arXiv subjects

Evangelos A. Theodorou

Publications and source records attributed to Evangelos A. Theodorou.

122 records · Page 7Linked to original sources

arXiv2018

Vision-Based High Speed Driving with a Deep Dynamic Observer

In this paper we present a framework for combining deep learning-based road detection, particle filters, and Model Predictive Control (MPC) to drive aggressively using only a monocular camera, IMU, and wheel speed sensors. This framework uses deep convolutional neural networks combined with LSTMs to learn a local cost map representation of the track in front of the vehicle. A particle filter uses this dynamic observation model to localize in a schematic map, and MPC is used to drive aggressively using this particle filter based state estimate. We show extensive real world testing results, and demonstrate reliable operation of the vehicle at the friction limits on a complex dirt track. We reach speeds above 27 mph (12 m/s) on a dirt track with a 105 foot (32m) long straight using our 1:5 scale test vehicle. A video of these results can be found at https://www.youtube.com/watch?v=5ALIK-z-vUg

cs.RO↗

arXiv2018

Accelerating Imitation Learning with Predictive Models

Sample efficiency is critical in solving real-world reinforcement learning problems, where agent-environment interactions can be costly. Imitation learning from expert advice has proved to be an effective strategy for reducing the number of interactions required to train a policy. Online imitation learning, which interleaves policy evaluation and policy optimization, is a particularly effective technique with provable performance guarantees. In this work, we seek to further accelerate the convergence rate of online imitation learning, thereby making it more sample efficient. We propose two model-based algorithms inspired by Follow-the-Leader (FTL) with prediction: MoBIL-VI based on solving variational inequalities and MoBIL-Prox based on stochastic first-order updates. These two methods leverage a model to predict future gradients to speed up policy learning. When the model oracle is learned online, these algorithms can provably accelerate the best known convergence rate up to an order. Our algorithms can be viewed as a generalization of stochastic Mirror-Prox (Juditsky et al., 2011), and admit a simple constructive FTL-style analysis of performance.

cs.LG↗

arXiv2018

Hierarchical Optimization for Whole-Body Control of Wheeled Inverted Pendulum Humanoids

In this paper, we present a whole-body control framework for Wheeled Inverted Pendulum (WIP) Humanoids. WIP Humanoids are redundant manipulators dynamically balancing themselves on wheels. Characterized by several degrees of freedom, they have the ability to perform several tasks simultaneously, such as balancing, maintaining a body pose, controlling the gaze, lifting a load or maintaining end-effector configuration in operation space. The problem of whole-body control is to enable simultaneous performance of these tasks with optimal participation of all degrees of freedom at specified priorities for each objective. The control also has to obey constraint of angle and torque limits on each joint. The proposed approach is hierarchical with a low level controller for body joints manipulation and a high-level controller that defines center of mass (CoM) targets for the low-level controller to control zero dynamics of the system driving the wheels. The low-level controller plans for shorter horizons while considering more complete dynamics of the system, while the high-level controller plans for longer horizon based on an approximate model of the robot for computational efficiency.

cs.RO↗

arXiv2018

Variational Inference for Stochastic Control of Infinite Dimensional Systems

This paper develops a variational inference framework for control of infinite dimensional stochastic systems. We employ a measure theoretic approach which relies on the generalization of Girsanov's theorem, as well as the relation between relative entropy and free energy. The derived control scheme is applicable to a large class of stochastic, infinite dimensional systems, and can be used for trajectory optimization and model predictive control. Our work opens up new research avenues at the intersection of stochastic control, inference and information theory for dynamical systems described by stochastic partial differential equations.

math.OC↗

arXiv2018

A mean-field game model for homogeneous flocking

Empirically derived continuum models of collective behavior among large populations of dynamic agents are a subject of intense study in several fields, including biology, engineering and finance. We formulate and study a mean-field game model whose behavior mimics an empirically derived non-local homogeneous flocking model for agents with gradient self-propulsion dynamics. The mean-field game framework provides a non-cooperative optimal control description of the behavior of a population of agents in a distributed setting. In this description, each agent's state is driven by optimally controlled dynamics that result in a Nash equilibrium between itself and the population. The optimal control is computed by minimizing a cost that depends only on its own state, and a mean-field term. The agent distribution in phase space evolves under the optimal feedback control policy. We exploit the low-rank perturbative nature of the non-local term in the forward-backward system of equations governing the state and control distributions, and provide a linear stability analysis demonstrating that our model exhibits bifurcations similar to those found in the empirical model. The present work is a step towards developing a set of tools for systematic analysis, and eventually design, of collective behavior of non-cooperative dynamic agents via an inverse modeling approach.

nlin.AO↗

arXiv2017

Safe Learning of Quadrotor Dynamics Using Barrier Certificates

To effectively control complex dynamical systems, accurate nonlinear models are typically needed. However, these models are not always known. In this paper, we present a data-driven approach based on Gaussian processes that learns models of quadrotors operating in partially unknown environments. What makes this challenging is that if the learning process is not carefully controlled, the system will go unstable, i.e., the quadcopter will crash. To this end, barrier certificates are employed for safe learning. The barrier certificates establish a non-conservative forward invariant safe region, in which high probability safety guarantees are provided based on the statistics of the Gaussian Process. A learning controller is designed to efficiently explore those uncertain states and expand the barrier certified safe region based on an adaptive sampling scheme. In addition, a recursive Gaussian Process prediction method is developed to learn the complex quadrotor dynamics in real-time. Simulation results are provided to demonstrate the effectiveness of the proposed approach.

cs.LG↗

arXiv2017

Aggressive Deep Driving: Model Predictive Control with a CNN Cost Model

We present a framework for vision-based model predictive control (MPC) for the task of aggressive, high-speed autonomous driving. Our approach uses deep convolutional neural networks to predict cost functions from input video which are directly suitable for online trajectory optimization with MPC. We demonstrate the method in a high speed autonomous driving scenario, where we use a single monocular camera and a deep convolutional neural network to predict a cost map of the track in front of the vehicle. Results are demonstrated on a 1:5 scale autonomous vehicle given the task of high speed, aggressive driving.

cs.RO↗

arXiv2017

Autonomous Racing with AutoRally Vehicles and Differential Games

Safe autonomous vehicles must be able to predict and react to the drivers around them. Previous control methods rely heavily on pre-computation and are unable to react to dynamic events as they unfold in real-time. In this paper, we extend Model Predictive Path Integral Control (MPPI) using differential game theory and introduce Best-Response MPPI (BR-MPPI) for real-time multi-vehicle interactions. Experimental results are presented using two AutoRally platforms in a racing format with BR-MPPI competing against a skilled human driver at the Georgia Tech Autonomous Racing Facility.

cs.RO↗

arXiv2017

Information Theoretic Model Predictive Control: Theory and Applications to Autonomous Driving

We present an information theoretic approach to stochastic optimal control problems that can be used to derive general sampling based optimization schemes. This new mathematical method is used to develop a sampling based model predictive control algorithm. We apply this information theoretic model predictive control (IT-MPC) scheme to the task of aggressive autonomous driving around a dirt test track, and compare its performance to a model predictive control version of the cross-entropy method.

cs.RO↗

arXiv2017

Stochastic trajectory optimization for mechanical systems with parametric uncertainties

In this paper we develop a novel, discrete-time optimal control framework for mechanical systems with uncertain model parameters. We consider finite-horizon problems where the performance index depends on the statistical moments of the stochastic system. Our approach constitutes an extension of the original Differential Dynamic Programming method and handles uncertainty through generalized Polynomial Chaos (gPC) theory. The developed iterative scheme is capable of controlling the probabilistic evolution of the dynamic system and can be used in planning and control. Moreover, its scalable and fast converging nature play a key role when dealing with complex, high-dimensional problems. Based on Lagrangian mechanics principles, we also prove that Variational Integrators can be designed to properly propagate and linearize the gPC representations of stochastic, forced mechanical systems in discrete time. We utilize this benefit to further improve the efficiency of our trajectory-optimization methodology. Numerical simulations are included to validate the applicability of our approach.

math.OC↗

arXiv2017

Differential Dynamic Programming for time-delayed systems

Trajectory optimization considers the problem of deciding how to control a dynamical system to move along a trajectory which minimizes some cost function. Differential Dynamic Programming (DDP) is an optimal control method which utilizes a second-order approximation of the problem to find the control. It is fast enough to allow real-time control and has been shown to work well for trajectory optimization in robotic systems. Here we extend classic DDP to systems with multiple time-delays in the state. Being able to find optimal trajectories for time-delayed systems with DDP opens up the possibility to use richer models for system identification and control, including recurrent neural networks with multiple timesteps in the state. We demonstrate the algorithm on a two-tank continuous stirred tank reactor. We also demonstrate the algorithm on a recurrent neural network trained to model an inverted pendulum with position information only.

eess.SY↗

arXiv2016

Learning Optimal Control via Forward and Backward Stochastic Differential Equations

In this paper we present a novel sampling-based numerical scheme designed to solve a certain class of stochastic optimal control problems, utilizing forward and backward stochastic differential equations (FBSDEs). By means of a nonlinear version of the Feynman-Kac lemma, we obtain a probabilistic representation of the solution to the nonlinear Hamilton-Jacobi-Bellman equation, expressed in the form of a decoupled system of FBSDEs. This system of FBSDEs can then be simulated by employing linear regression techniques. To enhance the efficiency of the proposed scheme when treating more complex nonlinear systems, we then derive an iterative modification based on Girsanov's theorem on the change of measure, which features importance sampling. The modified scheme is capable of learning the optimal control without requiring an initial guess. We present simulations that validate the algorithm and demonstrate its efficiency in treating nonlinear dynamics.

eess.SY↗

arXiv2016

Sample Efficient Path Integral Control under Uncertainty

We present a data-driven optimal control framework that can be viewed as a generalization of the path integral (PI) control approach. We find iterative feedback control laws without parameterization based on probabilistic representation of learned dynamics model. The proposed algorithm operates in a forward-backward manner which differentiate from other PI-related methods that perform forward sampling to find optimal controls. Our method uses significantly less samples to find optimal controls compared to other approaches within the PI control family that relies on extensive sampling from given dynamics models or trials on physical systems in model-free fashions. In addition, the learned controllers can be generalized to new tasks without re-sampling based on the compositionality theory for the linearly-solvable optimal control framework. We provide experimental results on three different systems and comparisons with state-of-the-art model-based methods to demonstrate the efficiency and generalizability of the proposed framework.

eess.SY↗

arXiv2014

Model-based Path Integral Stochastic Control: A Bayesian Nonparametric Approach

Over the last few years, sampling-based stochastic optimal control (SOC) frameworks have shown impressive performances in reinforcement learning (RL) with applications in robotics. However, such approaches require a large amount of samples from many interactions with the physical systems. To improve learning efficiency, we present a novel model-based and data-driven SOC framework based on path integral formulation and Gaussian processes (GPs). The proposed approach learns explicit and time-varying optimal controls autonomously from limited sampled data. Based on this framework, we propose an iterative control scheme with improved applicability in higher-dimensional and more complex control tasks. We demonstrate the effectiveness and efficiency of the proposed framework using two nontrivial examples. Compared to state-of-the-art RL methods, the proposed framework features superior control learning efficiency.

eess.SY↗