Table of contents

• Table of contents
• About the project
• System Description
  • Simulation Modes
    • Deterministic Mode
    • Monte-Carlo Mode
  • Resources
  • Robot Task Types
  • Robot Types
  • Robot Attributes
  • Configurations of SRRS
  • Build Quality Assignment
    • Deterministic Mode
    • Monte-Carlo Mode
  • Calculating Task Risk
    • Deterministic Mode
    • Monte-Carlo Mode
• Analysis Metrics
  • RAM Metrics Calculation
    • MTBF
    • MTTR
    • MDT
    • Operational Availability (Aoss)
• SRRS Simulation
  • Simulation Parameters
  • Requirements
    • Simulation Requirements
    • Stakeholder Requirements
• Output
  • Habitat Growth Visualization
    • Deterministic Mode Habitat Growth
    • Monte-Carlo Mode Habitat Growth
• Trade-Off Analysis
  • Mission Statements
  • Mission Statement Rankings
  • Mission Statement Ranks according to Rank-Order Distribution of attributes
  • Monte-Carlo Results for each configuration
  • Mission MAVF Tables
    • Mission Statement 1 - Need to finish Replication
    • Mission Statement 2 - Need high Collection capacity
    • Mission Statement 3 - Need high Assembling capacity
    • Mission Statement 4 - Need high Print capacity
    • Mission Statement 5 - Need high Average build quality
    • Mission Statement 6 - Hight MTBF
    • Mission Statement 7 - Low MTTR
    • Mission Statement 8 - Low MDT
    • Mission Statement 9 - High Aoss
    • Mission Statement 10 - Total Robots
  • MAVF Summary Table
• Consistency Analysis
• References

About the project

The project aims to simulate the performance of 6 different system configurations for self-replicating robot systems (SRRSs). A simulation shall be developed to provide a means to implement, assess and compare these system configurations and to perform trade-off analysis to yield a recommendation of the best course of action (COA) for the user to employ.

For this analysis, the self-replicating robot systems are categorized into 6 categories (system configurations). The simulation is conducted with parameters that may fit a variety of mission constraints in order to inform the decision-makers on how an SRRS should be configured and commanded. 

As launching materials into space can be prohibitively expensive, which may drive a need for utilizing in-situ materials, the primary consumer for this analysis is the aerospace industry with organizations such as National Aeronautics and Space Administration (NASA) and SpaceX. In an aerospace application, a mission might use an SRRS to print a larger structure (such as a habitat), and therefore, a number of 3D print-capable robots would be needed. 

The simulation of different system configurations of the SRRSs will be used to formulate results that shall be utilized as heuristics which shall aid in determining which types of buildable robots or how many such robots shall be built for a particular mission or objective. For instance, the initial resources provided to the system may influence the rate at which different system configurations can expand. The 6 configurations shall be compared against the following metrics; assembly capacity, collection capacity, printing capacity, and the number of robots built.

System Description

The user shall be required to input the initial amounts of resources to the SRRS simulation namely: the printable materials, non-printable materials, raw materials, and environmental materials. The user shall also provide a build quality range for the factory-made initial robot that shall replicate and create more robots. The BDD for SRRS is shown below.

The internal flow of information is described in the IBD below.

Following this, the user shall be provided with the robot colony’s assembly capacity, collection capacity, print capacity, the total number of robots, their build quality at different time steps, Mean time between failures(MTBF), mean time to repair (MTTR), Mean Down Time (MDT), Operational Availability (Aoss), and Reliability as a function of time for 6 different robot configurations in the form of output. In addition to this, the simulation shall also output the MTBF for the system, the MTTR, the Aoss, and the reliability as a function of time for a particular configuration. The response model for the SRRS simulation for Deterministic and Monte-Carlo modes is shown below.

A single configuration shall be selected from the 6 configurations using Multi-Attribute Value Function (MAVF) analysis given the ratings for the metrics using Rank Order Distribution to calculate swing weights as shown below.

The Use Case diagram for the SRRS is shown below.

For verification testing, the following analyses of interest were conducted:

1. Verify that the Deterministic Mode meets system requirements.
2. Verify that the MC Mode meets system requirements.
3. Verify that the Multi-Attribute Value Function(MAVF) Analysis Mode meets system requirements.
4. Finding defects in SRRS Simulation mode and its elements namely the deterministic mode, MC mode, and MAVF Analysis mode so that they may be corrected prior to acceptance testing.

Three test scenarios were considered for verification and validation of the SRRS and its simulation. The simulation was designed as shown in the BDD as shown.

Simulation Modes

Deterministic Mode

Monte-Carlo Mode

Resources

There are four different types of resources that shall be considered in the simulation system. These resource types are as follows:

1. Non-Printable components: components that the robot system does not have the capability to print (or otherwise make in-situ), such as control units (processors) and motors.
2. Printable components: components that are fabricated by the robot system during the simulation, such as frames and other structural elements for new robots.
3. Raw printing materials: materials that are used in the printing process. The printing process would yield the printable component resource type, so the raw material type requires a fabricating step before materials are usable (as components) to build new robots.
4. The environment also has a certain amount of raw printing material available that robots can collect.

Robot Task Types

There are five task types in the simulation: three which perform an action (depicted in Figure 1), one which represents a default state indicating that a robot is currently performing no action (idle), and one which represents a robot under failure mode as it undergoes self-repair.

1. Collect: A task type where the robot gathers raw printing materials from the environment and adds the gathered materials to the robot system’s inventory. Upon completion of this task, raw printing materials are removed from the environment and added to the robot system’s resource pool. 
2. Print: A task type where the robot takes raw printing materials and fabricates them into printable components. Upon completion of this task, raw printing materials are removed from the robot system’s resource pool, and printable components are added to the robot system’s resource pool. 
3. Assemble: A task type where the robot takes non-printable components and printable components from the robot system’s resource pool and assembles them into a new robot. This task type has a duration that varies by the robot type being assembled. Upon completion of this task, the newly assembled robot is added to the robot system.
4. Idle: A default task type that is assigned to any robot not performing any other action during a time step. This task type has no associated duration because it does not have any completion actions/events.
5. Repair: A task type that is assigned to the robot when it encounters a risk in performing a task which results in a failure. The robot is then said to be under repair with the down time being the task duration of the task it failed to perform. The next task that shall be assigned to the robot is the task it failed to perform. If it is unable to do the task it fails to perform, then it may be assigned another task or set to being idle.

Robot Types

There are four types of robots: normal, printer, assembler, and replicator. In each time-step, each robot is either idle, gathering resources, printing components, assembling a new robot or undergoing repair. However, certain robot types are restricted in what types of tasks they can perform as shown in following table.

The state machine diagrams for each of the robot types are shown below.

Robot Attributes

The material cost of each robot type is directly related to its capabilities. Capability costs for each included capability are added together to determine the cost of the robot type. For example, the normal robot type cost is just the base cost, while the printer robot type’s cost is calculated by adding the base cost plus the printing capability cost.

Configurations of SRRS

The categorization consists of a combination of two separate classifications. The first classification, the replication approach, consists of centralized, decentralized, and hierarchical. The second classification, the production approach, consists of heterogeneous and homogeneous. Table 3 shows which robot types are produced in a certain system configuration.

An important capability of a self-replicating robot system is the ability to fabricate parts and assemble new robots. This introduces the question of the quality of the built robot, as a robot built in-situ may have quality defects (without the ability to simply discard it with minimal impacts, such as in a factory setting). To facilitate assessment, the simulation assigns each robot a build quality. A robot’s build quality value ranges from zero to one, with one being very high quality and zero being very poor quality. The quality value is a decimal value.

There are two types of simulation modes namely Deterministic Mode and Monte-Carlo Mode. The build quality assignment to new robots and the task risks pertaining to failure modes of the robots are calculated in a pre-determined fashion and stochastic fashion for the Deterministic and Monte-Carlo modes respectively.

Build Quality Assignment

As either an assembler or a replicator can assemble a new robot, the build quality of the robot is primarily attributed to the build quality of the robot assembling the new robot. Therefore, the builder’s (assembler or replicator) build quality is ‘transferred’ to the new robot.

Deterministic Mode

Robot Quality ← Assembler/Replicator Quality

Monte-Carlo Mode

rand ← random(0, 1)
if rand > (1.0 − Quality_incr_Chance):
  RobotQuality ← AssemblerQuality + random(Quality_incr_Lower, Quality_incr_Upper)
else if rand < Quality_decr_Chance:
  RobotQuality ← AssemblerQuality − random(Quality_decr_Lower, Quality_decr_Upper)
else:
  RobotQuality ← AssemblerQuality

Calculating Task Risk

Deterministic Mode

The Deterministic Mode is designed in such a way that a robot shall fail to perform a task after a said number of tasks, given by the variable numTasksBeforeFailure. The variable numTasksRemainingBeforeFailure is initialized to the value of numTasksBeforeFailure and it is decremented everytime a robot succesfully performs a task and then when it reaches a value of 0, the robot encounters a failure and is reverted to the repair state and the numTasksRemainingBeforeFailure value is reset to numTasksBeforeFailure value.

if robot.getNumTasksRemainingBeforeFailure() = 0:
    robot.taskFail()
    repairing(robot)
else:
    robot.addOperationalTime(robot.get_task_dur())
    # collecting, assembling, or printing task resource reduction
    robot.taskSuccess()
    robot.reduceNumTasksRemainingBeforeFailure()

Monte-Carlo Mode

The output of the function taskRisk is a variable(riskTask) with decimal value between (0,1) and the RiskThreshold variable is used to determine if the robot encounters failure or not. If the value of riskTask is greater than RiskThreshold then the robot is said to have encountered a failure due to high risk, otherwise it continues to perform its tasks as required.

def taskRisk(robot):
  rand = round(random.uniform(0,1),decimalPlaces)
  currTask = robot.get_curr_task()
    if(currTask == "idle"):
        RiskTask_Type = 0
    elif(currTask == "collecting"):
        RiskTask_Type = 1
    elif(currTask == "assembling"):
        RiskTask_Type = 1
    elif(currTask == "printing"):
        RiskTask_Type = 1
    elif(currTask == "repair"):
        RiskTask_Type = 0
  if robot.factory == True:
    riskTask = (1.0 - robot.get_buid_qual()) * (RiskTask_Type + rand * RiskFactory_Modifier)
  else:
    riskTask = (1.0 - robot.get_buid_qual()) * (RiskTask_Type + rand * RiskQuality_Modifier)
  return riskTask

Analysis Metrics

The primary metrics for which data are collected by the simulation include are as follows:

1. Assembly capacity: The number of robots that have the assembly capability at the end of a simulation run. This includes replicator and assembler robot types, which have not succumbed to a task risk and lost their capability. 
2. Collection capacity: The number of robots that have the collect capability at the end of a simulation run. All robot types have this capability in this simulation, so this is always equal to the current number of robots in the system. 
3. Print capacity: The number of robots that have the print capability at the end of a simulation run. This includes replicator and printer robot types, which have not succumbed to a task risk and lost their capability. 
4. The total number of robots built using the system configuration.
5. Mean Time Between Failures (MTBF)
6. Mean Time To Repair (MTTR)
7. Mean Down Time (MDT)
8. Operational Availability (Aoss)
9. The time taken to finish replication i.e., by exhausting Non-Printable materials.
10. Average Build Quality of the entire robot colony.

RAM Metrics Calculation

In SRRS, the overall system is the robot colony and its components are the individual robots of the colony. From a reliability modeling perspective, a robot colony is clearly a parallel system of N components (robots). We propose that the colony shall be modeled as a k-out-of-N: G system. That is, a system of N parallel elements requires that at least k of these elements are operational (Good) for the overall system to function correctly.

The failure rate and the repair rate is calculated by the following formulae:

λsys = [λ1*λ2*...*λn*(μ1+μ2+...+μn)] ÷ (μ1*μ2*...*μn)
μsys = μ1+μ2+...+μn

MTBF

MTBF = Number of operational time steps ÷ Number of failures MTBFsys = 1 ÷ λsys

MTTR

MTTR = Number of unplanned maintenance (or) repair time steps ÷ Number of repairs MTTRsys = 1 ÷ μsys

MDT

MDT = Total Downtime / Number of Downtime Events MDTsys = ∑(1 ÷ MDTrobot)

Operational Availability (Aoss)

Aoss = MTBFsys/ (MTBFsys + MDTsys)

SRRS Simulation

Simulation Parameters

Requirements

Simulation Requirements

Stakeholder Requirements

Output

Habitat Growth Visualization

The number of Robots ‘In-service’ and ‘Out-of-service’ are plotted as results for the different configurations. The report link decribes the intrinsic nature of these 6 different configurations and the analysis performed.

Deterministic Mode Habitat Growth

Monte-Carlo Mode Habitat Growth

Trade-Off Analysis

Mission Statements

Mission Statement Rankings

Mission Statement Ranks according to Rank-Order Distribution of attributes

Monte-Carlo Results for each configuration

The mean values for each output metric derived from the Monte-Carlo Simulation for 1000 iternations is tabulated below.

The range of values for each metric is as follows:

Mission MAVF Tables

Mission Statement 1 - Need to finish Replication

Mission Statement 2 - Need high Collection capacity

Mission Statement 3 - Need high Assembling capacity

Mission Statement 4 - Need high Print capacity

Mission Statement 5 - Need high Average build quality

Mission Statement 6 - Hight MTBF

Mission Statement 7 - Low MTTR

Mission Statement 8 - Low MDT

Mission Statement 9 - High Aoss

Mission Statement 10 - Total Robots

MAVF Summary Table

Consistency Analysis

The confidence interval is calculated by using the Z-score for the required confidence interval and using the Marginal Error which is determined using the following formula:

where $\bar{x}$ is the mean value, $\sigma$ is the standard deviation, $n$ is the number of samples (number of MC runs) and $Z$ is the Z-score used from the following table.

The confidence intervals for the 6 SRRS configurations are shown below.

References

• Jones, A., & Straub, J. (2021). Simulation and Analysis of Self-Replicating Robot Decision-Making Systems. Computers, 10(1), 9. https://doi.org/10.3390/computers10010009
• Jones A, Straub J. Concepts for 3D Printing-Based Self-Replicating Robot Command and Coordination Techniques. Machines. 2017; 5(2):12. https://doi.org/10.3390/machines5020012