Adaptive planar curve tracking control and robustness analysis under state constraints and unknown curvature

Abstract

We provide adaptive controllers for curve tracking in the plane, under unknown curvatures and control uncertainty, which is a central problem in robotics. The system dynamics include a nonlinear dependence on the curvature, and are coupled with an estimator for the unknown curvature, to form the augmented error dynamics. We prove input-to-state stability of the augmented error dynamics with respect to an input that is represented by additive uncertainty on the control, under polygonal state constraints and under suitable known bounds on the curvature and on the control uncertainty. When the uncertainty is zero, this gives tracking of the curve and convergence of the curvature estimate to the unknown curvature. Our curvature identification result is a significant improvement over earlier results, which do not ensure parameter identification, or which identify the control gain but not the curvature.

Tracking and parameter identification for model reference adaptive control

“…If in addition B is C 1 with each (d∕dt)b j also bounded and J = I p×p , then we can apply the method from Lemma 1 with G(t,  0 (q(t)) + q r (t)) and in (26) replaced by G(t,  0 (q(t)) + q r (t))B (t) and respectively, and with row i G(s, q r (s)) in the PE condition (22) replaced by row i G(s, q r (s))B (s) for each i, which makes it possible to identify the unknown weights i , for any number L of basis functions. This contrasts with Section 7 of the work of Malisoff et al 18 where the unknown time-varying parameter was a linear combination of time-varying basis functions with constant weights, but where it was only possible to identify the unknown weights when the number of basis functions was L = 1.…”

“…In its basic form, the PE condition is the requirement that the reference trajectory is such that the regressor satisfies a PE inequality when evaluated along the given reference trajectory 17 ; see Section 4.1 for our relaxed PE condition. For two-dimensional curve tracking for gyroscopic models, our works 18,19 proved globally asymptotically stable tracking and parameter identification results using a novel barrier Lyapunov function approach that ensured robustness with respect to actuator uncertainties under polygonal state constraints; see also the work of Malisoff and Zhang 20 for three-dimensional (3D) analogs. The adaptive control work 21 provides time-varying gains to ensure exponential convergence for some nonlinear systems and to ensure convergence of the parameter estimates to a constant vector (which might not be the true value of the unknown parameter vector).…”

Coordinate-free Isoline Tracking in Unknown 2-D Scalar Fields

“…In this work, we are interested in the scenario that both the concentration distribution F (p) and the GPS position of the sensing robot are unknown. Moreover, we cannot measure a continuum of the scalar field, which implies that the gradientbased methods [1], [9], [16] cannot be applied here.…”

“…The isoline tracking refers to the tactic that a mobile robot reaches and then tracks a predefined contour in a scalar field, which is widely applied in the areas of detection, exploration, monitoring, and etc. In the literature, it is also named as curve tracking [1], boundary tracking [2], [3], level set tracking [4]. In fact, it covers the celebrated target circumnavigation as a special case [5]- [7].…”

Analysis of path following and obstacle avoidance for multiple wheeled robots in a shared workspace

“…However, in real world scenarios, assuming that the environment is static is unrealistic in most cases, and the environment should more realistically be modelled as dynamic: therefore, in the field of mobile robotics, the problem of safe navigation in dynamic environments is one of the most important challenges to be addressed [9,10]. The challenge becomes more complex and tough when the information about the dynamic obstacles and the environment is not available, even if such information is often assumed to be present in many research works [11,12,13,14,15]. This information may include the complete map of the environments, the position and the orientation of the obstacles in the map, the nature of the obstacles (whether the shape of the obstacles is constant or varies over time) and the motion of the obstacles (whether the obstacle is moving with a constant or time-varying velocity).…”