Probabilistic Collision Constraint for Motion Planning in Dynamic Environments

Online generation of collision free trajectories is of prime importance for autonomous navigation. Dynamic environments, robot motion and sensing uncertainties adds further challenges to collision avoidance systems. This paper presents an approach for collision avoidance in dynamic environments, incorporating robot and obstacle state uncertainties. We derive a tight upper bound for collision probability between robot and obstacle and formulate it as a motion planning constraint which is solvable in real time. The proposed approach is tested in simulation considering mobile robots as well as quadrotors to demonstrate that successful collision avoidance is achieved in real time application. We also provide a comparison of our approach with several state-of-the-art methods.Comment: Accepted for presentation at the 16th International Conference on Intelligent Autonomous Systems (IAS-16

Particle Computation: Complexity, Algorithms, and Logic

We investigate algorithmic control of a large swarm of mobile particles (such as robots, sensors, or building material) that move in a 2D workspace using a global input signal (such as gravity or a magnetic field). We show that a maze of obstacles to the environment can be used to create complex systems. We provide a wide range of results for a wide range of questions. These can be subdivided into external algorithmic problems, in which particle configurations serve as input for computations that are performed elsewhere, and internal logic problems, in which the particle configurations themselves are used for carrying out computations. For external algorithms, we give both negative and positive results. If we are given a set of stationary obstacles, we prove that it is NP-hard to decide whether a given initial configuration of unit-sized particles can be transformed into a desired target configuration. Moreover, we show that finding a control sequence of minimum length is PSPACE-complete. We also work on the inverse problem, providing constructive algorithms to design workspaces that efficiently implement arbitrary permutations between different configurations. For internal logic, we investigate how arbitrary computations can be implemented. We demonstrate how to encode dual-rail logic to build a universal logic gate that concurrently evaluates and, nand, nor, and or operations. Using many of these gates and appropriate interconnects, we can evaluate any logical expression. However, we establish that simulating the full range of complex interactions present in arbitrary digital circuits encounters a fundamental difficulty: a fan-out gate cannot be generated. We resolve this missing component with the help of 2x1 particles, which can create fan-out gates that produce multiple copies of the inputs. Using these gates we provide rules for replicating arbitrary digital circuits.Comment: 27 pages, 19 figures, full version that combines three previous conference article

Minimum-Energy Exploration and Coverage for Robotic Systems

This dissertation is concerned with the question of autonomously and efficiently exploring three-dimensional environments. Hence, three robotics problems are studied in this work: the motion planning problem, the coverage problem and the exploration problem. The work provides a better understanding of motion and exploration problems with regard to their mathematical formulation and computational complexity, and proposes solutions in the form of algorithms capable of being implemented on a wide range of robotic systems.Because robots generally operate on a limited power source, the primary focus is on minimizing energy while moving or navigating in the environment. Many approaches address motion planning in the literature, however few attempt to provide a motion that aims at reducing the amount of energy expended during that process. We present a new approach, we call integral-squared torque approximation, that can be integrated with existing motion planners to find low-energy and collision-free paths in the robot\u27s configuration space.The robotics coverage problem has many real-world applications such as removing landmines or surveilling an area. We prove that this problem is inherently difficult to solve in its general case, and we provide an approach that is shown to be probabilistically complete, and that aims at minimizing a cost function (such as energy.) The remainder of the dissertation focuses on minimum-energy exploration, and offers a novel formulation for the problem. The formulation can be directly applied to compare exploration algorithms. In addition, an approach that aims at reducing energy during the exploration process is presented, and is shown through simulation to perform better than existing algorithms

Multi-Robot Exploration of Underwater Structures

This paper discusses a novel approach for the exploration of an underwater structure. A team of robots splits into two roles: certain robots approach the structure collecting detailed information (proximal observers) while the rest (distal observers) keep a distance providing an overview of the mission and assist in the localization of the proximal observers via a Cooperative Localization framework. Proximal observers utilize a novel robust switching model-based/visual-inertial odometry to overcome vision-based localization failures. Exploration strategies for the proximal and the distal observer are discussed.publishedVersio