Decentralized Motion Planning with Collision Avoidance for a Team of UAVs under High Level Goals

This paper addresses the motion planning problem for a team of aerial agents under high level goals. We propose a hybrid control strategy that guarantees the accomplishment of each agent's local goal specification, which is given as a temporal logic formula, while guaranteeing inter-agent collision avoidance. In particular, by defining 3-D spheres that bound the agents' volume, we extend previous work on decentralized navigation functions and propose control laws that navigate the agents among predefined regions of interest of the workspace while avoiding collision with each other. This allows us to abstract the motion of the agents as finite transition systems and, by employing standard formal verification techniques, to derive a high-level control algorithm that satisfies the agents' specifications. Simulation and experimental results with quadrotors verify the validity of the proposed method.Comment: Submitted to the IEEE International Conference on Robotics and Automation (ICRA), Singapore, 201

Optimal Control of MDPs with Temporal Logic Constraints

In this paper, we focus on formal synthesis of control policies for finite Markov decision processes with non-negative real-valued costs. We develop an algorithm to automatically generate a policy that guarantees the satisfaction of a correctness specification expressed as a formula of Linear Temporal Logic, while at the same time minimizing the expected average cost between two consecutive satisfactions of a desired property. The existing solutions to this problem are sub-optimal. By leveraging ideas from automata-based model checking and game theory, we provide an optimal solution. We demonstrate the approach on an illustrative example.Comment: Technical report accompanying the CDC 2013 pape

Optimal Receding Horizon Control for Finite Deterministic Systems with Temporal Logic Constraints

In this paper, we develop a provably correct optimal control strategy for a finite deterministic transition system. By assuming that penalties with known probabilities of occurrence and dynamics can be sensed locally at the states of the system, we derive a receding horizon strategy that minimizes the expected average cumulative penalty incurred between two consecutive satisfactions of a desired property. At the same time, we guarantee the satisfaction of correctness specifications expressed as Linear Temporal Logic formulas. We illustrate the approach with a persistent surveillance robotics application.Comment: Technical report accompanying the ACC 2013 pape

Learning how to combine sensory-motor functions into a robust behavior

AbstractThis article describes a system, called Robel, for defining a robot controller that learns from experience very robust ways of performing a high-level task such as “navigate to”. The designer specifies a collection of skills, represented as hierarchical tasks networks, whose primitives are sensory-motor functions. The skills provide different ways of combining these sensory-motor functions to achieve the desired task. The specified skills are assumed to be complementary and to cover different situations. The relationship between control states, defined through a set of task-dependent features, and the appropriate skills for pursuing the task is learned as a finite observable Markov decision process (MDP). This MDP provides a general policy for the task; it is independent of the environment and characterizes the abilities of the robot for the task

Model Predictive Control with and without Terminal Weight: Stability and Algorithms

This paper presents stability analysis tools for model predictive control (MPC) with and without terminal weight. Stability analysis of MPC with a limited horizon but without terminal weight is a long-standing open problem. By using a modified value function as an Lyapunov function candidate and the principle of optimality, this paper establishes stability conditions for this type of widely spread MPC algorithms. A new stability guaranteed MPC algorithm without terminal weight (MPCS) is presented. With the help of designing a new sublevel set defined by the value function of one-step ahead stage cost, conditions for checking its recursive feasibility and stability of the proposed MPC algorithm are presented. The new stability condition and the derived MPCS overcome the difficulties arising in the existing terminal weight based MPC framework, including the need of searching a suitable terminal weight and possible poor performance caused by an inappropriate terminal weight. This work is further extended to MPC with a terminal weight for the completeness. Numerical examples are presented to demonstrate the effectiveness of the proposed tool, whereas the existing stability analysis tools are either not applicable or lead to quite conservative results. It shows that the proposed tools offer a number of mechanisms to achieve stability: adjusting state and/or control weights, extending the length of horizon, and adding a simple extra constraint on the first or second state in the optimisation