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Non-holonomic path generation

The non-holonomic path planning problem has been addressed by many researchers, e.g., [8, 4]. However, most of the algorithms deal with static worlds and generate pre-planned global paths. In the robot soccer domain, this is not possible as the domain is inherently dynamic and response times need to be very high. Furthermore, the world dynamics include also possible interference from other robots (e.g., pushing), making precisely mapped out paths ineffective and unnecessary.

We devised and implemented a reactive controller for our system, which is computationally inexpensive, deals with dynamic environments, and recovers from noisy command execution and possible interferences. A reactive controller also has possible disadvantages, as it may generate sub-optimal paths, due to local minima. We introduced a failure recovery routine to handle such failures.

The navigational movement control for our robots is hence done via reactive control. The control rules described below are inspired by the Braitenburg vehicle [3]. The Braitenburg love vehicle defines a reactive control mechanism that directs a differential-drive robot to a certain target. A similar behavior is required in the system; however, the love vehicle's control mechanism is too simplistic and, in some start configurations, tends to converge to the goal very slowly. We devised a modified set of reactive control formulae that allows for effective adjustment of the control trajectory:


where v and tex2html_wrap_inline536 are the desired translational and rotational velocities, respectively, tex2html_wrap_inline538 is the direction of the target relative to the robot tex2html_wrap_inline540 , tex2html_wrap_inline542 is the in-place rotational velocity, and tex2html_wrap_inline544 and tex2html_wrap_inline546 are the base translational and rotational velocities, respectively. The translational and rotational velocities can be translated to differential drive parameters via a simple, invertible linear transform. This set of control formulae differs from the love vehicle in that it takes into account the orientation of the robot with respect to the target and explicitly adds rotational control. This set of control rules implicitly allows for heading independence, i.e., the control rules allow for both forward and backward movements, whichever one is most efficient to execute. Figure 3 shows an actual run of the reactive control algorithm described above.

Figure 3: Sample trace of the execution of the reactive control algorithm. The target point is marked with a cross.

next up previous
Next: Ball handling Up: Single-agent Behaviors Previous: Single-agent Behaviors

Peter Stone
Sun Dec 7 06:55:46 EST 1997