An Interval Approach for Stability Analysis: Application to Sailboat Robotics

Abstract

Abstract-This paper proposes an interval based method for the validation of reliable and robust navigation rules for mobile robots. The main idea is to show that for all feasible perturbations, there exists a safe subset of the state space such that the system cannot escape. The methodology is illustrated on the line following problem of a sailboat and then validated on an actual experiment where an actual sailboat robot, named Vaimos, sails autonomously from Brest to Douarnenez (more than 100 km).

Speed Optimization Control for Wheeled Robot Navigation with Obstacle Avoidance Based on Viability Theory

“…At time k, when a proper parameter t set is given, the robot finds its own state [0, 0, 0, v (k) , ω (k) ] T is on or beyond the viability boundary (18). At this time, the robot dose not collide with the obstacle y st = ax st + c, c > 0.…”

“…At this time, the robot dose not collide with the obstacle y st = ax st + c, c > 0. But the state of the robot has collision with the viability boundary (18) in the high dimension. So we need a piecewise constant control (u 1 , u 2 ) to make the robot states back into the boundary (18).…”

“…But the state of the robot has collision with the viability boundary (18) in the high dimension. So we need a piecewise constant control (u 1 , u 2 ) to make the robot states back into the boundary (18). The admissible control range can be obtained by viability condition (9).…”

“…In order to use viability condition (9), we should change the robot model to have the boundary (18) states [x t , y t , φ t , v t ] T . The gradient of viability boundary (18) related to these states is…”

“…Because viability are based on set-valued analysis and nonsmooth analysis, it is elusive for engineering application. In [18], V stability theory which is similar to viability is used for the navigation of a sailing robot. The performance is excellent.…”