Sampling-Based Temporal Logic Path Planning

In this paper, we propose a sampling-based motion planning algorithm that finds an infinite path satisfying a Linear Temporal Logic (LTL) formula over a set of properties satisfied by some regions in a given environment. The algorithm has three main features. First, it is incremental, in the sense that the procedure for finding a satisfying path at each iteration scales only with the number of new samples generated at that iteration. Second, the underlying graph is sparse, which guarantees the low complexity of the overall method. Third, it is probabilistically complete. Examples illustrating the usefulness and the performance of the method are included.Comment: 8 pages, 4 figures; extended version of the paper presented at IROS 201

Bearing-only formation control with auxiliary distance measurements, leaders, and collision avoidance

We address the controller synthesis problem for distributed formation control. Our solution requires only relative bearing measurements (as opposed to full translations), and is based on the exact gradient of a Lyapunov function with only global minimizers (independently from the formation topology). These properties allow a simple proof of global asymptotic convergence, and extensions for including distance measurements, leaders and collision avoidance. We validate our approach through simulations and comparison with other stateof-the-art algorithms.ARL grant W911NF-08-2-0004, ARO grant W911NF-13-1-0350, ONR grants N00014-07-1-0829, N00014-14-1-0510, N00014-15-1-2115, NSF grant IIS-1426840, CNS-1521617 and United Technologies

Construction of control barrier function and C2C^2 reference trajectory for constrained attitude maneuvers

Constrained attitude maneuvers have numerous applications in robotics and aerospace. In our previous work, a general framework to this problem was proposed with resolution completeness guarantee. However, a smooth reference trajectory and a low-level safety-critical controller were lacking. In this work, we propose a novel construction of a $C^2$ continuous reference trajectory based on B\'ezier curves on $SO(3)$ that evolves within predetermined cells and eliminates previous stop-and-go behavior. Moreover, we propose a novel zeroing control barrier function on $SO(3)$ that provides a safety certificate over a set of overlapping cells on $SO(3)$ while avoiding nonsmooth analysis. The safety certificate is given as a linear constraint on the control input and implemented in real-time. A remedy is proposed to handle the states where the coefficient of the control input in the linear constraint vanishes. Numerical simulations are given to verify the advantages of the proposed method.Comment: Extended version of an accepted paper at IEEE CDC 202

On the Coordinated Navigation of Multiple Independent Disk-Shaped Robots

This paper addresses the coordinated navigation of multiple independently actuated disk-shaped robots - all placed within the same disk-shaped workspace. Assuming perfect sensing, shared centralized communications and computation, as well as perfect actuation, we encode complete information about the goal, obstacles and workspace boundary using an artificial potential function over the cross product space of the robots’ simultaneous configurations. The closed-loop dynamics governing the motion of each robot take the form of the appropriate projection of the gradient of this function. We show, with some reasonable restrictions on the allowable goal positions, that this function is an essential navigation function - a special type of artificial potential function that is ensured of connecting the kinematic planning with the dynamic execution in a manner that guarantees collision-free navigation of each robot to its destination from almost all initial free placements. We summarize the results of an extensive simulation study investigating such practical issues as average resulting trajectory length and robustness against simulated sensor noise