arXiv subjects

Marco Pavone

Publications and source records attributed to Marco Pavone.

At least 343 records · Page 19Linked to original sources

arXiv2019

The Trajectron: Probabilistic Multi-Agent Trajectory Modeling With Dynamic Spatiotemporal Graphs

Developing safe human-robot interaction systems is a necessary step towards the widespread integration of autonomous agents in society. A key component of such systems is the ability to reason about the many potential futures (e.g. trajectories) of other agents in the scene. Towards this end, we present the Trajectron, a graph-structured model that predicts many potential future trajectories of multiple agents simultaneously in both highly dynamic and multimodal scenarios (i.e. where the number of agents in the scene is time-varying and there are many possible highly-distinct futures for each agent). It combines tools from recurrent sequence modeling and variational deep generative modeling to produce a distribution of future trajectories for each agent in a scene. We demonstrate the performance of our model on several datasets, obtaining state-of-the-art results on standard trajectory prediction metrics as well as introducing a new metric for comparing models that output distributions.

cs.RO↗

arXiv2019

Robust Tracking with Model Mismatch for Fast and Safe Planning: an SOS Optimization Approach

In the pursuit of real-time motion planning, a commonly adopted practice is to compute a trajectory by running a planning algorithm on a simplified, low-dimensional dynamical model, and then employ a feedback tracking controller that tracks such a trajectory by accounting for the full, high-dimensional system dynamics. While this strategy of planning with model mismatch generally yields fast computation times, there are no guarantees of dynamic feasibility, which hampers application to safety-critical systems. Building upon recent work that addressed this problem through the lens of Hamilton-Jacobi (HJ) reachability, we devise an algorithmic framework whereby one computes, offline, for a pair of "planner" (i.e., low-dimensional) and "tracking" (i.e., high-dimensional) models, a feedback tracking controller and associated tracking bound. This bound is then used as a safety margin when generating motion plans via the low-dimensional model. Specifically, we harness the computational tool of sum-of-squares (SOS) programming to design a bilinear optimization algorithm for the computation of the feedback tracking controller and associated tracking bound. The algorithm is demonstrated via numerical experiments, with an emphasis on investigating the trade-off between the increased computational scalability afforded by SOS and its intrinsic conservativeness. Collectively, our results enable scaling the appealing strategy of planning with model mismatch to systems that are beyond the reach of HJ analysis, while maintaining safety guarantees.

eess.SY↗

arXiv2019

Learning Stabilizable Nonlinear Dynamics with Contraction-Based Regularization

We propose a novel framework for learning stabilizable nonlinear dynamical systems for continuous control tasks in robotics. The key contribution is a control-theoretic regularizer for dynamics fitting rooted in the notion of stabilizability, a constraint which guarantees the existence of robust tracking controllers for arbitrary open-loop trajectories generated with the learned system. Leveraging tools from contraction theory and statistical learning in Reproducing Kernel Hilbert Spaces, we formulate stabilizable dynamics learning as a functional optimization with convex objective and bi-convex functional constraints. Under a mild structural assumption and relaxation of the functional constraints to sampling-based constraints, we derive the optimal solution with a modified Representer theorem. Finally, we utilize random matrix feature approximations to reduce the dimensionality of the search parameters and formulate an iterative convex optimization algorithm that jointly fits the dynamics functions and searches for a certificate of stabilizability. We validate the proposed algorithm in simulation for a planar quadrotor, and on a quadrotor hardware testbed emulating planar dynamics. We verify, both in simulation and on hardware, significantly improved trajectory generation and tracking performance with the control-theoretic regularized model over models learned using traditional regression techniques, especially when learning from small supervised datasets. The results support the conjecture that the use of stabilizability constraints as a form of regularization can help prune the hypothesis space in a manner that is tailored to the downstream task of trajectory generation and feedback control, resulting in models that are not only dramatically better conditioned, but also data efficient.

math.OC↗

arXiv2019

A Differentiable Augmented Lagrangian Method for Bilevel Nonlinear Optimization

Many problems in modern robotics can be addressed by modeling them as bilevel optimization problems. In this work, we leverage augmented Lagrangian methods and recent advances in automatic differentiation to develop a general-purpose nonlinear optimization solver that is well suited to bilevel optimization. We then demonstrate the validity and scalability of our algorithm with two representative robotic problems, namely robust control and parameter estimation for a system involving contact. We stress the general nature of the algorithm and its potential relevance to many other problems in robotics.

cs.RO↗

arXiv2019

On the interaction between Autonomous Mobility-on-Demand systems and the power network: models and coordination algorithms

We study the interaction between a fleet of electric, self-driving vehicles servicing on-demand transportation requests (referred to as Autonomous Mobility-on-Demand, or AMoD, system) and the electric power network. We propose a model that captures the coupling between the two systems stemming from the vehicles' charging requirements and captures time-varying customer demand and power generation costs, road congestion, battery depreciation, and power transmission and distribution constraints. We then leverage the model to jointly optimize the operation of both systems. We devise an algorithmic procedure to losslessly reduce the problem size by bundling customer requests, allowing it to be efficiently solved by off-the-shelf linear programming solvers. Next, we show that the socially optimal solution to the joint problem can be enforced as a general equilibrium, and we provide a dual decomposition algorithm that allows self-interested agents to compute the market clearing prices without sharing private information. We assess the performance of the mode by studying a hypothetical AMoD system in Dallas-Fort Worth and its impact on the Texas power network. Lack of coordination between the AMoD system and the power network can cause a 4.4% increase in the price of electricity in Dallas-Fort Worth; conversely, coordination between the AMoD system and the power network could reduce electricity expenditure compared to the case where no cars are present (despite the increased demand for electricity) and yield savings of up $147M/year. Finally, we provide a receding-horizon implementation and assess its performance with agent-based simulations. Collectively, the results of this paper provide a first-of-a-kind characterization of the interaction between electric-powered AMoD systems and the power network, and shed additional light on the economic and societal value of AMoD.

eess.SY↗

arXiv2019

Trajectory Optimization on Manifolds: A Theoretically-Guaranteed Embedded Sequential Convex Programming Approach

Sequential Convex Programming (SCP) has recently gained popularity as a tool for trajectory optimization due to its sound theoretical properties and practical performance. Yet, most SCP-based methods for trajectory optimization are restricted to Euclidean settings, which precludes their application to problem instances where one must reason about manifold-type constraints (that is, constraints, such as loop closure, which restrict the motion of a system to a subset of the ambient space). The aim of this paper is to fill this gap by extending SCP-based trajectory optimization methods to a manifold setting. The key insight is to leverage geometric embeddings to lift a manifold-constrained trajectory optimization problem into an equivalent problem defined over a space enjoying a Euclidean structure. This insight allows one to extend existing SCP methods to a manifold setting in a fairly natural way. In particular, we present a SCP algorithm for manifold problems with refined theoretical guarantees that resemble those derived for the Euclidean setting, and demonstrate its practical performance via numerical experiments.

math.OC↗

arXiv2019

Reduced Order Model Predictive Control For Setpoint Tracking

Despite the success of model predictive control (MPC), its application to high-dimensional systems, such as flexible structures and coupled fluid/rigid-body systems, remains a largely open challenge due to excessive computational complexity. A promising solution approach is to leverage reduced order models for designing the model predictive controller. In this paper we present a reduced order MPC scheme that enables setpoint tracking while robustly guaranteeing constraint satisfaction for linear, discrete, time-invariant systems. Setpoint tracking is enabled by designing the MPC cost function to account for the steady-state error between the full and reduced order models. Robust constraint satisfaction is accomplished by solving (offline) a set of linear programs to provide bounds on the errors due to bounded disturbances, state estimation, and model approximation. The approach is validated on a synthetic system as well as a high-dimensional linear model of a flexible rod, obtained using finite element methods.

eess.SY↗

arXiv2019

A Risk-Sensitive Finite-Time Reachability Approach for Safety of Stochastic Dynamic Systems

A classic reachability problem for safety of dynamic systems is to compute the set of initial states from which the state trajectory is guaranteed to stay inside a given constraint set over a given time horizon. In this paper, we leverage existing theory of reachability analysis and risk measures to devise a risk-sensitive reachability approach for safety of stochastic dynamic systems under non-adversarial disturbances over a finite time horizon. Specifically, we first introduce the notion of a risk-sensitive safe set as a set of initial states from which the risk of large constraint violations can be reduced to a required level via a control policy, where risk is quantified using the Conditional Value-at-Risk (CVaR) measure. Second, we show how the computation of a risk-sensitive safe set can be reduced to the solution to a Markov Decision Process (MDP), where cost is assessed according to CVaR. Third, leveraging this reduction, we devise a tractable algorithm to approximate a risk-sensitive safe set, and provide theoretical arguments about its correctness. Finally, we present a realistic example inspired from stormwater catchment design to demonstrate the utility of risk-sensitive reachability analysis. In particular, our approach allows a practitioner to tune the level of risk sensitivity from worst-case (which is typical for Hamilton-Jacobi reachability analysis) to risk-neutral (which is the case for stochastic reachability analysis).

eess.SY↗

arXiv2019

Learning Sampling Distributions for Robot Motion Planning

A defining feature of sampling-based motion planning is the reliance on an implicit representation of the state space, which is enabled by a set of probing samples. Traditionally, these samples are drawn either probabilistically or deterministically to uniformly cover the state space. Yet, the motion of many robotic systems is often restricted to "small" regions of the state space, due to, for example, differential constraints or collision-avoidance constraints. To accelerate the planning process, it is thus desirable to devise non-uniform sampling strategies that favor sampling in those regions where an optimal solution might lie. This paper proposes a methodology for non-uniform sampling, whereby a sampling distribution is learned from demonstrations, and then used to bias sampling. The sampling distribution is computed through a conditional variational autoencoder, allowing sample generation from the latent space conditioned on the specific planning problem. This methodology is general, can be used in combination with any sampling-based planner, and can effectively exploit the underlying structure of a planning problem while maintaining the theoretical guarantees of sampling-based approaches. Specifically, on several planning problems, the proposed methodology is shown to effectively learn representations for the relevant regions of the state space, resulting in an order of magnitude improvement in terms of success rate and convergence to the optimal cost.

cs.RO↗

arXiv2019

Scalable and Congestion-aware Routing for Autonomous Mobility-on-Demand via Frank-Wolfe Optimization

We consider the problem of vehicle routing for Autonomous Mobility-on-Demand (AMoD) systems, wherein a fleet of self-driving vehicles provides on-demand mobility in a given environment. Specifically, the task it to compute routes for the vehicles (both customer-carrying and empty travelling) so that travel demand is fulfilled and operational cost is minimized. The routing process must account for congestion effects affecting travel times, as modeled via a volume-delay function (VDF). Route planning with VDF constraints is notoriously challenging, as such constraints compound the combinatorial complexity of the routing optimization process. Thus, current solutions for AMoD routing resort to relaxations of the congestion constraints, thereby trading optimality with computational efficiency. In this paper, we present the first computationally-efficient approach for AMoD routing where VDF constraints are explicitly accounted for. We demonstrate that our approach is faster by at least one order of magnitude with respect to the state of the art, while providing higher quality solutions. From a methodological standpoint, the key technical insight is to establish a mathematical reduction of the AMoD routing problem to the classical traffic assignment problem (a related vehicle-routing problem where empty traveling vehicles are not present). Such a reduction allows us to extend powerful algorithmic tools for traffic assignment, which combine the classic Frank-Wolfe algorithm with modern techniques for pathfinding, to the AMoD routing problem. We provide strong theoretical guarantees for our approach in terms of near-optimality of the returned solution.

math.OC↗

arXiv2019

GuSTO: Guaranteed Sequential Trajectory Optimization via Sequential Convex Programming

Sequential Convex Programming (SCP) has recently seen a surge of interest as a tool for trajectory optimization. However, most available methods lack rigorous performance guarantees and they are often tailored to specific optimal control setups. In this paper, we present GuSTO (Guaranteed Sequential Trajectory Optimization), an algorithmic framework to solve trajectory optimization problems for control-affine systems with drift. GuSTO generalizes earlier SCP-based methods for trajectory optimization (by addressing, for example, goal-set constraints and problems with either fixed or free final time) and enjoys theoretical convergence guarantees in terms of convergence to, at least, a stationary point. The theoretical analysis is further leveraged to devise an accelerated implementation of GuSTO, which originally infuses ideas from indirect optimal control into an SCP context. Numerical experiments on a variety of trajectory optimization setups show that GuSTO generally outperforms current state-of-the-art approaches in terms of success rates, solution quality, and computation times.

math.OC↗

arXiv2019

Network Offloading Policies for Cloud Robotics: a Learning-based Approach

Today's robotic systems are increasingly turning to computationally expensive models such as deep neural networks (DNNs) for tasks like localization, perception, planning, and object detection. However, resource-constrained robots, like low-power drones, often have insufficient on-board compute resources or power reserves to scalably run the most accurate, state-of-the art neural network compute models. Cloud robotics allows mobile robots the benefit of offloading compute to centralized servers if they are uncertain locally or want to run more accurate, compute-intensive models. However, cloud robotics comes with a key, often understated cost: communicating with the cloud over congested wireless networks may result in latency or loss of data. In fact, sending high data-rate video or LIDAR from multiple robots over congested networks can lead to prohibitive delay for real-time applications, which we measure experimentally. In this paper, we formulate a novel Robot Offloading Problem --- how and when should robots offload sensing tasks, especially if they are uncertain, to improve accuracy while minimizing the cost of cloud communication? We formulate offloading as a sequential decision making problem for robots, and propose a solution using deep reinforcement learning. In both simulations and hardware experiments using state-of-the art vision DNNs, our offloading strategy improves vision task performance by between 1.3-2.6x of benchmark offloading strategies, allowing robots the potential to significantly transcend their on-board sensing accuracy but with limited cost of cloud communication.

cs.RO↗

arXiv2019

Robust and Adaptive Planning under Model Uncertainty

Planning under model uncertainty is a fundamental problem across many applications of decision making and learning. In this paper, we propose the Robust Adaptive Monte Carlo Planning (RAMCP) algorithm, which allows computation of risk-sensitive Bayes-adaptive policies that optimally trade off exploration, exploitation, and robustness. RAMCP formulates the risk-sensitive planning problem as a two-player zero-sum game, in which an adversary perturbs the agent's belief over the models. We introduce two versions of the RAMCP algorithm. The first, RAMCP-F, converges to an optimal risk-sensitive policy without having to rebuild the search tree as the underlying belief over models is perturbed. The second version, RAMCP-I, improves computational efficiency at the cost of losing theoretical guarantees, but is shown to yield empirical results comparable to RAMCP-F. RAMCP is demonstrated on an n-pull multi-armed bandit problem, as well as a patient treatment scenario.

cs.AI↗

arXiv2018

On Infusing Reachability-Based Safety Assurance within Probabilistic Planning Frameworks for Human-Robot Vehicle Interactions

Action anticipation, intent prediction, and proactive behavior are all desirable characteristics for autonomous driving policies in interactive scenarios. Paramount, however, is ensuring safety on the road --- a key challenge in doing so is accounting for uncertainty in human driver actions without unduly impacting planner performance. This paper introduces a minimally-interventional safety controller operating within an autonomous vehicle control stack with the role of ensuring collision-free interaction with an externally controlled (e.g., human-driven) counterpart. We leverage reachability analysis to construct a real-time (100Hz) controller that serves the dual role of (1) tracking an input trajectory from a higher-level planning algorithm using model predictive control, and (2) assuring safety through maintaining the availability of a collision-free escape maneuver as a persistent constraint regardless of whatever future actions the other car takes. A full-scale steer-by-wire platform is used to conduct traffic weaving experiments wherein the two cars, initially side-by-side, must swap lanes in a limited amount of time and distance, emulating cars merging onto/off of a highway. We demonstrate that, with our control stack, the autonomous vehicle is able to avoid collision even when the other car defies the planner's expectations and takes dangerous actions, either carelessly or with the intent to collide, and otherwise deviates minimally from the planned trajectory to the extent required to maintain safety.

cs.RO↗

arXiv2018

Risk-Sensitive Generative Adversarial Imitation Learning

We study risk-sensitive imitation learning where the agent's goal is to perform at least as well as the expert in terms of a risk profile. We first formulate our risk-sensitive imitation learning setting. We consider the generative adversarial approach to imitation learning (GAIL) and derive an optimization problem for our formulation, which we call it risk-sensitive GAIL (RS-GAIL). We then derive two different versions of our RS-GAIL optimization problem that aim at matching the risk profiles of the agent and the expert w.r.t. Jensen-Shannon (JS) divergence and Wasserstein distance, and develop risk-sensitive generative adversarial imitation learning algorithms based on these optimization problems. We evaluate the performance of our algorithms and compare them with GAIL and the risk-averse imitation learning (RAIL) algorithms in two MuJoCo and two OpenAI classical control tasks.

cs.LG↗

arXiv2018

Learning Stabilizable Dynamical Systems via Control Contraction Metrics

We propose a novel framework for learning stabilizable nonlinear dynamical systems for continuous control tasks in robotics. The key idea is to develop a new control-theoretic regularizer for dynamics fitting rooted in the notion of stabilizability, which guarantees that the learned system can be accompanied by a robust controller capable of stabilizing any open-loop trajectory that the system may generate. By leveraging tools from contraction theory, statistical learning, and convex optimization, we provide a general and tractable semi-supervised algorithm to learn stabilizable dynamics, which can be applied to complex underactuated systems. We validated the proposed algorithm on a simulated planar quadrotor system and observed notably improved trajectory generation and tracking performance with the control-theoretic regularized model over models learned using traditional regression techniques, especially when using a small number of demonstration examples. The results presented illustrate the need to infuse standard model-based reinforcement learning algorithms with concepts drawn from nonlinear control theory for improved reliability.

eess.SY↗

arXiv2018

Robot Motion Planning in Learned Latent Spaces

This paper presents Latent Sampling-based Motion Planning (L-SBMP), a methodology towards computing motion plans for complex robotic systems by learning a plannable latent representation. Recent works in control of robotic systems have effectively leveraged local, low-dimensional embeddings of high-dimensional dynamics. In this paper we combine these recent advances with techniques from sampling-based motion planning (SBMP) in order to design a methodology capable of planning for high-dimensional robotic systems beyond the reach of traditional approaches (e.g., humanoids, or even systems where planning occurs in the visual space). Specifically, the learned latent space is constructed through an autoencoding network, a dynamics network, and a collision checking network, which mirror the three main algorithmic primitives of SBMP, namely state sampling, local steering, and collision checking. Notably, these networks can be trained through only raw data of the system's states and actions along with a supervising collision checker. Building upon these networks, an RRT-based algorithm is used to plan motions directly in the latent space - we refer to this exploration algorithm as Learned Latent RRT (L2RRT). This algorithm globally explores the latent space and is capable of generalizing to new environments. The overall methodology is demonstrated on two planning problems, namely a visual planning problem, whereby planning happens in the visual (pixel) space, and a humanoid robot planning problem.

cs.RO↗

arXiv2018

Meta-Learning Priors for Efficient Online Bayesian Regression

Gaussian Process (GP) regression has seen widespread use in robotics due to its generality, simplicity of use, and the utility of Bayesian predictions. The predominant implementation of GP regression is a nonparameteric kernel-based approach, as it enables fitting of arbitrary nonlinear functions. However, this approach suffers from two main drawbacks: (1) it is computationally inefficient, as computation scales poorly with the number of samples; and (2) it can be data inefficient, as encoding prior knowledge that can aid the model through the choice of kernel and associated hyperparameters is often challenging and unintuitive. In this work, we propose ALPaCA, an algorithm for efficient Bayesian regression which addresses these issues. ALPaCA uses a dataset of sample functions to learn a domain-specific, finite-dimensional feature encoding, as well as a prior over the associated weights, such that Bayesian linear regression in this feature space yields accurate online predictions of the posterior predictive density. These features are neural networks, which are trained via a meta-learning (or "learning-to-learn") approach. ALPaCA extracts all prior information directly from the dataset, rather than restricting prior information to the choice of kernel hyperparameters. Furthermore, by operating in the weight space, it substantially reduces sample complexity. We investigate the performance of ALPaCA on two simple regression problems, two simulated robotic systems, and on a lane-change driving task performed by humans. We find our approach outperforms kernel-based GP regression, as well as state of the art meta-learning approaches, thereby providing a promising plug-in tool for many regression tasks in robotics where scalability and data-efficiency are important.

cs.RO↗