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Worse yet, what if a part of that path curve cannot be checked because it is bending around the corner of a nearby obstacle and hence is invisible These questions suggest that in a planning/control system with included dynamics a path step cannot be planned separately from at least a few steps that will follow it The robot must make sure that the step it now contemplates will not result in some future steps where the collision is inevitable How many steps look-ahead is enough This is one thing that we need to gure out Below we will study the said effects, with the same objective as before to design provably correct sensor-based motion planning algorithms As before, the presence of uncertainty implies that no global optimality of the path is feasible Notice, however, that given the need to plan for a few steps ahead, we can attempt local optimization.

My head popped up, and I could see the New York Stock Exchange down the street I put my head back down..

While improving the overall path, sometimes dramatically, in general a path segment that is optimal within the robot s eld of vision says nothing about the path global optimality..

Finally, the testbench is self-checking. It is assumed that each of the individual functional tests comprehensively checks the conditions within the hardware models, reports any mismatches to the standard output or the log le, and increments the error count. When the simulation completes, a success or failure is indicated by the nal statement. This basic automation greatly reduces the amount of time spent verifying vectors.

By the way, which optimization criterion is to be used We will consider two criteria The salient feature of one criterion is that, while maintaining the maximum velocity allowed by its dynamics, the robot will attempt to maximize its instantaneous turning angle toward the required direction of motion This will allow it to nish every turning maneuver in minimum time In a path with many turns, this should save a good deal of time In the second strategy (which also assumes the maximum velocity compatible with collision avoidance), the robot will attempt a time-optimal arrival at its (constantly shifting) intermediate target Intermediate targets will typically be on the boundary of the robot s eld of vision Similar to the model used in 3, our mobile robot operates in twodimensional physical space lled with a locally nite number of unknown stationary obstacles of arbitrary shapes.

Planning is done in small steps (say, 30 or 50 times per second, which is typical for real-world robotics), resulting in continuous motion The robot is equipped with sensors, such as vision or range nders, which allow it to detect and measure distances to surrounding objects within its sensing range Robot vision works within some limited or unlimited radius of vision, which allows some steps look-ahead (say, 20 or 30 or more) Unless obstacles occlude one another, the robot will see them and use this information to plan appropriate actions Occlusions effectively limit a robot s input information and call for more careful planning Control of body dynamics ts very well into the feedback nature of the SIM (Sensing Intelligence Motion) paradigm To be sure, such control can in principle be incorporated in the Piano Mover s paradigm as well.

It is good design practice to create an automated, self-checking testbench. This will save a signi cant amount of time down the road as the testbench grows.

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One way to do this is, for example, to divide the motion planning process into two stages: First, a path is produced that satis es the geometric constraints, and then this path is modi ed to t the dynamic constraints [79], possibly in a time-optimal fashion [80 82] Among the rst attempts to explicitly incorporate body dynamics into robot motion planning were those by O Dunlaing [83] for the one-dimensional case and by Canny et al [84] in their kinodynamic planning approach for the twodimensional case In the latter work the proposed algorithm was shown to run in exponential time and to require space that is polynomial in the input.