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Chapter 49 — Modeling and Control of Wheeled Mobile Robots

Claude Samson, Pascal Morin and Roland Lenain

This chaptermay be seen as a follow up to Chap. 24, devoted to the classification and modeling of basic wheeled mobile robot (WMR) structures, and a natural complement to Chap. 47, which surveys motion planning methods for WMRs. A typical output of these methods is a feasible (or admissible) reference state trajectory for a given mobile robot, and a question which then arises is how to make the physical mobile robot track this reference trajectory via the control of the actuators with which the vehicle is equipped. The object of the present chapter is to bring elements of the answer to this question based on simple and effective control strategies.

The chapter is organized as follows. Section 49.2 is devoted to the choice of controlmodels and the determination of modeling equations associated with the path-following control problem. In Sect. 49.3, the path following and trajectory stabilization problems are addressed in the simplest case when no requirement is made on the robot orientation (i. e., position control). In Sect. 49.4 the same problems are revisited for the control of both position and orientation. The previously mentionned sections consider an ideal robot satisfying the rolling-without-sliding assumption. In Sect. 49.5, we relax this assumption in order to take into account nonideal wheel-ground contact. This is especially important for field-robotics applications and the proposed results are validated through full scale experiments on natural terrain. Finally, a few complementary issues on the feedback control of mobile robots are briefly discussed in the concluding Sect. 49.6, with a list of commented references for further reading on WMRs motion control.

Tracking of an admissible trajectory with a car-like vehicle

Author  Pascal Morin, Claude Samson

Video ID : 181

This is an animation showing the tracking of an admissible reference trajectory (red vehicle) with a car-like vehicle (green vehicle). The robot is able to ensure asymptotic convergence of the tracking error to zero, based on the feedback controller presented in Chap. 49.4, Springer Handbook of Robotics, 2nd edn (2016).

Tracking of arbitrary trajectories with a truck-like vehicle

Author  Pascal Morin, Claude Samson

Video ID : 182

This is an animation showing the application of the transverse function approach for the tracking of an omnidirectional frame (in blue) with a nonholonomic truck-like robot. The robot is able to maintain bounded, tracking errors in both position and orientation despite the motion of the blue frame in arbitrary directions. The animation illustrates results presented in Chap. 49.4, Springer Handbook of Robotics, 2nd edn (2016).

Tracking of an omnidirectional frame with a unicycle-like robot

Author  Guillaume Artus, Pascal Morin, Claude Samson

Video ID : 243

This video shows an experiment performed in 2005 with a unicyle-like robot. A video camera mounted at the top of a robotic arm enabled estimation of the 2-D pose (position/orientation) of the robot with respect to a visual target consisting of three white bars. These bars materialized an omnidirectional moving frame. The experiment demonstrated the capacity of the nonholonomic robot to track in both position and orientation this ominidirectional frame, based on the transverse function control approach.

Mobile robot control in off-road conditions and under high dynamics

Author  Roland Lenain

Video ID : 435

This video illustrates the motion-control strategy detailed in Chap. 49, Springer Handbook of Robotics, 2nd edn (2016), when the ideal rolling-without-sliding conditions are not met. In the two segments, the robot follows a previously recorded trajectory, using RTK GPS. The first segment illustrates the capabilities on uneven ground at low speed, while the second shows results at high speed. Accuracy within a few centimeters is obtained thanks to adaptive and predictive approaches, whereas accuracy close to 1 m in the first case and 5 m for the second case are observed using the rolling-without-sliding assumption.