmed through structural analysis.
Fig. 8

Drawing of the single-finger grasping tool

5.1.3 Assembled Grasping Tool

The whole gripper structure is shown in Fig. 9. A triangular-base palm is present to which the three fingers are attached. This palm has the same shape of the handle. In this way, a superposition between the gripper and the hand is executed and a higher holding stability is reached. Furthermore, the three-finger mechanisms are located inside a cylindrical tube. It contains also the actuator interface and a ball-screw transmission mechanism to transfer the linear actuator motion to the mechanical system.
Fig. 9

Re-entry vehicle LEO payload grasping tool. Above: front view. Below: lateral view. The dimensions are expressed in mm

5.2 Materials

For what concerns, the choice of the materials, a trade-off among steel, stainless steel, aluminum 6061-T6, and titanium is performed. These are the most common materials for space applications [34]. Here, it is expedient to select the same material both for the handle and the gripper. As choice criteria: the static friction coefficient, the Young modulus, the density, and the yield stress. The static friction coefficient takes into account the contact coupling between the handle and the grasping tool phalanxes. The Young modulus reflects the material elasticity and the density of the material mass. The yield stress gives a preliminary result about the structural analysis. The trade-off results are reported in Table 2. An average stress of 5 MPa is obtained, taking into account that the order of magnitude of the forces in the system is ~ 50 N and that the system dimensions are ~ 10 mm2.
Table 2

Trade-off results to select the material for the robotic gripper-handle system, see [34]

Material

µ (–)

E (GPa)

ρ (g/cm2)

E/ρ (GPa cm3/g)

σy(MPa)

Thermal expansion (10−6/K)

Steel

0.74

200

7.75÷8.05

24.8÷25.8

448

110÷130

Stainless steel

0.80

196

7.85÷8.06

24.3÷24.9

520

10.1÷17.3

Aluminum 6061-T6

1.1÷1.7

69

2.7

25.5

276

23.1

Titanium

0.36

110.3

4.54

24.3

130

8.6

After this trade-off study, aluminum 6061-T6 is the best choice. This is because:
  • Al presents a very high static friction coefficient value (dry Al on dry Al). This is a key feature in our system to maximize the gripper-handle holding force.

  • Al presents a very low density and a very high E/ρ ratio.

  • Al presents a yield stress high enough to guarantee operability for this current application.

  • Al presents a higher thermal expansion coefficient. However, for this design study, it operates well in the environmental temperature gradient.

However, to have a higher yield stress value and a lower thermal expansion coefficient, other aluminum alloys or composites could be introduced, which, however, show the other disadvantages such as a higher density or a higher conductivity. For now, μ, ρ, and E/ρ are the most important design constraints for this design phase. Moreover, the palm (18 mm thick) and the second phalanx of each finger present a layer (3 mm thick) of Torlon [35]. It is a polyamide imide that absorbs and dissipates impact energy. It is used in space applications. It offers low friction and wear, high pressure and velocity limits, excellent mechanical properties, and heat resistance. This is used to damp the impact between the handle and the gripper.

5.3 Kinematic Analysis

Here, the kinematic functional model of a single finger is reported. The kinematics of the whole gripper constituted by three fingers is not described. Focusing on single-gripper kinematics and deeply describing it have been considered more valuable than showing a general kinematics functional model for the three-finger gripper.

5.3.1 Forward Kinematics

The forward kinematics refers to the calculation of the position and orientation of its end-effector frame from its joint values.

To model the forward kinematics, Matlab software was used. The finger scheme is shown in Fig. 10. A systematic method of deriving the 2D-forward kinematics is performed attaching reference frames to each of the links; the eight link reference frames are, respectively, labeled with capital letters. The forward kinematics can then be written as a product of eight SE(2) matrices. To pass from a reference frame attached to a point to the next one, some rototranslation matrices have been defined. During the working operation of this mechanism, two phases are noticeable. First of all, there is a phase that goes from the position at rest up to the closure of the distal phalanx. After that, the second phase is characterized by the closure of the first phalanx and by the subsequent rotation of the finger structure.
Fig. 10

Single-finger MATLAB scheme

5.3.2 Inverse Kinematics

2D-inverse kinematics refers to the use of the kinematics equations to determine the joint parameters that provide a desired position of the end-effector. In this case, the only responsible for the main motion of the finger is the linear actuator attached to point A. Its intrinsic variable is l0. As inverse kinematics analysis, the workspace (x, y) variations of the points constituting the finger mechanism are reported as consequences of the variation of l0 due to the linear actuator operation. The workspaces of points A, B, C, and D are reported in Fig. 11. For each point, the red line refers to the first phase working operation, while the blue line refers to the second phase. The workspaces of points E, G, I, and L are reported in Fig. 12. For each point, the solid line refers to the first phase working operation, while the dotted line to the second phase. All the workspace show trends that reflect expected evolutions.
Fig. 11

Point A (upper left), B (upper right), C (lower left), and D (lower right) workspace as variation of l0. For each point, the solid line refers to the first phase working operation, while the dotted line to the second phase

Fig. 12

Point E (upper left), G (upper right), I (lower left), and L (lower right) workspace as variation of l0. For each point, the solid line refers to the first phase working operation, while the dotted line to the second phase

In particular, all these plots are obtained through l0 discrete steps variation. Therefore, for every desired point (x, y) of point L (distal phalanx tip) workspace, the other joints and the l0 position are known.

5.4 Dynamic Analysis

The mechanical system is constituted by three main components:
  1. 1.

    the motor and the gear box;

     
  2. 2.

    the torque transmission mechanism (ball screw);

     
  3. 3.

    the grasping mechanism (three-finger under-actuated mechanism).

     
These components are captured in three red rectangles in Fig. 13.
Fig. 13

Mechanical components constituting the gripper. From left to right: grasping mechanism, ball-screw mechanism, motor, and the gear box

For this design study, each component is characterized [36, 37]:
  1. 1.

    Actuator Maxon BLDC 353399 EC 32, 15 W, 24 V with integrated electronics, with cover.

     
Gear box Maxon spur gearbox 110453 GS 38 A, 18:1, efficiency 73% with holding brake.
  1. 2.

    Ball screw (preload): screw diameter 10 mm, screw length 130 mm, lead 5 mm, and efficiency 95%.

     
  2. 3.

    Grasping mechanism retention force 31.7 N (30 kg payload) and assumed efficiency 90%.

     
MSC Adams software has been used for performing the dynamic analysis. In Fig. 14, the gripper-payload configuration is presented using MSC Adams.
Fig. 14

MSC Adams system simulation. The payload inertial properties were reported (30 kg mass, inertia moments) such as the ones of the gripper and the kinematic connections between its different parts

The grasping of the handle and consequently of the payload is shown in Fig. 15. The arrows represent the forces exchanged between the second phalanxes of each finger and the handle side, such as the handle palm and the handle surface. The contact forces between the handle (Al 6061) and the fingers (Al 6061) and between the handle (Al 6061) and the palm (Torlon) have been modeled in the proper way (Coulomb contact).
Fig. 15

Detail of the closure phase of the grasping mechanism-handle system. The arrows represent the forces exchanged between the second phalanxes of each finger and the handle side, such as the handle palm and the handle surface. The gripper cover is here transparent to better show how the rigid tendons work

The retention contact force between the palm and the handle has been computed a (8.5 N), after the grasping transition period. It is larger than the estimated force necessary for a 30 kg-payload holding (~ 5.5 N) in a zero-g environment.

6 Dynamic Analysis—A Complete Example

Another more complete example, using SolidWorks Motion with precise contact feature, is shown below regarding a particular case. Here, the handle starts at a distance of 37.5 mm (22.4, − 14.2, 26.4) with respect to the gripper palm. Even, in this case, the grasping activity results are to be successful. Some of the pictures describing what happen during the maneuver are reported.

Simulation analysis data regarding the position variation of the handle center of mass with respect to the gripper are reported in Fig. 16.
Fig. 16

Simulation analysis data regarding the position variation of the handle center of mass with respect to the gripper palm. The handle has been positioned at a distance of 37.5 mm (22.4 mm, − 14.2 mm, 26.4 mm) with respect to the gripper palm. a Maneuver starts. b Distal phalanx contacts the handle side. c Fingers bring the handle to the correct position. d Fingers close on the handle side using also the nearest phalanx. e Grasping is performed successfully. f Grasping retains the handle surface against the gripper palm

The linear velocity (solid line) and the angular velocity (dotted line) of the handle during the capture are reported in Fig. 17. To show the robustness of this mechanical design, the initial velocity for the payload + handle ensemble is set to be 3 mm/s (y-axis) and 5°/s (around x-axis). Both these curves show to converge towards zero after the capture has been performed. Moreover, tests have been conducted in a simulation environment to validate this gripper model with respect to the position and attitude requirements, respectively, and ± 30 mm and ± 6°.
Fig. 17

Linear and angular velocity of the handle-payload system as a function of time during the grasping maneuver. The initial velocity for the payload + handle ensemble is set to be 3 mm/s (y-axis) and 5 mm/s (around x-axis)

7 Functional Model

The general control architecture of a re-entry vehicle grasping robotic control system is shown in Fig. 18. There are three main blocks: the Control Overall System Block, the Control Arm Block, and the Control Robotic Hand Block.
Fig. 18

Re-entry vehicle gripper grasping robotic control system. There are three main blocks: the control overall system block, the control arm block, and the control robotic hand block

The control block of the robotic hand consists of a subroutine that is implemented inside control arm. As outputs (sensor data), there are:
  • marker alignment data;

  • wrist actuator encoders;

  • finger actuator encoder;

  • finger actuator force-torque sensor;

  • phalanx tactile sensors: tactile sensors [38, 39].

The inputs (actuator commands) are the following:
  • wrist actuator commands;

  • finger actuator commands.

7.1 BLDC Motor System-Level Model

To describe the BLDC motor actuator, an existing MATLAB–Simulink library has been adjusted to this case [40]. The motor and driver are modeled as a single masked subsystem. In this model of a BLDC motor, the standard configuration is modeled, whereby an inner feedback loop controls current and an outer feedback loop controls motor speed. Simulation results characterizing the motor are shown in Fig. 19 The first plot is the motor speed (rpm) as a function of time, the second plot is the mechanical power (W) as a function of time, and the third plot is the motor efficiency (%) as a function of time. All these plots follow the same expected trend due to the voltage system. For what concerns the efficiency, it reaches about 60%. This is due also to the fact that an oversized servomotor is adopted (a more powerful motor to have a lower torque) to guarantee a higher robustness to the system, instead of having a higher efficiency correlated to higher risks.
Fig. 19

From top to bottom: rotor speed (rpm), mechanical power (W), and efficiency (%) as a function of time. All these plots follow the same expected trend due to the voltage system

A proportional and an integral gain have been chosen to assure a reasonable small time constant (0.2 s) for the current controller.

7.2 Control Architecture

It is essential to model space robot systems in terms of dynamic facing problems inevitably unique to this field [41]. In this regard, it is necessary to distinguish between the systems currently used, a free-flying system, and a free-floating system. In the first, the spacecraft’s position and attitude are controlled by means of jet thrusters or reaction wheels during the manipulator activity; clearly, such systems provide highly redundancy and versatility making their workspace almost unlimited. However, the big drawback is the consumption of excessive amounts of attitude control fuel, expensive, and non-renewable resource in space, which could greatly limit the useful on-orbit life of the system. To avoid this problem, it is possible to use free-floating systems, in which the spacecraft can move freely in response to the dynamical disturbances caused by the manipulator’s motion, not being actively controlled in position and attitude. In this case, the latter type of system is considered being, moreover, more advantageous in case of capture of a fragile payload [42]. Considering such system composed by a manipulator arm mounted on a base spacecraft that is floating in the inertial space without any external forces or moments applied, it is evident that the movements of the manipulator have effects on the base and vice versa. To well understand, this dynamic coupling is necessary to refer to the motion equation of a generic space robot, that, assuming, in the operational space, the linear and angular velocities of the base \( x^{\prime}_{\text{b}} = \left[ {\dot{p}_{\text{b}} \dot{\omega }_{\text{b}} } \right]^{t} \in R^{6 \times 1} \) (respectively, end-effector linear and angular velocities) respect to the inertial frame and the motion rate of the joints \( \dot{q} \in R^{n \times 1} \)\( \dot{q} \in R^{n \times 1} \) (n are the manipulator degree of freedom) as the generalized coordinates, is expressed as follows:
$$ \left[ {\begin{array}{*{20}c} {H_{\text{b}} } & {H_{\text{bm}} } \\ {H_{\text{bm}}^{\text{T}} } & {H_{\text{m}} } \\ \end{array} } \right]\left[ {\begin{array}{*{20}c} {\ddot{x}_{\text{b}} } \\ {\ddot{q}} \\ \end{array} } \right] + \left[ {\begin{array}{*{20}c} {c_{\text{b}} } \\ {c_{\text{m}} } \\ \end{array} } \right] = \left[ {\begin{array}{*{20}c} {F_{\text{b}} } \\ \tau \\ \end{array} } \right] + \left[ {\begin{array}{*{20}c} {J_{\text{b}}^{\text{T}} } \\ {J_{\text{m}}^{\text{T}} } \\ \end{array} } \right]F_{\text{h}} . $$

7.3 Control Strategy—Impedance Control

The strategy to track a target used during the simulation for the robot chaser is based on an impedance control [43]. This choice has been driven by the need to have a control that could be adapted to the main phases of a servicing mission: RV&D and stabilization. Indeed, the impedance control, being a dynamic model-based compensation control, guarantees accurate tracking of the desired end-effector trajectory, essential to perform the approach maneuvers, and, at the same time, provides a control of the contact forces that are carried out during the capture phase of the target, including their measurements in the control loop. The particular feature of this type of control is to ensure that the end-effector of the manipulator behaves like an impedance, equivalent to a mass-damper-spring system. It is the possibility of adjusting such mechanical impedance that makes this control more suitable than others for this application. Furthermore, the control is defined in the operational space for two main reasons. First of all, the motion specification, i.e., the trajectories to follow, is assigned in the Cartesian space; thus, if the control is referred to the joint space, an inverse kinematics algorithm is needed to convert the variables in those corresponding in the joint space. This process has an increasing computational load when the inversion of the first- and second-order differential kinematics are required to convert the desired time history of the end-effector position, velocity, and acceleration in the corresponding quantities in joint space. Instead, referring to the operational space, the trajectory inversion is replaced with a coordinate transformation, using the direct kinematics relations to transform the measured joint space variables in the corresponding operational space, which will be compared with the desired values. Notice that, in this case, the kinematics equations are inside the loop, thus having to perform many computations for each loop, the system could run at a lower sampling frequency compared to joint-based systems, which may lead to degrading the stability and the disturbance rejection capabilities of the overall control system. Despite this limitation, the operational-based control is required when the manipulator has to interact with the environment (in this case with the handle located on the target satellite). Indeed, if it is necessary to control both position and contact forces, a joint space control can provide only the first one with the risk of incurring in errors due to a not complete knowledge of the environment. The impedance control utilized during the experiments is a Cartesian force-based control, i.e., the command signal that it generates is a generalized force, including forces and moments. It is designed in two fundamental steps: decoupling and linearization in the operational space and imposition of the desired impedance model to correctly react to the external forces/moments acting on the end-effector of the arm (Fh).

Further results regarding the application of this control law to the whole system and, in particular, to the gripper will be shown in a future work.

8 Conclusion

In this work, a robotic manipulator system and, in particular, a gripper able to grasp a payload in LEO is described. This action takes place in a semi-cooperative RV scenario without docking. To obtain the desired goals, the following results have been reached:
  • The designed gripper respects the project guidelines and guarantees payload grasping and holding: mass ≈ 2.5 kg (< 3 kg), with a 25% margin; volume ≈ 10 l (< 16 l), with a 25% margin; power = 15 W, with a 25% margin.

  • The grasping tool system requirement identification has been developed in terms of gripper requirements identification and handle requirement identification;

  • Various prehension methods were studied. The gripper which resulted is an impactive–ingressive robotic hand grasping a handle. Requirements for both these components are given through trade-off studies considering various criteria. Only a single actuator is adopted to govern two degrees of freedom per finger. An under-actuation strategy is selected and a new gripper phalanx actuation approach is performed;

  • A gripper development baseline configuration has been executed in terms of geometric models, materials, software functional model, and single-finger kinematic and dynamic analysis functional models;

  • First configuration designs are shown and the adopted choices are discussed.

Notes

Acknowledgements

This research was carried out at Politecnico di Torino and Thales Alenia Space Italy, under SAPERE and STRONG projects. These projects are under a contract with the Italian Ministry of Education, Research and University. Copyright 2016. All rights reserved.

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Copyright information

© Chinese Society of Astronautics 2019

Authors and Affiliations

  1. 1.Department of Mechanical and Aerospace EngineeringPolitecnico di TorinoTurinItaly

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