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.

Zhichao Li, Omur Arslan, Nikolay Atanasov

This paper considers the problem of fast and safe autonomous navigation in partially known environments. Our main contribution is a control policy design based on ellipsoidal trajectory bounds obtained from a quadratic state-dependent distance metric. The ellipsoidal bounds are used to embed directional preference in the control design, leading to system behavior that is adapted to the local environment geometry, carefully considering medial obstacles while paying less attention to lateral ones. We use a virtual reference governor system to adaptively follow a desired navigation path, slowing down when system safety may be violated and speeding up otherwise. The resulting controller is able to navigate complex environments faster than common Euclidean-norm and Lyapunov-function-based designs, while retaining stability and collision avoidance guarantees.

Jinwook Huh, Omur Arslan, Daniel D. Lee

In this paper, we introduce a new probabilistically safe local steering primitive for sampling-based motion planning in complex high-dimensional configuration spaces. Our local steering procedure is based on a new notion of a convex probabilistically safe corridor that is constructed around a configuration using tangent hyperplanes of confidence ellipsoids of Gaussian mixture models learned from prior collision history. Accordingly, we propose to expand a random motion planning graph towards a sample goal using its projection onto probabilistically safe corridors, which efficiently exploits the local geometry of configuration spaces for selecting proper steering direction and adapting steering stepsize. We observe that the proposed local steering procedure generates effective steering motion around difficult regions of configuration spaces, such as narrow passages, while minimizing collision likelihood. We evaluate the proposed steering method with randomized motion planners in a number of planning scenarios, both in simulation and on a physical 7DoF robot arm, demonstrating the effectiveness of our safety guided local planner over the standard straight-line planner.

Vasileios Vasilopoulos, William Vega-Brown, Omur Arslan et al.

This paper considers the problem of completing assemblies of passive objects in nonconvex environments, cluttered with convex obstacles of unknown position, shape and size that satisfy a specific separation assumption. A differential drive robot equipped with a gripper and a LIDAR sensor, capable of perceiving its environment only locally, is used to position the passive objects in a desired configuration. The method combines the virtues of a deliberative planner generating high-level, symbolic commands, with the formal guarantees of convergence and obstacle avoidance of a reactive planner that requires little onboard computation and is used online. The validity of the proposed method is verified both with formal proofs and numerical simulations.

Omur Arslan, Daniel E. Koditschek

In distributed mobile sensing applications, networks of agents that are heterogeneous respecting both actuation as well as body and sensory footprint are often modelled by recourse to power diagrams --- generalized Voronoi diagrams with additive weights. In this paper we adapt the body power diagram to introduce its "free subdiagram," generating a vector field planner that solves the combined sensory coverage and collision avoidance problem via continuous evaluation of an associated constrained optimization problem. We propose practical extensions (a heuristic congestion manager that speeds convergence and a lift of the point particle controller to the more practical differential drive kinematics) that maintain the convergence and collision guarantees.

Omur Arslan, Dan P. Guralnik, Daniel E. Koditschek

We introduce the use of hierarchical clustering for relaxed, deterministic coordination and control of multiple robots. Traditionally an unsupervised learning method, hierarchical clustering offers a formalism for identifying and representing spatially cohesive and segregated robot groups at different resolutions by relating the continuous space of configurations to the combinatorial space of trees. We formalize and exploit this relation, developing computationally effective reactive algorithms for navigating through the combinatorial space in concert with geometric realizations for a particular choice of hierarchical clustering method. These constructions yield computationally effective vector field planners for both hierarchically invariant as well as transitional navigation in the configuration space. We apply these methods to the centralized coordination and control of $n$ perfectly sensed and actuated Euclidean spheres in a $d$-dimensional ambient space (for arbitrary $n$ and $d$). Given a desired configuration supporting a desired hierarchy, we construct a hybrid controller which is quadratic in $n$ and algebraic in $d$ and prove that its execution brings all but a measure zero set of initial configurations to the desired goal with the guarantee of no collisions along the way.

Omur Arslan, Daniel E. Koditschek

We propose a new anytime hierarchical clustering method that iteratively transforms an arbitrary initial hierarchy on the configuration of measurements along a sequence of trees we prove for a fixed data set must terminate in a chain of nested partitions that satisfies a natural homogeneity requirement. Each recursive step re-edits the tree so as to improve a local measure of cluster homogeneity that is compatible with a number of commonly used (e.g., single, average, complete) linkage functions. As an alternative to the standard batch algorithms, we present numerical evidence to suggest that appropriate adaptations of this method can yield decentralized, scalable algorithms suitable for distributed/parallel computation of clustering hierarchies and online tracking of clustering trees applicable to large, dynamically changing databases and anomaly detection.