Journal of Robotics, Networking and Artificial Life, Vol. 3, No. 3 (December 2016), 174-181

Spatial Grasp Language (SGL) for Distributed Management and Control
Peter Simon Sapaty

Institute of Mathematical Machines and Systems
National Academy of Sciences, Kiev, Ukraine
E-mail: peter.sapaty@gmail.com

Abstract
A full description of the high-level language for solving arbitrary problems in heterogeneous, distributed, anddynamic worlds, both physical and virtual, will be presented and discussed. The language is based on holistic andgestalt principles representing semantic level solutions in distributed environments in the form of self-evolving
spatial patterns. The latter are covering, grasping and matching distributed systems while creating active
infrastructures in them operating in a global-goal-driven manner but without any central resources.
Keywords: spatial intelligence, Spatial Grasp Language, self-evolving scenarios, parallel networked interpretation,
integral solutions, distributed control.

1. Introduction
We are witnessing a dramatic change in the character ofnational and international activity, especially in crisisand conflict situations, with the use of asymmetric andhybrid methods and solutions. A new high-levelnetworking approach is being developed [1-6] which
can be useful for solving such world problems. It isbased on holistic and gestalt ideas allowing us to grasp
the whole first [7-9] rather than traditional approaches
based on communicating parts or agents [10].
The resultant Spatial Grasp Technology (SGT) with
Spatial Grasp Language (SGL) as its key element has
been prototyped and tested on numerous applications.
In general, it operates as symbolically shown in Fig. 1.
A high-level scenario for any task in a distributed worldis represented as an active self-evolving pattern rather
than traditional program, sequential or parallel.
This pattern, expressing top semantics and key
decisions of the problem to be solved spatially
propagates, replicates, modifies, covers and matches
theworld,
creating
distributed
operational
infrastructures throughout it, with final results retainedin the environments or returned as a high knowledge tothe starting point(s).

The paper describes full specification of the latest
version of SGL currently used in a number of projects
related to intelligent management and control of large
distributed dynamic systems. SGL is the latest and mostadvanced version in a row of spatial languages using
free but globally controlled movement of program codein networks, with previous variants named as WAVE[1], WAVE-WP [2] and DSL [11].

Fig.1. How SGT operates in general.

2. The SGL Worlds
SGL
differs
fundamentallyfromtraditional
programming languages. Rather than working withinformation in a computer memory it allows us todirectly move through, observe, and make any actions

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Peter Simon Sapaty

and decisions in fully distributed environments,
whether physical or virtual. SGL directly operates with:• Physical World (PW), continuous and infinite,where each point can be identified and accessed byphysical coordinates.
• Virtual World (VW), which is discrete and consistsof nodes and semantic links between them, both
capable of containing arbitrary information.
• Executive world (EW), consisting of active doers
with communication channels between them, which
can represent any devices, humans including,operating on the previous two worlds.
Different combination and integration of these worlds
can be possible within the same formalism.
3. Top SGL Syntax

SGL constants can represent information, physicalmatter (or objects), self-identifying custom items,
special words as modifiers for different constructs, or
arbitrary structures, as grasps again:
constant  information | matter | custom | special | grasp

SGL variables, called “spatial”, containing informationor matter, can be stationary or mobile an named as:
variable  global | heritable | frontal | nodal | environmental

And rules belonging to the following classes:
rule  movement | creation | echoing | verification |assignment | advancement | branching | transference |timing | granting | type | usage | application | grasp

The final option, grasp, allows rules also to be theresults of spatial development of any SGL scenarios.
4. SGL Main Features

SGL has a recursive structure shown in Fig. 2.

4.1. How scenarios evolve

Fig. 2. SGL recursive syntax.

Such organization allows us to express any spatial
algorithm, create and manage any distributed structuresand systems, static or dynamic, passive or active, also
solve any problems in, on, and over them.
The SGL topmost definition with scenario named as
grasp can be as follows:
grasp  constant | variable | rule [({ grasp,})]where syntactic categories are shown in italics, verticalbar separates alternatives, square brackets identify
optional constructs, and parentheses and commas being
the language symbols. Braces indicate repetitive parts
with the delimiter (here comma) at the right.
An SGL scenario, or grasp in its simplest form canbe just a constant presenting the result explicitly. It canalso be a variable containing data assigned to it
previously. The third variant is a rule, which can be
optionally supplied with parameters (enclosed inparentheses and separated by comma if more than one).
These parameters, due to recursion, can generally bearbitrary grasps again (from constants or variables toscenarios of any complexity and space-time coverage).

• SGL scenario is considered developing in steps,
which can be parallel, with new steps produced on
the basis of previous steps.
• Any step is always associated with a point or
position of the world in which the scenario or its
particular part is currently developing.
• Each step provides a resultant value (single ormultiple) representing information, matter or both,and a resulting control state (states ranging by theirstrength) in the points reached.
• Different scenario parts may evolve from a step inordered, unordered, or parallel manner, providing
new independent or interdependent steps.
• Different parts can succeed each other, with newparts evolving from steps got by previous parts.
• This (potentially parallel and distributed) scenario
evolution
mayproceedinsynchronous,
asynchronous or combined mode.
• SGL operations and decisions in evolving scenario
parts can use states and values returned from otherparts whatever complex and remote they might be,thus combining forward and backward operations.
• Different steps from the same or different scenario
parts can associate with the same world points,
sharing information in them.
• Staying with world points, it is possible to change
local parameters in them, whether physical or
virtual, impacting the worlds via these locations.
• Scenarios navigating distributed spaces can create
arbitrary
distributed
physicalorvirtualinfrastructures in them, which may operate on theirown. They can also subsequently (or even during

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175Spatial Grasp Language (SGL) for

their creation) be navigated, updated and processedby the same or other scenarios.
• Overall organization can be provided by a variety of
SGL rules which may be arbitrarily nested.
Any sequential or parallel, centralized or distributed,
stationary or mobile algorithms operating with bothinformation and physical matter can be written in SGL
at any levels and their combinations.
4.2. Sense and nature of rules
A rule representing any SGL action or decision may, forexample, belong to the following categories:• Elementary arithmetic, string, or logic operation.
• Move or hop in a physical, virtual, execution or
combined space.
• Hierarchical fusion and return of (potentiallyremote) data.
• Distributed control, both sequential and parallel, andin breadth or depth.
• A variety of special contexts detailing navigation in
space and embraced operations and decisions.
• Type and sense of a value or its chosen usage,
guiding automatic language interpretation.
• Creation or removal of nodes and/or links in
distributed knowledge networks, allowing us towork with arbitrary structures.
• A rule can also be a compound one integrating otherrules, due to recursion.
All rules, regardless of nature or complexity, pursue thesame ideology and organization, as follows.
• They start from a certain world position, being
initially linked to it.
• Perform or control the needed operations which may
be stepwise, parallel and arbitrarily complex.
• Produce concluding results by final steps, expressedby control states and values there.
• The final steps may associate with the same (where
the rule started) or new world positions.
This uniformity allows us to compose integral spatial
algorithms of any complexity and world coverage,
operating altogether under unified control.
4.3. Spatial variables
The spatial variables are created upon declaration by
special rules or by first assignment to them, being as:• Global variables – most expensive, can serve any
SGL scenarios and be shared by their different
branches. Their existence can depend on features of
distributed environments and implementation.
• Heritable variables – stationary, serving only thecurrent and all subsequent steps, generally multiple
and parallel, which can share them.
• Frontal variables – mobile, associating with thecurrent step and accompanying scenario evolution;
being transferred between subsequent steps andreplicated if a number of new steps emerge.
• Environmental variables – stationary or mobile,allowing us to access, analyze, and change different
features of worlds navigated.
• Nodal variables – a temporary property of world
positions, being shared by all activities reachingthese nodes under the same scenario identity.
These types of variables, especially when used together,allow us to create advanced algorithms working directlyin space, actually in between components of distributed
systems rather than in them.
4.4. Control states and their hierarchical merge
The following control states appear after performing
different scenario steps. Indicating local progress, they
are used for distributed control of multiple processes.
• thru – reflects full success of the current branch of
the scenario with capability of further development.
• done – indicates success of the current scenario stepasplannedtermination,
without
furtherdevelopment of this branch from the current step.
• fail – indicates failure of the current branch, withno possibility of further development from it.
• fatal – reports terminal failure with nonlocal
effect, triggering abortion of all evolving scenario
processes together with associated data.
These control states appearing in different branches of aparallel and distributed scenario are used to obtaingeneralized states at higher levels for proper decisions.
The generalization is based on their power, frommaximum to minimum: fatal, thru, done, fail.
5. Description of Main SGL Constructs
5.1. Constants
String can be represented as any sequence of charactersembraced in opening-closing single quotation marks.
Instead of single quotes ‘’, a sequence of characters canalso be placed into opening-closing braces {}. The latter
will indicate the text as a potential scenario code to be
optimized. Number can be represented traditionallylike: [sign]{digit}[.{digit}[E[sign]{digit}]]. Physicalmatter (objects) can be expressed by a sequence ofcharacters embraced in opening-closing double quotes“”. The above self-identified constants can also be set

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Peter Simon Sapaty

via explicit naming of their types by corresponding
rules.
Special verbal constants can be used as standard
parameters (modifiers) in different rules. The basic listof these: thru, done, fail, fatal, infinite, nil,any, all, other, passed, existing, neighbors,
direct, noback, firstcome, forward, backward,
global, local, synchronous, asynchronous,
virtual,physical,
executive,
engaged,vacant, existing, passed.

Constants can also be arbitrarily complex, as
aggregates (hierarchical including) – i.e. grasps again.
5.2. Variables

Different types of variables can be self-identifiable, by
the way their names written. Variables of different
types can also have any identifiers if explicitly declaredby special rules. In case of self-identification theyshould start with capitals G, H, F or N, respectively, forglobal, heritable, frontal, and nodal variables,
Environmental variables have names in all capitals:• TYPE – indicates the type of a node the current step
associates with (i.e. virtual, physical,
executive, or combination).
• CONTENT – returns content/name of the current node(with virtual/executive dimension, or both).
• ADDRESS – returns address of the virtual node.
• QUALITIES – identifies parameters associated withthe current physical position.
• WHERE – keeps physical coordinates of the current
node. Assigning causes movement to new position.
• BACK – keeps internal system link to the precedingworld node.
• PREVIOUS – refers to a unique address of theprevious virtual node.
• PREDECESSOR – refers to the content/name of thepreceding world node.
• DOER – keeps name of the device which interprets
current SGL code.
• RESOURCES – keeps a list of available orrecommended resources for scenario execution.
• LINK – keeps a name (same as content) of thevirtual link which has just been passed.
• DIRECTION – keeps direction (along, against, or
neutral) of the passed virtual link.
• WHEN – assigning value to this variable sets up an
absolute starting time for the following branch.
• TIME – returns current absolute time, being readonly global variable.

• SPEED – reflects/changes current speed of physicalmovement of the current node.
• STATE – can be used for explicit setting the state of
the current step.
• VALUE – when accessed, returns resultant value ofthe latest operation.
• COLOR – keeps identity of the current SGL scenario
or its branch propagating with it.
• IN, OUT – special variables for data exchanges
reading with the outside world.
• STATUS – retrieving or setting the status of a doer
node in which the scenario is currently staying.
Other environmental variables for extended applications
can be introduced by unique words in all capitals too, or
set up by special rules.
5.3. Rules
5.3.1. Movement
Rules of this class result in virtual hopping to theexisting nodes or real movement to new physicallocations with current frontal variables and control.
• hop – sets virtual propagation to node(s) in virtual,
execution, or combined worlds, directly or via links
connecting them.
• move, shift – sets real movement in physicalworld given by coordinates or their deviations.
• follow – allows us to propagate in both virtualand physical spaces by following the set up routes.
5.3.2. Creation
This class of rules creates or removes nodes and/or
links leading to them during distributed world
navigation.
• create, linkup -- creates new link-node pairs, oronly links to existing nodes.
• delete, unlink -- removes links together withnodes they should lead to, or links only.
5.3.3. Echoing
The rules of this class use terminal control states andterminal values from the embraced scenario (which may
be remote) to obtain the resultant state and value in theworld point it started, the latter being its terminal point.
These include: state, order, rake, sum, count,

first, last, min, max, random, average, element,
sortup, sortdown, reverse, add, subtract,
multiply, divide, degree, separate, unite,
attach, append, common, withdraw , access.

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Spatial Grasp Language (SGL) for

5.3.4. Verification
These rules provide control state thru or failreflecting the result of certain verification procedures,
also nil as own resultant value, while remaining in thesame world positions after completion.
equal,
notequal,
less,
They
include:lessorequal,more,moreorequal,
bigger,smaller, heavier, lighter, longer, shorter,
empty,
nonempty,
belongs,
notbelongs,
intersects, notintersects.

5.3.5. Assignment
This class of rules assigns the result of the rightscenario operand (which may be arbitrarily remote, also
as a list of values) to the variable or set of variables
directly named or reached by the left scenario operand,which may be remote too, being: assign,
assignpeers.
5.3.6. Advancement
Rules of this class organize forward or in depth
advancement in space and time. They can work insynchronous or asynchronous mode.
• advance – organizes stepwise advancement inphysical, virtual, executive or combined spaces, also
in a pure computational space.
• slide – works similar to the previous rule unlesscurrent scenario fails to succeed, the next scenario
will be applied then, and so on.
• repeat – invokes the embraced scenario as manytimes as possible, with each new iteration taking
place from final positions of previous invocation.
5.3.7. Branching
These rules allow the embraced set of scenario operands
develop in breadth, each from the same starting
position, with the resultant set of positions and order of
their appearance depending on a concrete rule• branch – most general variant with independenceof scenario operands from each other.
• sequential – organizing strictly sequential
invocation of all scenario operands.
• parallel – fully parallel development of all
scenario operands from the same starting position.
• if – usually with three scenario operands. If firstsucceeds, the second activated, otherwise third.
• or – allows only one operand with the resulting
state thru or done to be registered as successful.

• orsequential – launches scenario operands in asequential manner, as they are written.
• orparallel – activates all scenario operands inparallel, choosing first successful in time.
• and – activates all scenario operands, demanding
all to be successful, regardless of invocation order.
• andsequential – activates operands in written
order, terminating when first resulting with fail.
• andparallel – activates all operands in parallel,terminating when first in time fails.
• choose – chooses a branch in their sequence before
its execution, using certain parameters.
• firstrespond – selects first branch in time
replying termination, regardless of success• cycle – repeatedly invokes embraced scenario fromsame position until it results with success, allpositions reached constitute the result.
• loop – differs from the previous in that the resultant
set of positions include only the set produced by thelast successful invocation.
• sling – invokes repeatedly the embraced scenario
until it succeeds, always resulting in the samestarting position.
• whirl – endlessly repeating the embraced scenario
from the starting position regardless of its success or
failure.
• split – performs, if needed, additional static ordynamic partitioning of the embraced scenario.
fringe – providing the most general variant ofsplitting for any scenario after its execution.
5.3.8. TransferenceThis class of rules organizes different control or datatransference activity, accessing local or external
procedures and worlds. Includes the following: run,call, input, output, transmit, send, receive.

5.3.9. Timing
sleep, allowed – establishes time delay defined by

the embraced operand, or sets time limit by the first
operand for activity on the second operand.
5.3.10. Granting

This class of rules provides different services foradvanced management of embraced scenarios, like
protecting from fatal events, blocking shared resources
or freeing the evolving branches from superior control.

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It includes the following: contain, release, free ,blind, lift, none, stay , seize.
5.3.11. Type and usage
These rules explicitly assign types to different
constructs generally represented as strings, or clarify
their usage in different rules, including the following:
global,heritable,
frontal,nodal,
environmental,
matter,number,string,scenario, address, coordinate, content, index,
time, speed, name, place, center, range, doer,
human, robot, node[s], link[s], unit.

5.3.12. Application
Additional application, or custom, rules can allow SGL
to be extended unlimitedly while effectively embracingand embedding specifics of different application areas.
They can be used similarly to other language rules
while obeying established internal interpretation
principles and unified command and control.
6. Full SGL Summary
The following is full SGL formal description
summarizing the listed above language constructs.
 constant | variable | rule [({ grasp,})] information | matter | custom | special | grasp
 global | heritable | frontal | nodal | environmental
 movement | creation | echoing | verification |assignment | advancement | branching |transference | timing | granting | type | usage |application | grasp
information  string | scenario | number
string ‘{character}’scenario
 {{character}}number [sign]{digit}[.{digit}[e[sign]{digit}]]matter “{character}”
special thru | done | fail | fatal | infinite |nil | any | all | other | passed |existing | neighbors | direct |noback | firstcome | forward |backward | global | local |sync[hronous] | async[hronous] |virtual | physical | executive |engaged | vacant | existing | passed
global G{alphameric}heritable
 H{alphameric}frontal F{alphameric}nodal
 N{alphameric}environmental  TYPE | CONTENT | ADDRESS |QUALITIES | WHERE | BACK | PREVIOUS |PREDECESSOR | DOER | RESOURCES |LINK | DIRECTION | WHEN | TIME | SPEED |STATE | VALUE | COLOR | IN | OUT | STATUS
movement hop | move | shift | follow
creation create | linkup | delete | unlink
grasp
constant
variablerule state | order | rake | sum | count | first |last | min | max | random | average |element | sortup | sortdown | reverse |add | subtract | multiply | divide |degree | separate | unite | attach |append | common | withdraw | accessverification
 equal | notequal | less |less[or]equal | more | more[or]equal |bigger | smaller | heavier | lighter |longer | shorter | empty | nonempty |belongs | notbelongs |intersects | notintersects
assignment
 assign | assignpeers
advancement  advance | slide | repeatbranching branch | sequential | parallel | if | or |orsequential | orparallel | and |andsequential | andparallel |choose | firstrespond | cycle | loop |sling | whirl | split | fringetransference  run | call | input | output |transmit | send | receive
timing sleep | allowed
granting
 contain | release | free | blind |lift | none | stay | seizetype
 global | heritable | frontal | nodal |environmental | matter | number |string | scenario
usage address | coordinate | content |index | time | speed | name | place |center | range | doer | human |soldier |robot | node[s] | link[s] | unit
echoing

7. Elementary Examples in SGL
Let us consider some elementary scenarios in SGL fromthe mentioned three worlds (PW, VW, and EW).
• Assignment of the sum of three constants 27, 33,
and 55.6 to a variable named Result:assign(Result, add(27, 33, 55.6))• Independent moves in physical space to coordinates(x1, y3) and (x5, y8): move(x1, y3), move(x5,y8)• Creation of a virtual node Peter: create(Peter)• Extending the previous virtual network (so far
containing node Peter only) with a new link-nodepair for Peter as father of Alex:
hop(Peter); create(+fatherof, Alex)• Giving direct order to robot Shooter to fire at certain
coordinates (x, y): hop(Shooter); fire(x, y)• Ordering John to engage robot Shooter to fire at (x,y), with John confirming the action: hop(John);
if((hop(Shooter); fire(x,y)), output(OK))

8. SGL Networked Interpretation
The developed technology if used in distributed
environments operates as follows. A network of SGL

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Spatial Grasp Language (SGL) forinterpreters (as universal control modules U, Fig. 3)
embedded in key system points (humans, robots,
sensors, mobile phones, etc.) collectively interprets
mission scenarios written in SGL. Capable ofrepresenting any parallel and distributed algorithms,
these scenarios can start from any node, covering at
runtime the whole world or its parts needed with
operations and control.

9. Some SGT Application Areas
The following are some researched, discussed, andreported applications of SGT and SGL summarizing
their advantages.
•••

Fig. 3. Self-spreading spatial scenarios in SGL.

The spreading scenarios can create knowledge
infrastructures arbitrarily distributed between systemcomponents, as in Fig. 4a.

•

•

•

a

•

b

Fig. 4. Scenario activity results: a) creation of spatial
infrastructures; b) distributed scenario interaction.

Navigated by same or other scenarios, these caneffectively support distributed databases, command andcontrol (C2), situation awareness and autonomous
decisions, also simulate any other existing or hypothetic
computational and/or control models. Many SGL
scenarios can operate within the same environments,
spatially cooperating or competing in the networked
space as overlapping fields of solutions, see Fig. 4b.
The dynamic network of SGL interpreters covering
any distributed spaces, the whole world including, canbe considered as a new type of parallel supercomputer,which can have any (including runtime changing)
networking topology and operate without any central
facilities or control. A backbone of the networked
interpreter is its spatial track system providing global
awareness and automatic C2 over multiple distributed
processes, also creating, supporting, and managing(including removing when becoming useless) different
distributed information and control resources••

Graph and network theory [1, 2]. Highly parallel and fully
distributed solutions of main graph and network problems
have been programmed in earlier versions of SGL anddemonstrated in distributed networks.
Distributed interactive simulation [12, 13]. The
technology had been researched for both live control oflarge dynamic systems like battlefields and distributed
interactive simulation of them, any combination too.
Solving social problems [14, 15]. SGL appeared to be
useful in social systems area, like support of elderly andhandicapped people in modern societies, from intelligent
homes improving their everyday life to finding and tracing(if lost, for example).
Human terrain [16]. SGT allows this new topic, originallycoined in military, to be used in a broader sense and scalethan initially planned, allowing us to solve national andinternational problems peacefully.
Sensor networks [17]. Multiple sensors scattered overlarge territories can behave altogether under SGT as a
spatial supercomputer operating efficiently even underrestricted communications.
Military robotics [18]. SGT paves the way for unified
transition up to fully unmanned systems with massive useof advanced robotics. One of practical benefits may beeffective management of robotic collectives, regardless of
their size by only a single human operator.
Intelligence, Surveillance and Reconnaissance (ISR) [19].
SGT can integrate distributed ISR facilities into flexible
goal-driven systems operating under unified commandand control, which can be automatic.
Air and missile defense [20]. Providing flexible and selfrecovering distributed C2 infrastructures, SGT can, forexample, effectively use distributed networks of cheap
ground or low-altitude sensors to discover, trace, anddestroy low flying objects with complex routes by mobile
intelligence.
Crisis management [21, 22]. SGT can support advanced
distributed systems for crisis management, where complex
relief missions, national and international, can beorganized and programmed quickly, on the fly.

10. Conclusions
We have described ideology, syntax, basics ofsemantics, and main constructs of a completely
different language, oriented on programming andprocessing of distributed spaces directly. With the useof it, the whole distributed world, equipped with
communicating SGL interpreters, can be considered as
an integral and universal spatial machine capable ofsolving arbitrary complex problems in this world

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Peter Simon Sapaty(machine rather than computer as it can directly operatewith physical matter and objects too). Multiple
communicating “processors” or doers of this machine,
being stationary or mobile, can include humans,
computers, robots, smart sensors, any mechanical andelectronic equipment capable of cooperatively solving
problems formulated in SGL.
Being understandable and suitable for both manned
and unmanned components, the language offers a real
way to unified transition to massively robotizedsystems, including fully unmanned ones, as within the
SGL operational scenarios any component can easilychange its manned to unmanned status and vice versa.
Acknowledgment
The author appreciates the invaluable support for years
and personal involvement in this project of Prof.
Masanori Sugisaka, especially in the fields of advanced
cooperative robotics, IT-based solutions of social
problems, distributed sensor networks, and crisis andemergency management.
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