The humble Trade Federation Battle Droid... I want to play one in Star Wars D20.
However, according to the Core Rules they have no autonomous functions, being essentially slaved to an orbiting "droid control ship" which controls all of the droids on the surface. However, the highest canon of all things Star Wars - the films themselves - disprove this.
The events of TPM showed us a few odd things about in the TradeFed war droids:
Dumb - The entire droid army ground to a halt when the orbiting droid control ship was destroyed. There is an obvious causal link between the two events, as described by the film's characters who expect the destruction of the orbiting control ship to have this effect.
Smart - The infantry droids have a rank structure, signified by their colour scheme. Some of the droids are commanders. Some of the droids are specialists. This is interesting because there would be no logical reason to designate certain droids as "commanders" if they are all just "dumb terminals" controlled by a central computer.
Smart - The infantry droids have a sense of humour, as evidenced by one droid which makes fun of Qui-Gon in the hangar bay before attempting to arrest him. This is interesting because it suggests that either the droids have local intelligence, or the orbiting droid control ship's central computer was deliberately causing the "dumb terminal" infantry droid to mimic intelligence and humour.
Smart - The droids react to stimuli independently, as seen when the fighter and infantry droids in the TradeFed battleship turned to look at the Republic cruiser landing in the opening sequence of the film. This is interesting because they would have no reason to react in such a manner if they are merely "dumb terminals" being controlled by the ship's central computer which already knows about the cruiser.
Smart - The droids do not know what other droids have seen, as demonstrated in the Theed hangar when the commander droid does not recognize Qui-Gon even though numerous other droids have already been in combat with him. There is no reason that a central computer would make an individual droid act as though it doesn't know what other droids have seen, if they are all in fact controlled from one point.
Smart - The droids talk to one another, as seen by the commanders giving orders to their subordinates. This would be totally inconsistent with the "central control" model.
Smart - The droids need to independently process environmental stimuli, as seen by the fact that individual droids all need to turn their heads to look at enemy targets before firing (something which should be unnecessary if their visual data input and location information is all being processed by a central intelligence).
Dumb - The droid army moved in precise synchronization when deployed during the battle with the Gungan army. This would be consistent with the centralized control model described in the SW1 cross-sections book. Smart - (It is also consistent with really well trained soldiers simply acting in step with each other.)
Dumb - The droids move without any apparent traces of fear or uncertainty whatsoever, and march fearlessly into the line of fire without any apparent concern for their own safety. During the battle with the Gungan army they moved forward in lock-step, marching inexorably toward the Gungan lines and refusing to break formation even when they began taking heavy losses. Smart - (This is consistent with droids being programs not to fear death. We see Clone Troopers, Storm Troopers, Jedi, and the crew of the Tantive IV do the same thing!)
Dumb - Infantry droids are not equipped with a wide variety of weapons, being armed only with ordinary blasters. If they had powerful anti-personnel airburst or chemical weapons at their disposal, they could have quickly eliminated the Gungan armies by simply having infantry droids carry those weapons through the shield barrier and deploy them.
Dumb - Droid tactics are not particularly creative. Against the Gungan theatre shields, they could have enjoyed quicker success with fewer losses by simply calling in an airstrike or orbital bombardment to bring down the shield. A human commander would have called down airstrikes or orbital bombardment to bring down the shield, rather than march his men directly into the teeth of the enemy defenses. A human commander might have alternatively called for heavier weapons to be brought to the field of battle, or for specialized weapons to cut his losses. (Of course, this just proves that the Neimodian Commanders-in-Cheif are dumb, not the droids.)
Mixed - The infantry droids on the planet's surface did not shut down until many seconds after the orbiting droid control ship was destroyed. The ship's bridge and central control section was destroyed first, followed by multiple scenes of pilots cheering, followed by the disintegration of the ship's toroidal section, followed by a quick cut to the surface of the planet where the droids began to shut down.
The infantry droids actually fell apart after the destruction of the droid control ship, as evidenced when Jar-Jar Binks touched one of the droids and its head popped off. Some observers are under the impression that the head merely dropped to its folded storage position, but it actually separated from the droid body and fell to the ground, as can be seen from careful inspection of the film.
Why would the droid army exhibit so many characteristics of independent, sentient robots when they were supposedly mere "dumb terminals" controlled by a distant intelligence? This is a very difficult question to answer. If they are "dumb terminals", then why would they have ranks? Why would they exhibit characteristics of humour? Why would they react independently to environmental stimuli, or need to individually process visual information before reacting to it? Why would they talk to one another? Why would one droid know something that another droid doesn't? All of the above characteristics tend to strongly suggest that the droids do have local intelligence. In fact, it is virtually inconceivable that war droids would exhibit such characteristics if they are indeed mere "dumb terminals". The selfless actions of the droids in combat may seem to refute this conclusion, but it is always possible that their droid brains were hardwired not to consider personal risk, and/or to obey orders without objection.
Another fact which conclusively disproves the "dumb terminal" idea is the fact that they continued to operate for a few seconds without orbital control signals. A few seconds may not sound like a lot, but it is still impossible under the "dumb terminal" model.
So if we have established that they must have autonomous intelligence, why would they shut down with the destruction of the droid control ship? Why would they need a control ship at all? These paradoxes are difficult to resolve, but not impossible to resolve. There are a two possibilities that I can see:
The droids are actually receiving a carrier signal from the control ship, which merely instructs them to continue operating. This may have been designed as a safety measure for the Neimoidians, who would otherwise be hopelessly outnumbered by their opponents in the unlikely event of a droid revolt. A droid revolt seems unlikely, but it is always possible that if the droids are sentient, they might object to their treatment. Another possibility is that the Neimoidians may fear that a competitor might have somehow maliciously reprogrammed the droids to revolt, hence a central point of control. This is a rather poor design decision from many aspects (there must be some better way to deal with the possibility of droid revolt or malicious re-programming), but we should remember that the Neimoidians are businessmen rather than soldiers or engineers. This signal would have a "keepalive" period which would explain the fact that the droids continued to operate for a short period of time, and there might actually been a self-destruct command built into the droids in the event that the keepalive signal was lost, thus explaining the fact that the droids actually fell apart after the loss of the signal.
The army assembled to fight the Gungans was substantially different from the droids on the TradeFed battleships or the units in Theed. Those droids might have been low-end units, as opposed to the higher-end units in Theed which had substantial local intelligence (like normal droids, such as R2 units and interpreter droids). The droids who fought the Gungans certainly seemed to exhibit a lower level of individual initiative. However, this would suggest that some of the droids on the planet (particularly the commander units in Theed) would have continued to function after the destruction of the control ship. According to the novelization, this didn't happen.
Regardless of what happened during TPM, we have clear proof during AotC that the Battle Droids are independent.
However, according to the Core Rules they have no autonomous functions, being essentially slaved to an orbiting "droid control ship" which controls all of the droids on the surface. However, the highest canon of all things Star Wars - the films themselves - disprove this.
The events of TPM showed us a few odd things about in the TradeFed war droids:
Dumb - The entire droid army ground to a halt when the orbiting droid control ship was destroyed. There is an obvious causal link between the two events, as described by the film's characters who expect the destruction of the orbiting control ship to have this effect.
Smart - The infantry droids have a rank structure, signified by their colour scheme. Some of the droids are commanders. Some of the droids are specialists. This is interesting because there would be no logical reason to designate certain droids as "commanders" if they are all just "dumb terminals" controlled by a central computer.
Smart - The infantry droids have a sense of humour, as evidenced by one droid which makes fun of Qui-Gon in the hangar bay before attempting to arrest him. This is interesting because it suggests that either the droids have local intelligence, or the orbiting droid control ship's central computer was deliberately causing the "dumb terminal" infantry droid to mimic intelligence and humour.
Smart - The droids react to stimuli independently, as seen when the fighter and infantry droids in the TradeFed battleship turned to look at the Republic cruiser landing in the opening sequence of the film. This is interesting because they would have no reason to react in such a manner if they are merely "dumb terminals" being controlled by the ship's central computer which already knows about the cruiser.
Smart - The droids do not know what other droids have seen, as demonstrated in the Theed hangar when the commander droid does not recognize Qui-Gon even though numerous other droids have already been in combat with him. There is no reason that a central computer would make an individual droid act as though it doesn't know what other droids have seen, if they are all in fact controlled from one point.
Smart - The droids talk to one another, as seen by the commanders giving orders to their subordinates. This would be totally inconsistent with the "central control" model.
Smart - The droids need to independently process environmental stimuli, as seen by the fact that individual droids all need to turn their heads to look at enemy targets before firing (something which should be unnecessary if their visual data input and location information is all being processed by a central intelligence).
Dumb - The droid army moved in precise synchronization when deployed during the battle with the Gungan army. This would be consistent with the centralized control model described in the SW1 cross-sections book. Smart - (It is also consistent with really well trained soldiers simply acting in step with each other.)
Dumb - The droids move without any apparent traces of fear or uncertainty whatsoever, and march fearlessly into the line of fire without any apparent concern for their own safety. During the battle with the Gungan army they moved forward in lock-step, marching inexorably toward the Gungan lines and refusing to break formation even when they began taking heavy losses. Smart - (This is consistent with droids being programs not to fear death. We see Clone Troopers, Storm Troopers, Jedi, and the crew of the Tantive IV do the same thing!)
Dumb - Infantry droids are not equipped with a wide variety of weapons, being armed only with ordinary blasters. If they had powerful anti-personnel airburst or chemical weapons at their disposal, they could have quickly eliminated the Gungan armies by simply having infantry droids carry those weapons through the shield barrier and deploy them.
Dumb - Droid tactics are not particularly creative. Against the Gungan theatre shields, they could have enjoyed quicker success with fewer losses by simply calling in an airstrike or orbital bombardment to bring down the shield. A human commander would have called down airstrikes or orbital bombardment to bring down the shield, rather than march his men directly into the teeth of the enemy defenses. A human commander might have alternatively called for heavier weapons to be brought to the field of battle, or for specialized weapons to cut his losses. (Of course, this just proves that the Neimodian Commanders-in-Cheif are dumb, not the droids.)
Mixed - The infantry droids on the planet's surface did not shut down until many seconds after the orbiting droid control ship was destroyed. The ship's bridge and central control section was destroyed first, followed by multiple scenes of pilots cheering, followed by the disintegration of the ship's toroidal section, followed by a quick cut to the surface of the planet where the droids began to shut down.
The infantry droids actually fell apart after the destruction of the droid control ship, as evidenced when Jar-Jar Binks touched one of the droids and its head popped off. Some observers are under the impression that the head merely dropped to its folded storage position, but it actually separated from the droid body and fell to the ground, as can be seen from careful inspection of the film.
Why would the droid army exhibit so many characteristics of independent, sentient robots when they were supposedly mere "dumb terminals" controlled by a distant intelligence? This is a very difficult question to answer. If they are "dumb terminals", then why would they have ranks? Why would they exhibit characteristics of humour? Why would they react independently to environmental stimuli, or need to individually process visual information before reacting to it? Why would they talk to one another? Why would one droid know something that another droid doesn't? All of the above characteristics tend to strongly suggest that the droids do have local intelligence. In fact, it is virtually inconceivable that war droids would exhibit such characteristics if they are indeed mere "dumb terminals". The selfless actions of the droids in combat may seem to refute this conclusion, but it is always possible that their droid brains were hardwired not to consider personal risk, and/or to obey orders without objection.
Another fact which conclusively disproves the "dumb terminal" idea is the fact that they continued to operate for a few seconds without orbital control signals. A few seconds may not sound like a lot, but it is still impossible under the "dumb terminal" model.
So if we have established that they must have autonomous intelligence, why would they shut down with the destruction of the droid control ship? Why would they need a control ship at all? These paradoxes are difficult to resolve, but not impossible to resolve. There are a two possibilities that I can see:
The droids are actually receiving a carrier signal from the control ship, which merely instructs them to continue operating. This may have been designed as a safety measure for the Neimoidians, who would otherwise be hopelessly outnumbered by their opponents in the unlikely event of a droid revolt. A droid revolt seems unlikely, but it is always possible that if the droids are sentient, they might object to their treatment. Another possibility is that the Neimoidians may fear that a competitor might have somehow maliciously reprogrammed the droids to revolt, hence a central point of control. This is a rather poor design decision from many aspects (there must be some better way to deal with the possibility of droid revolt or malicious re-programming), but we should remember that the Neimoidians are businessmen rather than soldiers or engineers. This signal would have a "keepalive" period which would explain the fact that the droids continued to operate for a short period of time, and there might actually been a self-destruct command built into the droids in the event that the keepalive signal was lost, thus explaining the fact that the droids actually fell apart after the loss of the signal.
The army assembled to fight the Gungans was substantially different from the droids on the TradeFed battleships or the units in Theed. Those droids might have been low-end units, as opposed to the higher-end units in Theed which had substantial local intelligence (like normal droids, such as R2 units and interpreter droids). The droids who fought the Gungans certainly seemed to exhibit a lower level of individual initiative. However, this would suggest that some of the droids on the planet (particularly the commander units in Theed) would have continued to function after the destruction of the control ship. According to the novelization, this didn't happen.
Regardless of what happened during TPM, we have clear proof during AotC that the Battle Droids are independent.