Professor Oussama Khatib, Robotics Laboratory, Department of Computer Science. The volume starts with a comprehensive tutorial by De Luca et al. Final word of thanks goes to Costanzo Manes for the pictorial illustration below.

IntroductionToRobotics-Lecture10 Instructor (Krasimir Kolarov):Good afternoon. My name is Krasimir Kolarov. I am going to be teaching the lecture today and also the co-author of the notes for the course.

So if you have any complaints, direct it to me. If you have any praises, direct it to Oussama. I did my [inaudible] here at Stanford about 16 years ago. So I was in your shoes, and I’ve been kinda doing a few lectures as well as some of the classes completely since. I’m not working in the robotics area right now, but I’m staying pretty current in that. So we’re going to start as usual with a short video snippet. Do you wanna play the video?

[Video] Suppose I need to deliver an emergency case of cold drinks to my friend Keith who lives about a half mile away, but I’m too busy to drive over. Fortunately, I have a 1990 model Nab Lab, a computer-controlled van equipped with television cameras to see the road, a scanning laser range finder that measures 3-D positions, computers to digitize and process the images and computer-controlled [inaudible]. I toss in the case of drinks and fire it up. The Nab Lab built a map earlier by watching as I drove it around the neighborhood, including the locations of roads, shapes of intersections and the locations of 3-D objects.

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I add a few annotations to the map to tell the Nab Lab where to speed up, when to slow down and where to stop. I hit the run switch, step out of the Nab Lab and [inaudible]. The Nab Lab has several different ways of seeing roads.

It needs hints from the map to know which roads to use [inaudible]. I told it to drive along the street using images from the color camera processed by a fast-simulated neuro-network [inaudible]. It digitizes images from a color camera and processes them to enhance the contrast between road and off-road. The enhanced images are fed to a simulated neuro-network, which has been trained by watching a human drive along similar roads.

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Now this neuro-network directly outputs steering angles to the Nab Lab’s steering wheel. When the Nab Lab approaches intersections, the cameras see only asphalt, and [inaudible] is unable to interpret the images. The map gives instructions to switch to landmark navigation.

A laser range finder finds 3-D objects on the side of the road it has previously recorded in the map, and uses those objects as landmarks to update its position on the map. Once the Nab Lab knows exactly where it is, it can drive fine using its inertial guidance system long enough to traverse or accurately turn through an intersection. Leaving the intersection, the Nab Lab’s map tells it to pay attention to its color cameras again and to increase its speed.

[Inaudible] finds the road again and steers the Nab Lab towards its call. Finally, the Nab Lab uses dead [inaudible] to predict when it should be approaching Keith’s house, uses 3-D sensing to find his mailbox and comes to a stop.

The drinks are still cold. [Crosstalk] Instructor (Krasimir Kolarov):There should be a sound with the video. I can make [inaudible]. It’s basically a navigation for a car. He’s riding in his car several years ago, actually, well before the [inaudible] that make Stanford so famous in that area. So this is one of [inaudible].

That’s – we can stop here. So that has to do – the topic of the lecture today is trajectory generation, and it’s quite relevant to the video that you saw because, in addition to the control functions – the sensor functions – the underground – the underlying mathematics is really planning for a path for an object among other objects, and that’s basically trajectory planning. So what we’re going to be talking about today is really the basic mathematics, and that can be used at higher level planning concluding the run with the navigation video.