Homography-Based Control Scheme for Mobile Robots With Nonholonomic and Field-of-View Constraints

Abstract

Abstract-In this paper, we present a visual servo controller that effects optimal paths for a nonholonomic, differential drive robot with field-of-view constraints imposed by the vision system. The control scheme relies on the computation of homographies between current and goal images, but unlike previous homography-based methods, it does not use the homography to compute estimates of pose parameters. Instead, the control laws are expressed directly in terms of individual entries in the homography matrix. In particular, we develop individual control laws for the three path classes that define the language of optimal paths: rotations, straight-line segments and logarithmic spirals. These control laws, as well as switching conditions that define how to sequence path segments, are defined in terms of the entries of homography matrices. The selection of the corresponding control law requires the homography decomposition before starting the navigation. We provide a controllability and stability analysis for our system, and give experimental results.

Direct homography control for highly maneuverable vehicles

“…Second the calculation of v x , v y , andα by different formulas and by using all four homography entries increases the robustness. Moreover, Equation (10) shows clearly that even with an unknown distance d from the goal pose to the feature plane P the direction of the translation is computable up to scale, whereas the rotation, as expected, is completely unaffected. The mapping K of the current states x to the homography matrix H can be deduced directly from (7) and has to be examined for the stability evaluation in the next chapter.…”

“…Hence, the control task itself is then described in Cartesian coordinates. A control scheme that tries to completely relinquish Cartesian variables in the control law is proposed in [10], where they try to control the entries of the homography matrix directly to increase the robustness and decrease the computational effort. This is not possible for all motion primitives and hence a decomposition of the homography matrix has to be executed for certain trajectories.…”

Model predictive cooperative localization control of multiple UAVs using potential function sensor constraints

“…For traditional backstepping controllers, sensor perception limits are addressed by switching the robot's formation control according to the compliance with the sensor constraints (Wang et al 2015). Another approach is to compute the optimal boundary trajectories to satisfy the sensor constraint and track these, as shown for non-holonomic robots in Bhattacharya and Hutchinson (2006) or for visual servoing in Bhattacharya et al (2007) and López-Nicolás et al (2010). Nevertheless, the task dependency of the control laws makes it challenging to formulate control laws for complex scenarios with constraints.…”

Vision Restricted Path Planning and Control for Underactuated Vehicles

“…Maniatopoulos et al (2013) proposes a control law that guides the vehicle towards a desired point by using model predictive control (MPC). In López-Nicolás et al (2010); Salaris et al (2011) different control schemes are proposed to follow the optimal path with an underactuated robot that can turn on the spot.…”