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, Jd , to form a d-DOF robot, and we parameterize the robot con guration using the corresponding joint variables With a reference system de ned at its connecting joint, each kinematic pair can be speci ed by four scalar parameters So, for the joint i, ai is the link.

elements. For instance, a software designer may use a for-loop to take X to the power of N as shown in the following snippet.

uncertainty involved; then the input information is, by de nition, incomplete and is likely obtained in real time from robot s sensors Note the algorithmic consequences of this distinction If complete information about the workspace is available, a reasonable method to proceed is to build a model of the robot and its workspace and use this model for motion planning The signi cant effort that is likely needed to build the model will be fully justi ed by the path computed from this model If, however, nothing or little is known beforehand, it makes little sense to spend an effort on building a model that is of doubtful relevance to reality In the above situation (b), the robot hence needs to think differently From its limited sensing data, it may be able to infer some topological properties of space.

dollars for the day, he d be asked to close his open positions and shut down until the next day I remember Craig Taylor talking about this How was the Daylight Limit determined Usually, as some percentage of capital lost, he continued, looking a bit sad at the empty dish in front of him No more olives I think we need to correct that He stood up, and this time, he ordered a full pound of them and returned smiling Then he started again: The team bought and sold as individuals usually But as they worked on during their first year, they started to take on a lot of similar positions Meaning, one guy would buy Sterling the British Pound then the next guy would do the same thing, on down the line, until they were all pretty deep into the same currency against the US.

PowerX = 1; for(i=0;i<N;i++) PowerX = PowerX * X;

It may be able to infer, for example, whether what it sees from its current position as two objects are actually parts of the same object If the conclusion is yes, the robot will not be trying to pass between these two objects If the conclusion is no, the robot will know that it deals with separate objects and may choose to pass between them The objects actual shapes will be of little concern to the robot What type of sensing is suitable for a competent motion planning It turns out that just about any sensing is ne: tactile, sonar, vision, laser ranger, infrared proximity, and so on We will learn a remarkable result that says that even the simplest tactile sensing, when used with proper motion planning algorithms, can guarantee that the robot will reach its target (provided that the target is reachable).

In fact, we will consistently prefer tactile sensing when developing algorithms, before attempting to use some richer sensing media; this will allow us to clarify the issues involved This is not to say that one should prefer tactile sensors in real tasks: As a blind person will likely produce a more circuitous route than a person with vision, the same will be true for a robot Being serious about collision avoidance means that robot motion planning algorithms must protect the whole robot body, every one of its points Accordingly, robot sensors must provide suf cient input information Intuitively, this requirement is not hard to understand for mobile robots Existing mobile robots typically have a camera or a range nder that rotates as needed, or sonar sensors that cover the whole robot s circumference Intuition is less helpful when talking about arm manipulators.

This algorithmic loop uses iteration to perform a multiply operation N times. Each time through the loop, the running variable is updated. This works well in software because for every loop iteration, an internal register is updated with the current value of PowerX. Synthesizable HDL, in contrast, does not have any implied registering that occurs during an iterative loop. Instead, all register operations are de ned explicitly. If a designer attempted to create the above structure in a similar way with synthesizable HDL, they might end up with something that looks like the following code segment.