Ömür Arslan

Ömür Arslan, Nikolay Atanasov

Safe autonomy is a critical requirement and a key enabler for robots to operate safely in unstructured complex environments. Control barrier functions and safe motion corridors are two widely used but technically distinct safety methods, functional and geometric, respectively, for safe motion planning and control. Control barrier functions are applied to the safety filtering of control inputs to limit the decay rate of system safety, whereas safe motion corridors are geometrically constructed to define a local safe zone around the system state for use in motion optimization and reference-governor design. This paper introduces a new notion of control barrier corridors, which unifies these two approaches by converting control barrier functions into local safe goal regions for reference goal selection in feedback control systems. We show, with examples on fully actuated systems, kinematic unicycles, and linear output regulation systems, that individual state safety can be extended locally over control barrier corridors for convex barrier functions, provided the control convergence rate matches the barrier decay rate, highlighting a trade-off between safety and reactiveness. Such safe control barrier corridors enable safely reachable persistent goal selection over continuously changing barrier corridors during system motion, which we demonstrate for verifiably safe and persistent path following in autonomous exploration of unknown environments.

Aykut İşleyen, Nathan van de Wouw, Ömür Arslan

Safe navigation around obstacles is a fundamental challenge for highly dynamic robots. The state-of-the-art approach for adapting simple reference path planners to complex robot dynamics using trajectory optimization and tracking control is brittle and requires significant replanning cycles. In this paper, we introduce a novel feedback motion planning framework that extends the applicability of low-order (e.g. position-/velocity-controlled) reference motion planners to high-order (e.g., acceleration-/jerk-controlled) robot models using motion prediction and reference governors. We use predicted robot motion range for safety assessment and establish a bidirectional interface between high-level planning and low-level control via a reference governor. We describe the generic fundamental building blocks of our feedback motion planning framework and give specific example constructions for motion control, prediction, and reference planning. We prove the correctness of our planning framework and demonstrate its performance in numerical simulations. We conclude that accurate motion prediction is crucial for closing the gap between high-level planning and low-level control.

Ömür Arslan, Aron Tiemessen

As a parametric polynomial curve family, Bézier curves are widely used in safe and smooth motion design of intelligent robotic systems from flying drones to autonomous vehicles to robotic manipulators. In such motion planning settings, the critical features of high-order Bézier curves such as curve length, distance-to-collision, maximum curvature/velocity/acceleration are either numerically computed at a high computational cost or inexactly approximated by discrete samples. To address these issues, in this paper we present a novel computationally efficient approach for adaptive approximation of high-order Bézier curves by multiple low-order Bézier segments at any desired level of accuracy that is specified in terms of a Bézier metric. Accordingly, we introduce a new Bézier degree reduction method, called parameterwise matching reduction, that approximates Bézier curves more accurately compared to the standard least squares and Taylor reduction methods. We also propose a new Bézier metric, called the maximum control-point distance, that can be computed analytically, has a strong equivalence relation with other existing Bézier metrics, and defines a geometric relative bound between Bézier curves. We provide extensive numerical evidence to demonstrate the effectiveness of our proposed Bézier approximation approach. As a rule of thumb, based on the degree-one matching reduction error, we conclude that an $n^\text{th}$-order Bézier curve can be accurately approximated by $3(n-1)$ quadratic and $6(n-1)$ linear Bézier segments, which is fundamental for Bézier discretization.