Motion-Planning and Control of Autonomous Vehicles to Satisfy Linear Temporal Logic Specifications

Motion-planning is an essential component of autonomous aerial and terrestrial vehicles. The canonical Motion-planning problem, which is widely studied in the literature, is of planning point-to-point motion while avoiding obstacles. However, the desired degree of vehicular autonomy has steadily risen, and has consequently led to motion-planning problems where a vehicle is required to accomplish a high-level intelligent task, rather than simply move between two points. One way of specifying such intelligent tasks is via linear temporal logic (LTL) formulae. LTL is a formal logic system that includes temporal operators such as always, eventually, and until besides the usual logical operators. For autonomous vehicles, LTL formulae can concisely express tasks such as persistent surveillance, safety requirements, and temporal orders of visits to multiple locations. Recent control theoretic literature has discussed the generation of reference trajectories and/or the synthesis of feedback control laws to enable a vehicle to move in manners that satisfy LTL specifications. A crucial step in such synthesis is the generation of a so-called discrete abstraction of a vehicle kinematic/dynamic model. Typical techniques of generating a discrete abstraction require strong assumptions on controllability and/or linearity. This dissertation discusses fast motion-planning and control techniques to satisfy LTL specifications for vehicle models with nonholonomic kinematic constraints, which do not satisfy the aforesaid assumptions. The main contributions of this dissertation are as follows. First, we present a new technique for constructing discrete abstractions of a Dubins vehicle model (namely, a vehicle that moves forward at a constant speed with a minimum turning radius). This technique relies on the so-called method of lifted graphs and precomputed reachable set calculations. Using this technique, we provide an algorithm to generate vehicle reference trajectories satisfying LTL specifications without requiring complete controllability in the presence of workspace constraints, and without requiring linearity or linearization of the vehicle model. Second, we present a technique for centralized motion-planning for a team of vehicles to collaboratively satisfy a common LTL specification. This technique is also based on the method of lifted graphs. Third, we present an incremental version of the proposed motion-planning techniques, which has an “anytime property. This property means that a feasible solution is computed quickly, and the iterative updates are made to this solution with a guarantee of convergence to an optimal solution. This version is suited for real-time implementation, where a hard bound on the computation time is imposed. Finally, we present a randomized sampling-based technique for generating reference trajectories that satisfy given LTL specifications. This technique is an alternative to the aforesaid technique based on lifted graphs. We illustrate the proposed techniques using numerical simulation examples. We demonstrate the superiority of the proposed techniques in comparison to the existing literature in terms of computational time and memory requirements

Geometric Approximations and their Application to Motion Planning

Geometric approximation methods are a preferred solution to handle complexities (such as a large volume or complex features such as concavities) in geometric objects or environments containing them. Complexities often pose a computational bottleneck for applications such as motion planning. Exact resolution of these complexities might introduce other complexities such as unmanageable number of components. Hence, approximation methods provide a way to handle these complexities in a manageable state by trading off some accuracy. In this dissertation, two novel geometric approximation methods are studied: aggregation hierarchy and shape primitive skeleton. The aggregation hierarchy is a hierarchical clustering of polygonal or polyhedral objects. The shape primitive skeleton provides an approximation of bounded space as a skeleton of shape primitives. These methods are further applied to improve the performance of motion planning applications. We evaluate the methods in environments with 2D and 3D objects. The aggregation hierarchy groups nearby objects into individual objects. The hierarchy is created by varying the distance threshold that determines which objects are nearby. This creates levels of detail of the environment. The hierarchy of the obstacle space is then used to create a decom-position of the complementary space (i.e, free space) into a set of sampling regions to improve the efficiency and accuracy of the sampling operation of the sampling based motion planners. Our results show that the method can improve the efficiency (10 − 70% of planning time) of sampling based motion planning algorithms. The shape primitive skeleton inscribes a set of shape primitives (e.g., sphere, boxes) inside a bounded space such that they represent the skeleton or the connectivity of the space. We apply the shape primitive skeletons of the free space and obstacle space in motion planning problems to improve the collision detection operation. Our results also show the use of shape primitive skeleton in both spaces improves the performance of collision detectors (by 20 − 70% of collision detection time) used in motion planning algorithms. In summary, this dissertation evaluates how geometric approximation methods can be applied to improve the performance of motion planning methods, especially, sampling based motion planning method

A heuristic approach for path planning for redundant robots

A new method to solve the trajectory generation for a redundant manipulator is proposed. It avoids traditional computationally intensive methods by relying on the human experience; The proposed method uses a fuzzy logic controller to generate the magnitude of the angles needed to move the end effector to the next target point. The inputs to the controller are the desired displacement of the end effector and the elements of the jacobian matrix that correspond to the considered joint, while the output is the angle magnitude of the joint needed to reach the target point; An algorithm is used to determine the sign of the output from the fuzzy logic controller. Inverse kinematics is used to bring the end-effector to the target point; Several fuzzy logic controllers combined with heuristic algorithms are used to avoid the obstacles in the workspace and to avoid self collision of the links

Clustering-Based Robot Navigation and Control

In robotics, it is essential to model and understand the topologies of configuration spaces in order to design provably correct motion planners. The common practice in motion planning for modelling configuration spaces requires either a global, explicit representation of a configuration space in terms of standard geometric and topological models, or an asymptotically dense collection of sample configurations connected by simple paths, capturing the connectivity of the underlying space. This dissertation introduces the use of clustering for closing the gap between these two complementary approaches. Traditionally an unsupervised learning method, clustering offers automated tools to discover hidden intrinsic structures in generally complex-shaped and high-dimensional configuration spaces of robotic systems. We demonstrate some potential applications of such clustering tools to the problem of feedback motion planning and control. The first part of the dissertation presents the use of hierarchical clustering for relaxed, deterministic coordination and control of multiple robots. We reinterpret this classical method for unsupervised learning as an abstract 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. Based on this new abstraction and a careful topological characterization of the associated hierarchical structure, a provably correct, computationally efficient hierarchical navigation framework is proposed for collision-free coordinated motion design towards a designated multirobot configuration via a sequence of hierarchy-preserving local controllers. The second part of the dissertation introduces a new, robot-centric application of Voronoi diagrams to identify a collision-free neighborhood of a robot configuration that captures the local geometric structure of a configuration space around the robot’s instantaneous position. Based on robot-centric Voronoi diagrams, a provably correct, collision-free coverage and congestion control algorithm is proposed for distributed mobile sensing applications of heterogeneous disk-shaped robots; and a sensor-based reactive navigation algorithm is proposed for exact navigation of a disk-shaped robot in forest-like cluttered environments. These results strongly suggest that clustering is, indeed, an effective approach for automatically extracting intrinsic structures in configuration spaces and that it might play a key role in the design of computationally efficient, provably correct motion planners in complex, high-dimensional configuration spaces

PMK : a knowledge processing framework for autonomous robotics perception and manipulation

Autonomous indoor service robots are supposed to accomplish tasks, like serve a cup, which involve manipulation actions. Particularly, for complex manipulation tasks which are subject to geometric constraints, spatial information and a rich semantic knowledge about objects, types, and functionality are required, together with the way in which these objects can be manipulated. In this line, this paper presents an ontological-based reasoning framework called Perception and Manipulation Knowledge (PMK) that includes: (1) the modeling of the environment in a standardized way to provide common vocabularies for information exchange in human-robot or robot-robot collaboration, (2) a sensory module to perceive the objects in the environment and assert the ontological knowledge, (3) an evaluation-based analysis of the situation of the objects in the environment, in order to enhance the planning of manipulation tasks. The paper describes the concepts and the implementation of PMK, and presents an example demonstrating the range of information the framework can provide for autonomous robots.Peer ReviewedPostprint (published version