Jonathan A. DeCastro

A Recursive Receding Horizon Planning for Unmanned Vehicles

This paper proposes a recursive receding horizon path planning algorithm for unmanned vehicles in nonuniform environments. In the proposed algorithm, the map is described by grids in which nodes are defined on corners of grids. The planning algorithm considers the map as four areas, namely, implementation, observation, explored, and unknown. The Implementation area is a subset of the Observation area, whereas the Explored area is the union of all the previous Observation areas. The path is planned with a receding horizon planning strategy to generate waypoints and in-between map updates. When a new map update occurs, the path is replanned within the current Observation area if necessary. If no such path exists, the search is extended to the Explored area. Paths can be planned by recursively searching available nodes inside the Explored area that can be connected to available nodes on the boundary of the Explored area. A robot platform is employed to conduct a series of experiments in a laboratory environment to verify the proposed path planning algorithm.

Synthesis of nonlinear continuous controllers for verifiably correct high-level, reactive behaviors

Planning robotic missions in environments shared by humans involves designing controllers that are reactive to the environment yet able to fulfill a complex high-level task. This paper introduces a new method for designing low-level controllers for nonlinear robotic platforms based on a discrete-state high-level controller encoding the behaviors of a reactive task specification. We build our method upon a new type of trajectory constraint which we introduce in this paper, reactive composition, to provide the guarantee that any high-level reactive behavior may be fulfilled at any moment during the continuous execution. We generate pre-computed motion controllers in a piecewise manner by adopting a sample-based synthesis method that associates a certificate of invariance with each controller in the sample set. As a demonstration of our approach, we simulate different robotic platforms executing complex tasks in a variety of environments.

Guaranteeing reactive high-level behaviors for robots with complex dynamics

Applying correct-by-construction planning techniques to robots with complex nonlinear dynamics requires new formal analysis methods which guarantee that the requested behaviors can be achieved in the continuous space. In this paper, we construct low-level controllers that ensure the execution of a high-level mission plan. Controllers are generated using trajectory-based verification to produce a set of robust reach tubes which strictly guarantee that the required motions achieve the desired task specification. Reach tubes, computed here by solving a series of sum-of-squares optimization problems, are composed in such a way that all trajectories ensure correct highlevel behaviors. We illustrate the new method using an input-limited unicycle robot satisfying task specifications expressed in linear temporal logic.

Collision-Free Reactive Mission and Motion Planning for Multi-robot Systems

This paper describes a holistic method for automatically synthesizing controllers for a team of robots operating in an environment shared with other agents. The proposed approach builds on recent advances in Reactive Mission Planning using Linear Temporal Logic, and Local Motion Planning using convex optimization. A local planner enforces the dynamic constraints of the robot and guarantees collision avoidance in 2D and 3D workspaces. A reactive mission planner takes a high-level specification that captures complex motion sequencing, and generates a correct-by-construction controller guaranteed to achieve the specified behavior and be reactive to sensor events. If there is no controller that fulfills the specification because of possible deadlock in the local planner, a minimal set of human-readable assumptions is generated as a certificate of the conditions on deadlock where the task is guaranteed. This is truly a synergistic method: the low-level motion planner enables scalability of the high-level plan synthesis with respect to dynamic obstacles, and the high-level mission planner enforces correctness of the low-level motion. We provide formal guarantees for our approach and demonstrate it via physical experiments with ground robots and simulations with a team of quadrotors.

Nonlinear Controller Synthesis and Automatic Workspace Partitioning for Reactive High-Level Behaviors

Motivated by the provably-correct execution of complex reactive tasks for robots with nonlinear, under-actuated dynamics, our focus is on the synthesis of a library of low-level controllers that implements the behaviors of a high-level controller. The synthesized controllers should allow the robot to react to its environment whenever dynamically feasible given the geometry of the workspace. For any behaviors that cannot guarantee the task given the dynamics, such behaviors should be transformed into dynamically-informative revisions to the high-level task. We therefore propose a framework for synthesizing such low-level controllers and, moreover, offer an approach for re-partitioning and abstracting the system based on the synthesized controller library. We accomplish these goals by introducing a synthesis approach that we call conforming funnels, in which controllers are synthesized with respect to the given high-level behaviors, the geometrical constraints of the workspace, and a robot dynamics model. Our approach computes controllers using a verification approach that optimizes over a wide range of possible controllers to guarantee the geometrical constraints are satisfied. We also devise an algorithm that uses the controllers to re-partition the workspace and automatically adapt the high-level specification with a new discrete abstraction generated on these new partitions. We demonstrate the controllers generated by our synthesis framework in an experimental setting with a KUKA youBot executing a box transportation task.

Dynamics-driven adaptive abstraction for reactive high-level mission and motion planning

We present a new framework for reactive synthesis that considers the dynamics of the robot when synthesizing correct-by-construction controllers for nonlinear systems. Many high-level synthesis approaches employ discrete abstractions to reason about the dynamics of the continuous system in a simplified manner. Often, these abstractions are expensive to compute. We circumvent the need to have detailed abstractions for nonlinear systems by proposing a framework for adapting abstractions based on partial solutions to the low-level controller synthesis problem. The contribution of this paper is a reactive synthesis algorithm that makes use of our adaptation procedure to update the high-level strategy each time the non-deterministic discrete abstraction is modified. We combine this with a verified low-level controller synthesis scheme capable of automatically synthesizing controllers for a wide class of nonlinear systems. This novel synthesis framework is demonstrated on a dynamical robot executing an autonomous inspection task.

Automated generation of dynamics-based runtime certificates for high-level control

This paper addresses the problem of synthesizing controllers for reactive missions carried out by dynamical systems operating in environments of known physical geometry but consisting of uncontrolled elements that the system must react to at execution time. Such problems have value in semi-structured industrial automation settings, especially those in which robots must behave collaboratively yet safely with their human counterparts. The proposed synthesis framework addresses cases where there exists no satisfying controller for the mission, given the dynamical system and the environment’s assumed behaviors. We introduce an approach that leverages information about an abstraction of the dynamical system to automatically generate a concise set of revisions to such specifications. We provide a graphical visualization tool as a design aid, allowing the revisions to be conveyed to the user interactively and added to the specification at the user’s discretion. Any accepted statements become certificates that, if satisfied at runtime, provide guarantees for the current mission on the given dynamics. Our approach is cast into a general framework that works with various discrete representations (i.e. abstractions) of the system dynamics. We present case studies that illustrate application of our approach to controller synthesis for two example robotic missions employing different abstractions of the system.

Reactive mission and motion planning with deadlock resolution avoiding dynamic obstacles

In the near future mobile robots, such as personal robots or mobile manipulators, will share the workspace with other robots and humans. We present a method for mission and motion planning that applies to small teams of robots performing a task in an environment with moving obstacles, such as humans. Given a mission specification written in linear temporal logic, such as patrolling a set of rooms, we synthesize an automaton from which the robots can extract valid strategies. This centralized automaton is executed by the robots in the team at runtime, and in conjunction with a distributed motion planner that guarantees avoidance of moving obstacles. Our contribution is a correct-by-construction synthesis approach to multi-robot mission planning that guarantees collision avoidance with respect to moving obstacles, guarantees satisfaction of the mission specification and resolves encountered deadlocks, where a moving obstacle blocks the robot temporally. Our method provides conditions under which deadlock will be avoided by identifying environment behaviors that, when encountered at runtime, may prevent the robot team from achieving its goals. In particular, (1) it identifies deadlock conditions; (2) it is able to check whether they can be resolved; and (3) the robots implement the deadlock resolution policy locally in a distributed manner. The approach is capable of synthesizing and executing plans even with a high density of dynamic obstacles. In contrast to many existing approaches to mission and motion planning, it is scalable with the number of moving obstacles. We demonstrate the approach in physical experiments with walking humanoids moving in 2D environments and in simulation with aerial vehicles (quadrotors) navigating in 2D and 3D environments.