Ioannis Exarchos

Ioannis Exarchos, Evangelos A. Theodorou

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.

Marcus A. Pereira, Camilo A. Duarte, Ioannis Exarchos et al.

In this paper, we introduce a novel deep learning based solution to the Powered-Descent Guidance (PDG) problem, grounded in principles of nonlinear Stochastic Optimal Control (SOC) and Feynman-Kac theory. Our algorithm solves the PDG problem by framing it as an $\mathcal{L}^1$ SOC problem for minimum fuel consumption. Additionally, it can handle practically useful control constraints, nonlinear dynamics and enforces state constraints as soft-constraints. This is achieved by building off of recent work on deep Forward-Backward Stochastic Differential Equations (FBSDEs) and differentiable non-convex optimization neural-network layers based on stochastic search. In contrast to previous approaches, our algorithm does not require convexification of the constraints or linearization of the dynamics and is empirically shown to be robust to stochastic disturbances and the initial position of the spacecraft. After training offline, our controller can be activated once the spacecraft is within a pre-specified radius of the landing zone and at a pre-specified altitude i.e., the base of an inverted cone with the tip at the landing zone. We demonstrate empirically that our controller can successfully and safely land all trajectories initialized at the base of this cone while minimizing fuel consumption.

Yifeng Jiang, Michelle Guo, Jiangshan Li et al.

Creating virtual humans with embodied, human-like perceptual and actuation constraints has the promise to provide an integrated simulation platform for many scientific and engineering applications. We present Dynamic and Autonomous Simulated Human (DASH), an embodied virtual human that, given natural language commands, performs grasp-and-stack tasks in a physically-simulated cluttered environment solely using its own visual perception, proprioception, and touch, without requiring human motion data. By factoring the DASH system into a vision module, a language module, and manipulation modules of two skill categories, we can mix and match analytical and machine learning techniques for different modules so that DASH is able to not only perform randomly arranged tasks with a high success rate, but also do so under anthropomorphic constraints and with fluid and diverse motions. The modular design also favors analysis and extensibility to more complex manipulation skills.

Keenon Werling, Dalton Omens, Jeongseok Lee et al.

We present a fast and feature-complete differentiable physics engine, Nimble (nimblephysics.org), that supports Lagrangian dynamics and hard contact constraints for articulated rigid body simulation. Our differentiable physics engine offers a complete set of features that are typically only available in non-differentiable physics simulators commonly used by robotics applications. We solve contact constraints precisely using linear complementarity problems (LCPs). We present efficient and novel analytical gradients through the LCP formulation of inelastic contact that exploit the sparsity of the LCP solution. We support complex contact geometry, and gradients approximating continuous-time elastic collision. We also introduce a novel method to compute complementarity-aware gradients that help downstream optimization tasks avoid stalling in saddle points. We show that an implementation of this combination in an existing physics engine (DART) is capable of a 87x single-core speedup over finite-differencing in computing analytical Jacobians for a single timestep, while preserving all the expressiveness of original DART.

Ioannis Exarchos, Karen Wang, Brian H. Do et al.

Soft robot serial chain manipulators with the capability for growth, stiffness control, and discrete joints have the potential to approach the dexterity of traditional robot arms, while improving safety, lowering cost, and providing an increased workspace, with potential application in home environments. This paper presents an approach for design optimization of such robots to reach specified targets while minimizing the number of discrete joints and thus construction and actuation costs. We define a maximum number of allowable joints, as well as hardware constraints imposed by the materials and actuation available for soft growing robots, and we formulate and solve an optimization problem to output a planar robot design, i.e., the total number of potential joints and their locations along the robot body, which reaches all the desired targets, avoids known obstacles, and maximizes the workspace. We demonstrate a process to rapidly construct the resulting soft growing robot design. Finally, we use our algorithm to evaluate the ability of this design to reach new targets and demonstrate the algorithm's utility as a design tool to explore robot capabilities given various constraints and objectives.

Tianrong Chen, Ziyi Wang, Ioannis Exarchos et al.

In this paper we present a scalable deep learning framework for finding Markovian Nash Equilibria in multi-agent stochastic games using fictitious play. The motivation is inspired by theoretical analysis of Forward Backward Stochastic Differential Equations (FBSDE) and their implementation in a deep learning setting, which is the source of our algorithm's sample efficiency improvement. By taking advantage of the permutation-invariant property of agents in symmetric games, the scalability and performance is further enhanced significantly. We showcase superior performance of our framework over the state-of-the-art deep fictitious play algorithm on an inter-bank lending/borrowing problem in terms of multiple metrics. More importantly, our approach scales up to 3000 agents in simulation, a scale which, to the best of our knowledge, represents a new state-of-the-art. We also demonstrate the applicability of our framework in robotics on a belief space autonomous racing problem.

Ioannis Exarchos, Yifeng Jiang, Wenhao Yu et al.

Transferring reinforcement learning policies trained in physics simulation to the real hardware remains a challenge, known as the "sim-to-real" gap. Domain randomization is a simple yet effective technique to address dynamics discrepancies across source and target domains, but its success generally depends on heuristics and trial-and-error. In this work we investigate the impact of randomized parameter selection on policy transferability across different types of domain discrepancies. Contrary to common practice in which kinematic parameters are carefully measured while dynamic parameters are randomized, we found that virtually randomizing kinematic parameters (e.g., link lengths) during training in simulation generally outperforms dynamic randomization. Based on this finding, we introduce a new domain adaptation algorithm that utilizes simulated kinematic parameters variation. Our algorithm, Multi-Policy Bayesian Optimization, trains an ensemble of universal policies conditioned on virtual kinematic parameters and efficiently adapts to the target environment using a limited number of target domain rollouts. We showcase our findings on a simulated quadruped robot in five different target environments covering different aspects of domain discrepancies.

Marcus Aloysius Pereira, Ziyi Wang, Ioannis Exarchos et al.

This paper introduces a new formulation for stochastic optimal control and stochastic dynamic optimization that ensures safety with respect to state and control constraints. The proposed methodology brings together concepts such as Forward-Backward Stochastic Differential Equations, Stochastic Barrier Functions, Differentiable Convex Optimization and Deep Learning. Using the aforementioned concepts, a Neural Network architecture is designed for safe trajectory optimization in which learning can be performed in an end-to-end fashion. Simulations are performed on three systems to show the efficacy of the proposed methodology.

Ioannis Exarchos, Marcus A. Pereira, Ziyi Wang et al.

In this work we propose the use of adaptive stochastic search as a building block for general, non-convex optimization operations within deep neural network architectures. Specifically, for an objective function located at some layer in the network and parameterized by some network parameters, we employ adaptive stochastic search to perform optimization over its output. This operation is differentiable and does not obstruct the passing of gradients during backpropagation, thus enabling us to incorporate it as a component in end-to-end learning. We study the proposed optimization module's properties and benchmark it against two existing alternatives on a synthetic energy-based structured prediction task, and further showcase its use in stochastic optimal control applications.

Ziyi Wang, Keuntaek Lee, Marcus A. Pereira et al.

This paper presents a novel approach to numerically solve stochastic differential games for nonlinear systems. The proposed approach relies on the nonlinear Feynman-Kac theorem that establishes a connection between parabolic deterministic partial differential equations and forward-backward stochastic differential equations. Using this theorem the Hamilton-Jacobi-Isaacs partial differential equation associated with differential games is represented by a system of forward-backward stochastic differential equations. Numerical solution of the aforementioned system of stochastic differential equations is performed using importance sampling and a Long-Short Term Memory recurrent neural network, which is trained in an offline fashion. The resulting algorithm is tested on two example systems in simulation and compared against the standard risk neutral stochastic optimal control formulations.

Marcus Pereira, Ziyi Wang, Ioannis Exarchos et al.

In this paper we propose a new methodology for decision-making under uncertainty using recent advancements in the areas of nonlinear stochastic optimal control theory, applied mathematics, and machine learning. Grounded on the fundamental relation between certain nonlinear partial differential equations and forward-backward stochastic differential equations, we develop a control framework that is scalable and applicable to general classes of stochastic systems and decision-making problem formulations in robotics and autonomy. The proposed deep neural network architectures for stochastic control consist of recurrent and fully connected layers. The performance and scalability of the aforementioned algorithm are investigated in three non-linear systems in simulation with and without control constraints. We conclude with a discussion on future directions and their implications to robotics.