Doctor Who really only has two avenues of storytelling. Nowadays, that has changed slightly but the basic elements are really the same as they always were. You can either pit the Doctor against a narrow set of mechanical baddies, a mad professor, an alien army or a combination of all of the above. The Robots of Death is really a combination of all of those elements. There is a reason that these elements have never really changed and that is that the viewers keep on coming in, not being put off by the complicated storylines, like the entirety of the Matt Smith era. Of course, there is great value in breaking that formula, many of the old adventures which are considered classics have done so, giving us something that feels fresh to watch. But during the early Fourth Doctor years, the show tinkered more with the genres it could tap into, particularly the horror and deeper science fiction elements. The Robots of Death finds its plot being spun from old Issac Asimov robot stories as Asimov was the first to combine science fiction with the more puzzling mysteries presented to us by Agatha Christie.
The Doctor's bad case of landing his TARDIS in trouble brings him and his new, knife wielding companion, Leela, to an isolated Sandminer, which is a huge vehicle which collects the valuable ores from the sandstorms of an unnamed planet. But they have also arrived in the middle of a murder spree, that many of the crew don't believe to be possible.
The sandminer is only crewed by a handful of humans who are vastly outnumbered by their robotic servants who are always ordered to do the dogs share of the work. In the opening scene, we learn that this sort of behaviour is perfectly acceptable in this society while a few clever strokes ensure we learn the story's main conflict. In the quiet moments between sandstorms, the crew often leave the bridge and put the robots in charge while the humans relaxed in luxury. It isn't too different from a Roman empire-like scene with servants waiting hand and foot on their masters and there is the worry of revolution bubbling under the surface. In fact, the first line of dialogue we hear is of a robot who twisted the arm of its master's off. While in this society, this might just be a urban legend, it helps to acknowledge the idea of terror the humans have of their robot servants. It is true that the more you rely on something, the more it will hurt you when it decides to turn against you. The robots in this culture have safety procedures, obviously it is possible that they could wreak havoc if they wanted too. And even the captain of the sandminer, Uvanov is introduced loosing a game of chess to his robot opponent after making all the wrong moves. While Uvanov is a bully to the crewmembers under his command but chess appears to be not the only game the robots are several steps ahead of him in.
But it isn't really the robots who have rebelled on their own, although given their treatment by some of the characters in this, I wouldn't blame them if it were. They are being turned evil by a man called Taren Capel. But why and how? These are questions which are explored over the course of the story.
Thanks to the presence of the Doctor, these questions do get answered. But there are already two detectives aboard, two detectives who aren't really very good if they haven't answered these questions yet. Poul is joined by robot, D84, the pair would make a better set of detectives under different circumstances, nowadays, they would probably get their own spinoff! But the pair are blind to their cultural limitations, which is especially disastrous for Poul, who is reduced to a gibbering madman at the idea of robots being killers. This is much darker than any Asimov tale, with the story focusing less why the robots aren't obeying their programming and more on the horrible aspects of death and murder. And the Doctor is only partly interested in playing detective, the only time he mentions that it is Dask who is really Taren Capel is right at the end when it is too late to do anything, despite him noticing signs that things are off from the word go.
The setting for the story is definitely more in line with the works of Agatha Christie than Asimov. The location is isolated and a small group of people, all of whom are suspicious and hate each other are trapped together. No one is their for pleasure but to make tonnes of money. But they have spent the best part of two-years together. And the two years trapped with people they hate as allowed anger to get in the way of their work and when the crisis escalates, Uvanov ends us with a mutiny on his hands. But it is the failure of the crew to pull together in this time of crisis that is the story's biggest strength, sure their outfits and headgear are a trifle outlandish but the way the characters were written and portrayed made them feel very real.
But even in works by Christie or Asimov, murders are treated as rare and strange, often set off by a standalone event like a robotic malfunction, a long grudge or a single plan of revenge by a member of the crew. The Robots of Death takes on a much more apocalyptic view on the proceedings. We learn from the crew that the robots are everywhere on their home world and the Doctor tells Leela that there are lots of robot-dependant civilisations in the galaxy. If one robot goes bad then all of them could. And this apocalyptic view fit in well with the vision of the series by script-editor Robert Holmes and author, Chris Boucher both of whom had something of a very cynical outlook on life. Boucher had written the previous story, the anti-religious, The Face of Evil. Boucher uses the isolated location to such a perfect degree that we get an excellent look at the way of life on the planet the crew members come from. He also makes it terrifyingly clear that their whole civilisation is under peril not just from the work of Taren Capel but because the foundations of their civilisation were already horribly weak.
It is the bubbling fear humans have of robots which gave this story is distinctive edge, humans are the lords and masters of robotic life and Taren Capel, as bonkers as he is, speaks as though he is a proletariat. And if that is a stretch for you, maybe you should consider the Doctor compares Uvanov's blasé attitude to Marie Antoinette. And Uvanov is a sideways look at Asimov but his name is even closer to the Russian name Ulyanov, so is it a coincidence that he is a balding man with a goatee?
And just a quick little comment on Leela. During the classic series it was quite rare for a writer to introduce a companion in their first story and then carry on to write their second. But through him producing eight episode for her over two stories, it really helps to define her. In her first scene for this story her confusion as to whether the Doctor's Yo-Yo is magic is comical, but her character is not comical, just out of her comfort zone. She is one of only a few who took exception of the TARDIS being bigger on the inside and asked the TARDIS why it is actually like that. Her character and that of the Doctor's are completely different but they are both similar in their spirits. They are both rebels who ran away from their cultures to see the greater universe beyond...