Sertac Karaman

Anytime Motion Planning using the RRT

The Rapidly-exploring Random Tree (RRT) algorithm, based on incremental sampling, efficiently computes motion plans. Although the RRT algorithm quickly produces candidate feasible solutions, it tends to converge to a solution that is far from optimal. Practical applications favor “anytime” algorithms that quickly identify an initial feasible plan, then, given more computation time available during plan execution, improve the plan toward an optimal solution. This paper describes an anytime algorithm based on the RRT* which (like the RRT) finds an initial feasible solution quickly, but (unlike the RRT) almost surely converges to an optimal solution. We present two key extensions to the RRT*, committed trajectories and branch-and-bound tree adaptation, that together enable the algorithm to make more efficient use of computation time online, resulting in an anytime algorithm for real-time implementation. We evaluate the method using a series of Monte Carlo runs in a high-fidelity simulation environment, and compare the operation of the RRT and RRT* methods. We also demonstrate experimental results for an outdoor wheeled

Vehicle Routing Problem with Metric Temporal Logic Specifications

This paper proposes a novel version of the vehicle routing problem (VRP). Instead of servicing all the customers, feasible solutions of the VRP instance are forced to satisfy a set of complex high-level tasks given as a metric temporal logic (MTL) specification, which allows complex quantitative timing constraints to be incorporated into the problem. For the resulting vehicle routing problem with metric temporal logic specifications (VRPMTL), a mixed-integer linear programming (MILP) based algorithm is provided that solves the problem to optimality. Examples for optimal multi-UAV mission planning are provided where MTL is used as a high level language to specify complex mission tasks.

Robust Sampling-based Motion Planning with Asymptotic Optimality Guarantees

This paper presents a novel sampling-based planner, CC-RRT*, which generates robust, asymptotically optimal trajectories in real-time for linear Gaussian systems subject to process noise, localization error, and uncertain environmental constraints. CC-RRT* provides guaranteed probabilistic feasibility, both at each time step and along the entire trajectory, by using chance constraints to efficiently approximate the risk of constraint violation. This algorithm expands on existing results by utilizing the framework of RRT* to provide guarantees on asymptotic optimality of the lowest-cost probabilistically feasible path found. A novel riskbased objective function, shown to be admissible within RRT*, allows the user to trade-off between minimizing path duration and risk-averse behavior. This enables the modeling of soft risk constraints simultaneously with hard probabilistic feasibility bounds. Simulation results demonstrate that CC-RRT* can efficiently identify smooth, robust trajectories for a variety of uncertainty scenarios and dynamics.

Sampling-based algorithms for optimal motion planning with deterministic μ-calculus specifications

Automatic generation of control programs that satisfy complex task specifications given in high-level specification languages such as temporal logics has been studied extensively. However, optimality of such control programs, for instance with respect to a cost function, has received relatively little attention. In this paper, we study the problem of optimal trajectory synthesis for a large class of specifications, given in the form of deterministic mu-calculus. We propose a sampling-based algorithm, based on the Rapidly-exploring Random Graphs (RRGs), that solves this problem with probabilistic completeness and asymptotic optimality guarantees. We evaluate our algorithm in a simulation studies involving a curvature constrained car. Our simulation results show that in this scenario the algorithm quickly discovers a trajectory that satisfies the specification, and improves this trajectory towards an optimal one if allowed more computation time. We also point out connections to (optimal) memoryless winning strategies in infinite parity games, which may be of independent interest.

Least-violating control strategy synthesis with safety rules

We consider the problem of automatic control strategy synthesis, for discrete models of robotic systems, to fulfill a task that requires reaching a goal state while obeying a given set of safety rules. In this paper, we focus on the case when the said task is not feasible without temporarily violating some of the rules. We propose an algorithm that {synthesizes} a motion which violates only lowest priority rules for the shortest amount of time. Although the proposed algorithm can be applied in a variety of control problems, throughout the paper, we motivate this problem with an autonomous car navigating in an urban environment while abiding by the rules of the road, such as always stay in the right lane and do not enter the sidewalk. We evaluate the algorithm on a case study with several illustrative scenarios.

Polling-systems-based control of high-performance provably-safe autonomous intersections

The rapid development of autonomous vehicles spurred a careful investigation of the potential benefits of all-autonomous transportation networks. Most studies conclude that autonomous systems can enable drastic improvements in performance. A widely studied concept is all-autonomous, collision-free intersections, where vehicles arriving in a traffic intersection with no traffic light adjust their speeds to cross through the intersection as quickly as possible. In this paper, we propose a coordination control algorithm for this problem, assuming stochastic models for the arrival times of the vehicles. The proposed algorithm provides provable guarantees on safety and performance. More precisely, it is shown that no collisions occur surely, and moreover a rigorous upper bound is provided for the expected wait time. The algorithm is also demonstrated in simulations. The proposed algorithms are inspired by polling systems. In fact, the problem studied in this paper leads to a new polling system where customers are subject to differential constraints, which may be interesting in its own right.

Incremental sampling-based algorithm for minimum-violation motion planning

This paper studies the problem of control strategy synthesis for dynamical systems with differential constraints to fulfill a given reachability goal while satisfying a set of safety rules. Particular attention is devoted to goals that become feasible only if a subset of the safety rules are violated. The proposed algorithm computes a control law, that minimizes the level of unsafety while the desired goal is guaranteed to be reached. This problem is motivated by an autonomous car navigating an urban environment while following rules of the road such as “always travel in right lane” and “do not change lanes frequently”. Ideas behind sampling based motion-planning algorithms, such as Probabilistic Road Maps (PRMs) and Rapidly-exploring Random Trees (RRTs), are employed to incrementally construct a finite concretization of the dynamics as a durational Kripke structure. In conjunction with this, a weighted finite automaton that captures the safety rules is used in order to find an optimal trajectory that minimizes the violation of safety rules. We prove that the proposed algorithm guarantees asymptotic optimality, i.e., almost-sure convergence to optimal solutions. We present results of simulation experiments and an implementation on an autonomous urban mobility-on-demand system.

Closed-loop pallet manipulation in unstructured environments

This paper addresses the problem of autonomous manipulation of a priori unknown palletized cargo with a robotic lift truck (forklift). Specifically, we describe coupled perception and control algorithms that enable the vehicle to engage and place loaded pallets relative to locations on the ground or truck beds. Having little prior knowledge of the objects with which the vehicle is to interact, we present an estimation framework that utilizes a series of classifiers to infer the objects structure and pose from individual LIDAR scans. The classifiers share a low-level shape estimation algorithm that uses linear programming to robustly segment input data into sets of weak candidate features. We present and analyze the performance of the segmentation method, and subsequently describe its role in our estimation algorithm. We then evaluate the performance of a motion controller that, given an estimate of a pallets pose, is employed to safely engage each pallet. We conclude with a validation of our algorithms for a set of real-world pallet and truck interactions.

Large-scale Task/Target Assignment for UAV Fleets Using a Distributed Branch and Price Optimization Scheme

Abstract In this work we consider the large-scale distributed task/target assignment problem across a fleet of autonomous UAVs. By using delayed column generation approach on the most primitive non-convex supply-demand formulation, a computationally tractable distributed coordination structure (i.e. a market created by the UAV fleet for tasks/targets) is exploited. This particular structure is solved via a fleet-optimal dual simplex ascent in which each UAV updates its respective flight plan costs with a linear update of way-point task values as evaluated by the market. We show synchronized and asynchronous distributed implementations of this approximation algorithm for dynamically changing scenarios with random pop-up targets. The tests performed on an in-house built network mission simulator provides numerical verification of the algorithm on a) bounded polynomial-time computational complexity and b) hard real-time performance for problem sizes on the order of hundred waypoints per UAV.

Development of a Cross-Compatible Micro-Avionics System for Aerorobotics

In this work, we present a micro-avionics system structured around the controller area network (CAN) bus data backbone. The system is designed to be cross-compatible across our experimental mini-helicopters and ground vehicles, and it is tailored to allow autonomous navigation and control for a variety of different research test cases. The expandable architecture deploys a hybrid selection of COTS Motorola (MPC555) and Arm processor boards (LPC2294), each with different operating systems and coding techniques (such as rapid algorithmic prototyping using automatic code generation via Matlab/Real Time Workshop Embedded Target). The micro-avionics system employs a complete sensor suite that provides real-time position, orientation and associated time-rate information. As a part of the on-going fleet autonomy experiments, we present the design of a novel wireless SmartCan node. This wireless node allows seamless CAN Bus access of low-level sensor and operational data of other vehicles within close proximity.