Trajectory tracking among landmarks and binary sensor-beams

We study a trajectory tracking problem for a mobile robot moving in the plane using combinatorial observations of the state. These observations come from crossing binary detection beams. A binary detection beam is a sensing abstraction arising from physical sensor beams or virtual beams that are derived from several sensing modalities, such as actual detection beams in the environment, changes in the angular order of landmarks around the robot, or recognizable markings in the plane. We solve the filtering problem from a geometric perspective and present its relation to linear recursive filters in control theory. Subsequently, we develop the acceleration control of the robot to track a given input trajectory, with a finite control set consisting on moving toward landmarks naturally modeling the robot as a switched dynamical system. We present experiments using an e-puck differential-drive robot, in which a useful estimate of the state for tracking is produced regardless of nontrivial uncertainty.

Authors

• Benjamín Tovar
• Todd D. Murphey

Keywords

• Robot sensing systems
• Trajectory
• Equations
• Mathematical model
• Switches
• System Dynamics
• Finite Set
• Control Theory
• State Observer
• Visual Perspective
• Filtering Problem
• Trajectory Tracking Problem
• Compassion
• Good Approximation
• Reference Frame
• Second Derivative
• Kalman Filter
• Final Time
• Visual Feedback
• Switching Time
• Update Rule
• Landmark Localization
• Linear Dynamics
• Local Frame
• Linear Quadratic Regulator
• Motion Primitives
• Local Reference Frame
• Robot Trajectory
• Global Reference Frame