arXiv subjects

Marco Pavone

Publications and source records attributed to Marco Pavone.

At least 379 records · Page 21Linked to original sources

arXiv2017

Real-Time Stochastic Kinodynamic Motion Planning via Multiobjective Search on GPUs

In this paper we present the PUMP (Parallel Uncertainty-aware Multiobjective Planning) algorithm for addressing the stochastic kinodynamic motion planning problem, whereby one seeks a low-cost, dynamically-feasible motion plan subject to a constraint on collision probability (CP). To ensure exhaustive evaluation of candidate motion plans (as needed to tradeoff the competing objectives of performance and safety), PUMP incrementally builds the Pareto front of the problem, accounting for the optimization objective and an approximation of CP. This is performed by a massively parallel multiobjective search, here implemented with a focus on GPUs. Upon termination of the exploration phase, PUMP searches the Pareto set of motion plans to identify the lowest cost solution that is certified to satisfy the CP constraint (according to an asymptotically exact estimator). We introduce a novel particle-based CP approximation scheme, designed for efficient GPU implementation, which accounts for dependencies over the history of a trajectory execution. We present numerical experiments for quadrotor planning wherein PUMP identifies solutions in ~100 ms, evaluating over one hundred thousand partial plans through the course of its exploration phase. The results show that this multiobjective search achieves a lower motion plan cost, for the same CP constraint, compared to a safety buffer-based search heuristic and repeated RRT trials.

cs.RO↗

arXiv2016

The Team Surviving Orienteers Problem: Routing Robots in Uncertain Environments with Survival Constraints

In this paper we study the following multi-robot coordination problem: given a graph, where each edge is weighted by the probability of surviving while traversing it, find a set of paths for $K$ robots that maximizes the expected number of nodes collectively visited, subject to constraints on the probability that each robot survives to its destination. We call this problem the Team Surviving Orienteers (TSO) problem. The TSO problem is motivated by scenarios where a team of robots must traverse a dangerous, uncertain environment, such as aid delivery in disaster or war zones. We present the TSO problem formally along with several variants, which represent "survivability-aware" counterparts for a wide range of multi-robot coordination problems such as vehicle routing, patrolling, and informative path planning. We propose an approximate greedy approach for selecting paths, and prove that the value of its output is bounded within a factor $1-e^{-p_s/λ}$ of the optimum where $p_s$ is the per-robot survival probability threshold, and $1/λ\le 1$ is the approximation factor of an oracle routine for the well-known orienteering problem. Our approach has linear time complexity in the team size and polynomial complexity in the graph size. Using numerical simulations, we verify that our approach is close to the optimum in practice and that it scales to problems with hundreds of nodes and tens of robots.

cs.RO↗

arXiv2016

Congestion-Aware Randomized Routing in Autonomous Mobility-on-Demand Systems

In this paper we study the routing and rebalancing problem for a fleet of autonomous vehicles providing on-demand transportation within a congested urban road network (that is, a road network where traffic speed depends on vehicle density). We show that the congestion-free routing and rebalancing problem is NP-hard and provide a randomized algorithm which finds a low-congestion solution to the routing and rebalancing problem that approximately minimizes the number of vehicles on the road in polynomial time. We provide theoretical bounds on the probability of violating the congestion constraints; we also characterize the expected number of vehicles required by the solution with a commonly-used empirical congestion model and provide a bound on the approximation factor of the algorithm. Numerical experiments on a realistic road network with real-world customer demands show that our algorithm introduces very small amounts of congestion. The performance of our algorithm in terms of travel times and required number of vehicles is very close to (and sometimes better than) the optimal congestion-free solution.

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arXiv2016

Routing Autonomous Vehicles in Congested Transportation Networks: Structural Properties and Coordination Algorithms

This paper considers the problem of routing and rebalancing a shared fleet of autonomous (i.e., self-driving) vehicles providing on-demand mobility within a capacitated transportation network, where congestion might disrupt throughput. We model the problem within a network flow framework and show that under relatively mild assumptions the rebalancing vehicles, if properly coordinated, do not lead to an increase in congestion (in stark contrast to common belief). From an algorithmic standpoint, such theoretical insight suggests that the problem of routing customers and rebalancing vehicles can be decoupled, which leads to a computationally-efficient routing and rebalancing algorithm for the autonomous vehicles. Numerical experiments and case studies corroborate our theoretical insights and show that the proposed algorithm outperforms state-of-the-art point-to-point methods by avoiding excess congestion on the road. Collectively, this paper provides a rigorous approach to the problem of congestion-aware, system-wide coordination of autonomously driving vehicles, and to the characterization of the sustainability of such robotic systems.

cs.MA↗

arXiv2016

Mixed Strategy for Constrained Stochastic Optimal Control

Choosing control inputs randomly can result in a reduced expected cost in optimal control problems with stochastic constraints, such as stochastic model predictive control (SMPC). We consider a controller with initial randomization, meaning that the controller randomly chooses from K+1 control sequences at the beginning (called K-randimization).It is known that, for a finite-state, finite-action Markov Decision Process (MDP) with K constraints, K-randimization is sufficient to achieve the minimum cost. We found that the same result holds for stochastic optimal control problems with continuous state and action spaces.Furthermore, we show the randomization of control input can result in reduced cost when the optimization problem is nonconvex, and the cost reduction is equal to the duality gap. We then provide the necessary and sufficient conditions for the optimality of a randomized solution, and develop an efficient solution method based on dual optimization. Furthermore, in a special case with K=1 such as a joint chance-constrained problem, the dual optimization can be solved even more efficiently by root finding. Finally, we test the theories and demonstrate the solution method on multiple practical problems ranging from path planning to the planning of entry, descent, and landing (EDL) for future Mars missions.

cs.RO↗

arXiv2016

Deterministic Sampling-Based Motion Planning: Optimality, Complexity, and Performance

Probabilistic sampling-based algorithms, such as the probabilistic roadmap (PRM) and the rapidly-exploring random tree (RRT) algorithms, represent one of the most successful approaches to robotic motion planning, due to their strong theoretical properties (in terms of probabilistic completeness or even asymptotic optimality) and remarkable practical performance. Such algorithms are probabilistic in that they compute a path by connecting independently and identically distributed random points in the configuration space. Their randomization aspect, however, makes several tasks challenging, including certification for safety-critical applications and use of offline computation to improve real-time execution. Hence, an important open question is whether similar (or better) theoretical guarantees and practical performance could be obtained by considering deterministic, as opposed to random sampling sequences. The objective of this paper is to provide a rigorous answer to this question. Specifically, we first show that PRM, for a certain selection of tuning parameters and deterministic low-dispersion sampling sequences, is deterministically asymptotically optimal. Second, we characterize the convergence rate, and we find that the factor of sub-optimality can be very explicitly upper-bounded in terms of the l2-dispersion of the sampling sequence and the connection radius of PRM. Third, we show that an asymptotically optimal version of PRM exists with computational and space complexity arbitrarily close to O(n) (the theoretical lower bound), where n is the number of points in the sequence. This is in stark contrast to the O(n logn) complexity results for existing asymptotically-optimal probabilistic planners. Finally, through numerical experiments, we show that planning with deterministic low-dispersion sampling generally provides superior performance in terms of path cost and success rate.

cs.RO↗

arXiv2016

Optimized and Trusted Collision Avoidance for Unmanned Aerial Vehicles using Approximate Dynamic Programming (Technical Report)

Safely integrating unmanned aerial vehicles into civil airspace is contingent upon development of a trustworthy collision avoidance system. This paper proposes an approach whereby a parameterized resolution logic that is considered trusted for a given range of its parameters is adaptively tuned online. Specifically, to address the potential conservatism of the resolution logic with static parameters, we present a dynamic programming approach for adapting the parameters dynamically based on the encounter state. We compute the adaptation policy offline using a simulation-based approximate dynamic programming method that accommodates the high dimensionality of the problem. Numerical experiments show that this approach improves safety and operational performance compared to the baseline resolution logic, while retaining trustworthiness.

cs.RO↗

arXiv2016

Risk Aversion in Finite Markov Decision Processes Using Total Cost Criteria and Average Value at Risk

In this paper we present an algorithm to compute risk averse policies in Markov Decision Processes (MDP) when the total cost criterion is used together with the average value at risk (AVaR) metric. Risk averse policies are needed when large deviations from the expected behavior may have detrimental effects, and conventional MDP algorithms usually ignore this aspect. We provide conditions for the structure of the underlying MDP ensuring that approximations for the exact problem can be derived and solved efficiently. Our findings are novel inasmuch as average value at risk has not previously been considered in association with the total cost criterion. Our method is demonstrated in a rapid deployment scenario, whereby a robot is tasked with the objective of reaching a target location within a temporal deadline where increased speed is associated with increased probability of failure. We demonstrate that the proposed algorithm not only produces a risk averse policy reducing the probability of exceeding the expected temporal deadline, but also provides the statistical distribution of costs, thus offering a valuable analysis tool.

math.OC↗

arXiv2016

Model Predictive Control of Autonomous Mobility-on-Demand Systems

In this paper we present a model predictive control (MPC) approach to optimize vehicle scheduling and routing in an autonomous mobility-on-demand (AMoD) system. In AMoD systems, robotic, self-driving vehicles transport customers within an urban environment and are coordinated to optimize service throughout the entire network. Specifically, we first propose a novel discrete-time model of an AMoD system and we show that this formulation allows the easy integration of a number of real-world constraints, e.g., electric vehicle charging constraints. Second, leveraging our model, we design a model predictive control algorithm for the optimal coordination of an AMoD system and prove its stability in the sense of Lyapunov. At each optimization step, the vehicle scheduling and routing problem is solved as a mixed integer linear program (MILP) where the decision variables are binary variables representing whether a vehicle will 1) wait at a station, 2) service a customer, or 3) rebalance to another station. Finally, by using real-world data, we show that the MPC algorithm can be run in real-time for moderately-sized systems and outperforms previous control strategies for AMoD systems.

eess.SY↗

arXiv2016

Fast, Safe, and Propellant-Efficient Spacecraft Planning under Clohessy-Wiltshire-Hill Dynamics

This paper presents a sampling-based motion planning algorithm for real-time and propellant-optimized autonomous spacecraft trajectory generation in near-circular orbits. Specifically, this paper leverages recent algorithmic advances in the field of robot motion planning to the problem of impulsively-actuated, propellant-optimized rendezvous and proximity operations under the Clohessy-Wiltshire-Hill (CWH) dynamics model. The approach calls upon a modified version of the Fast Marching Tree (FMT*) algorithm to grow a set of feasible trajectories over a deterministic, low-dispersion set of sample points covering the free state space. To enforce safety, the tree is only grown over the subset of actively-safe samples, from which there exists a feasible one-burn collision avoidance maneuver that can safely circularize the spacecraft orbit along its coasting arc under a given set of potential thruster failures. Key features of the proposed algorithm include: (i) theoretical guarantees in terms of trajectory safety and performance, (ii) amenability to real-time implementation, and (iii) generality, in the sense that a large class of constraints can be handled directly. As a result, the proposed algorithm offers the potential for widespread application, ranging from on-orbit satellite servicing to orbital debris removal and autonomous inspection missions.

eess.SY↗

arXiv2015

Stochastic Optimal Control With Dynamic, Time-Consistent Risk Constraints

In this paper we present a dynamic programing approach to stochastic optimal control problems with dynamic, time-consistent risk constraints. Constrained stochastic optimal control problems, which naturally arise when one has to consider multiple objectives, have been extensively investigated in the past 20 years, however, in most formulations, the constraints are formulated as either risk-neutral (i.e., by considering an expected cost), or by applying static, single-period risk metrics with limited attention to "time-consistency" (i.e., to whether such metrics ensure rational consistency of risk preferences across multiple periods). Recently, significant strides have been made in the development of a rigorous theory of dynamic, \emph{time-consistent} risk metrics for multi-period (risk-sensitive) decision processes, however, their integration within constrained stochastic optimal control problems has received little attention. The goal of this paper is to bridge this gap. First, we formulate the stochastic optimal control problem with dynamic, time-consistent risk constraints and we characterize the tail subproblems (which requires the addition of a Markovian structure to the risk metrics). Second, we develop a dynamic programming approach for its solution, which allows to compute the optimal costs by value iteration. Finally, we discuss both theoretical and practical features of our approach, such as generalizations, construction of optimal control policies, and computational aspects. A simple, two-state example is given to illustrate the problem setup and the solution approach.

math.OC↗

arXiv2015

A Framework for Time-Consistent, Risk-Averse Model Predictive Control: Theory and Algorithms

In this paper we present a framework for risk-averse model predictive control (MPC) of linear systems affected by multiplicative uncertainty. Our key innovation is to consider time-consistent, dynamic risk metrics as objective functions to be minimized. This framework is axiomatically justified in terms of time-consistency of risk preferences, is amenable to dynamic optimization, and is unifying in the sense that it captures a full range of risk assessments from risk-neutral to worst case. Within this framework, we propose and analyze an online risk-averse MPC algorithm that is provably stabilizing. Furthermore, by exploiting the dual representation of time-consistent, dynamic risk metrics, we cast the computation of the MPC control law as a convex optimization problem amenable to implementation on embedded systems. Simulation results are presented and discussed.

math.OC↗

arXiv2015

Trading Safety Versus Performance: Rapid Deployment of Robotic Swarms with Robust Performance Constraints

In this paper we consider a stochastic deployment problem, where a robotic swarm is tasked with the objective of positioning at least one robot at each of a set of pre-assigned targets while meeting a temporal deadline. Travel times and failure rates are stochastic but related, inasmuch as failure rates increase with speed. To maximize chances of success while meeting the deadline, a control strategy has therefore to balance safety and performance. Our approach is to cast the problem within the theory of constrained Markov Decision Processes, whereby we seek to compute policies that maximize the probability of successful deployment while ensuring that the expected duration of the task is bounded by a given deadline. To account for uncertainties in the problem parameters, we consider a robust formulation and we propose efficient solution algorithms, which are of independent interest. Numerical experiments confirming our theoretical results are presented and discussed.

cs.RO↗

arXiv2015

Decentralized Algorithms for 3D Symmetric Formations in Robotic Networks: a Contraction Theory Approach

This paper presents decentralized algorithms for formation control of multiple robots in three dimensions. Specifically, we leverage the mathematical properties of cyclic pursuit along with results from contraction and partial contraction theory to design decentralized control algorithms that ensure global convergence to symmetric formations. We first consider regular polygon formations as a base case, and then extend the results to Johnson solid and other polygonal mesh formations. The algorithms are further augmented to allow control over formation size and avoid collisions with other robots in the formation. The robustness properties of the algorithms are assessed in the presence of bounded additive disturbances and their effect on the quality of the formation is quantified. Finally, we present a general methodology for embedding the control laws on complex dynamical systems, in this case, quadcopters, and validate this approach via simulations and experiments on a fleet of quadcopters.

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arXiv2015

Optimal Sampling-Based Motion Planning under Differential Constraints: the Drift Case with Linear Affine Dynamics

In this paper we provide a thorough, rigorous theoretical framework to assess optimality guarantees of sampling-based algorithms for drift control systems: systems that, loosely speaking, can not stop instantaneously due to momentum. We exploit this framework to design and analyze a sampling-based algorithm (the Differential Fast Marching Tree algorithm) that is asymptotically optimal, that is, it is guaranteed to converge, as the number of samples increases, to an optimal solution. In addition, our approach allows us to provide concrete bounds on the rate of this convergence. The focus of this paper is on mixed time/control energy cost functions and on linear affine dynamical systems, which encompass a range of models of interest to applications (e.g., double-integrators) and represent a necessary step to design, via successive linearization, sampling-based and provably-correct algorithms for non-linear drift control systems. Our analysis relies on an original perturbation analysis for two-point boundary value problems, which could be of independent interest.

cs.RO↗

arXiv2015

A Convex Optimization Approach to Smooth Trajectories for Motion Planning with Car-Like Robots

In the recent past, several sampling-based algorithms have been proposed to compute trajectories that are collision-free and dynamically-feasible. However, the outputs of such algorithms are notoriously jagged. In this paper, by focusing on robots with car-like dynamics, we present a fast and simple heuristic algorithm, named Convex Elastic Smoothing (CES) algorithm, for trajectory smoothing and speed optimization. The CES algorithm is inspired by earlier work on elastic band planning and iteratively performs shape and speed optimization. The key feature of the algorithm is that both optimization problems can be solved via convex programming, making CES particularly fast. A range of numerical experiments show that the CES algorithm returns high-quality solutions in a matter of a few hundreds of milliseconds and hence appears amenable to a real-time implementation.

cs.RO↗

arXiv2015

Two Phase $Q-$learning for Bidding-based Vehicle Sharing

We consider one-way vehicle sharing systems where customers can rent a car at one station and drop it off at another. The problem we address is to optimize the distribution of cars, and quality of service, by pricing rentals appropriately. We propose a bidding approach that is inspired from auctions and takes into account the significant uncertainty inherent in the problem data (e.g., pick-up and drop-off locations, time of requests, and duration of trips). Specifically, in contrast to current vehicle sharing systems, the operator does not set prices. Instead, customers submit bids and the operator decides whether to rent or not. The operator can even accept negative bids to motivate drivers to rebalance available cars to unpopular destinations within a city. We model the operator's sequential decision-making problem as a \emph{constrained Markov decision problem} (CMDP) and propose and rigorously analyze a novel two phase $Q$-learning algorithm for its solution. Numerical experiments are presented and discussed.

cs.AI↗

arXiv2015

An Asymptotically-Optimal Sampling-Based Algorithm for Bi-directional Motion Planning

Bi-directional search is a widely used strategy to increase the success and convergence rates of sampling-based motion planning algorithms. Yet, few results are available that merge both bi-directional search and asymptotic optimality into existing optimal planners, such as PRM*, RRT*, and FMT*. The objective of this paper is to fill this gap. Specifically, this paper presents a bi-directional, sampling-based, asymptotically-optimal algorithm named Bi-directional FMT* (BFMT*) that extends the Fast Marching Tree (FMT*) algorithm to bi-directional search while preserving its key properties, chiefly lazy search and asymptotic optimality through convergence in probability. BFMT* performs a two-source, lazy dynamic programming recursion over a set of randomly-drawn samples, correspondingly generating two search trees: one in cost-to-come space from the initial configuration and another in cost-to-go space from the goal configuration. Numerical experiments illustrate the advantages of BFMT* over its unidirectional counterpart, as well as a number of other state-of-the-art planners.

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