arXiv subjects

Aaron D. Ames

Publications and source records attributed to Aaron D. Ames.

At least 253 records · Page 14Linked to original sources

arXiv2020

Partially Observable Games for Secure Autonomy

Technology development efforts in autonomy and cyber-defense have been evolving independently of each other, over the past decade. In this paper, we report our ongoing effort to integrate these two presently distinct areas into a single framework. To this end, we propose the two-player partially observable stochastic game formalism to capture both high-level autonomous mission planning under uncertainty and adversarial decision making subject to imperfect information. We show that synthesizing sub-optimal strategies for such games is possible under finite-memory assumptions for both the autonomous decision maker and the cyber-adversary. We then describe an experimental testbed to evaluate the efficacy of the proposed framework.

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arXiv2019

Towards Variable Assistance for Lower Body Exoskeletons

This paper presents and experimentally demonstrates a novel framework for variable assistance on lower body exoskeletons, based upon safety-critical control methods. Existing work has shown that providing some freedom of movement around a nominal gait, instead of rigidly following it, accelerates the spinal learning process of people with a walking impediment when using a lower body exoskeleton. With this as motivation, we present a method to accurately control how much a subject is allowed to deviate from a given gait while ensuring robustness to patient perturbation. This method leverages control barrier functions to force certain joints to remain inside predefined trajectory tubes in a minimally invasive way. The effectiveness of the method is demonstrated experimentally with able-bodied subjects and the Atalante lower body exoskeleton.

cs.RO↗

arXiv2019

Intermittent Connectivity for Exploration in Communication-Constrained Multi-Agent Systems

Motivated by exploration of communication-constrained underground environments using robot teams, we study the problem of planning for intermittent connectivity in multi-agent systems. We propose a novel concept of information-consistency to handle situations where the plan is not initially known by all agents, and suggest an integer linear program for synthesizing information-consistent plans that also achieve auxiliary goals. Furthermore, inspired by network flow problems we propose a novel way to pose connectivity constraints that scales much better than previous methods. In the second part of the paper we apply these results in an exploration setting, and propose a clustering method that separates a large exploration problem into smaller problems that can be solved independently. We demonstrate how the resulting exploration algorithm is able to coordinate a team of ten agents to explore a large environment.

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arXiv2019

Duality between density function and value function with applications in constrained optimal control and Markov Decision Process

Density function describes the density of states in the state space of a dynamic system or a Markov Decision Process (MDP). Its evolution follows the Liouville equation. We show that the density function is the dual of the value function in the optimal control problems. By utilizing the duality, constraints that are hard to enforce in the primal value function optimization such as safety constraints in robot navigation, traffic capacity constraints in traffic flow control can be posed on the density function, and the constrained optimal control problem can be solved with a primal-dual algorithm that alternates between the primal and dual optimization. The primal optimization follows the standard optimal control algorithm with a perturbation term generated by the density constraint, and the dual problem solves the Liouville equation to get the density function under a fixed control strategy and updates the perturbation term. Moreover, the proposed method can be extended to the case with exogenous disturbance, and guarantee robust safety under the worst-case disturbance. We apply the proposed method to three examples, a robot navigation problem and a traffic control problem in sim, and a segway control problem with experiment.

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arXiv2019

Distributed Feedback Controllers for Stable Cooperative Locomotion of Quadrupedal Robots: A Virtual Constraint Approach

This paper aims to develop distributed feedback control algorithms that allow cooperative locomotion of quadrupedal robots which are coupled to each other by holonomic constraints. These constraints can arise from collaborative manipulation of objects during locomotion. In addressing this problem, the complex hybrid dynamical models that describe collaborative legged locomotion are studied. The complex periodic orbits (i.e., gaits) of these sophisticated and high-dimensional hybrid systems are investigated. We consider a set of virtual constraints that stabilizes locomotion of a single agent. The paper then generates modified and local virtual constraints for each agent that allow stable collaborative locomotion. Optimal distributed feedback controllers, based on nonlinear control and quadratic programming, are developed to impose the local virtual constraints. To demonstrate the power of the analytical foundation, an extensive numerical simulation for cooperative locomotion of two quadrupedal robots with robotic manipulators is presented. The numerical complex hybrid model has 64 continuous-time domains, 192 discrete-time transitions, 96 state variables, and 36 control inputs.

math.OC↗

arXiv2019

Adaptive Safety with Control Barrier Functions

Adaptive Control Lyapunov Functions (aCLFs) were introduced 20 years ago, and provided a Lyapunov-based methodology for stabilizing systems with parameter uncertainty. The goal of this paper is to revisit this classic formulation in the context of safety-critical control. This will motivate a variant of aCLFs in the context of safety: adaptive Control Barrier Functions (aCBFs). Our proposed approach adaptively achieves safety by keeping the systems state within a safe set even in the presence of parametric model uncertainty. We unify aCLFs and aCBFs into a single control methodology for systems with uncertain parameters in the context of a Quadratic Program (QP) based framework. We validate the ability of this unified framework to achieve stability and safety in an adaptive cruise control (ACC) simulation.

eess.SY↗

arXiv2019

Optimal Safe Controller Synthesis: A Density Function Approach

This paper considers the synthesis of optimal safe controllers based on density functions. We present an algorithm for robust constrained optimal control synthesis using the duality relationship between the density function and the value function. The density function follows the Liouville equation and is the dual of the value function, which satisfies Bellman's optimality principle. Thanks to density functions, constraints over the distribution of states, such as safety constraints, can be posed straightforwardly in an optimal control problem. The constrained optimal control problem is then solved with a primal-dual algorithm. This formulation is extended to the case with external disturbances, and we show that the robust constrained optimal control can be solved with a modified primal-dual algorithm. We apply this formulation to the problem of finding the optimal safe controller that minimizes the cumulative intervention. An adaptive cruise control (ACC) example is used to demonstrate the efficacy of the proposed, wherein we compare the result of the density function approach with the conventional control barrier function (CBF) method.

math.OC↗

arXiv2019

Risk-Averse Planning Under Uncertainty

We consider the problem of designing policies for partially observable Markov decision processes (POMDPs) with dynamic coherent risk objectives. Synthesizing risk-averse optimal policies for POMDPs requires infinite memory and thus undecidable. To overcome this difficulty, we propose a method based on bounded policy iteration for designing stochastic but finite state (memory) controllers, which takes advantage of standard convex optimization methods. Given a memory budget and optimality criterion, the proposed method modifies the stochastic finite state controller leading to sub-optimal solutions with lower coherent risk.

cs.RO↗

arXiv2019

Improved Performance on Moving-Mass Hopping Robots with Parallel Elasticity

Robotic Hopping is challenging from the perspective of both modeling the dynamics as well as the mechanical design due to the short period of ground contact in which to actuate on the world. Previous work has demonstrated stable hopping on a moving-mass robot, wherein a single spring was utilized below the body of the robot. This paper finds that the addition of a spring in parallel to the actuator greatly improves the performance of moving mass hopping robots. This is demonstrated through the design of a novel one-dimensional hopping robot. For this robot, a rigorous trajectory optimization method is developed using hybrid systems models with experimentally tuned parameters. Simulation results are used to study the effects of a parallel spring on energetic efficiency, stability and hopping effort. We find that the double-spring model had 2.5x better energy efficiency than the single-spring model, and was able to hop using 40% less peak force from the actuator. Furthermore, the double-spring model produces stable hopping without the need for stabilizing controllers. These concepts are demonstrated experimentally on a novel hopping robot, wherein hop heights up to 40cm were achieved.

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arXiv2019

Stabilization of Exoskeletons through Active Ankle Compensation

This paper presents an active stabilization method for a fully actuated lower-limb exoskeleton. The method was tested on the exoskeleton ATALANTE, which was designed and built by the French start-up company Wandercraft. The main objective of this paper is to present a practical method of realizing more robust walking on hardware through active ankle compensation. The nominal gait was generated through the hybrid zero dynamic framework. The ankles are individually controlled to establish three main directives; (1) keeping the non-stance foot parallel to the ground, (2) maintaining rigid contact between the stance foot and the ground, and (3) closing the loop on pelvis orientation to achieve better tracking. Each individual component of this method was demonstrated separately to show each component's contribution to stability. The results showed that the ankle controller was able to experimentally maintain static balance in the sagittal plane while the exoskeleton was balanced on one leg, even when disturbed. The entire ankle controller was then also demonstrated on crutch-less dynamic walking. During testing, an anatomically correct manikin was placed in the exoskeleton, in lieu of a paraplegic patient. The pitch of the pelvis of the exoskeleton-manikin system was shown to track the gait trajectory better when ankle compensation was used. Overall, active ankle compensation was demonstrated experimentally to improve balance in the sagittal plane of the exoskeleton manikin system and points to an improved practical approach for stable walking.

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arXiv2019

First Steps Towards Full Model Based Motion Planning and Control of Quadrupeds: A Hybrid Zero Dynamics Approach

The hybrid zero dynamics (HZD) approach has become a powerful tool for the gait planning and control of bipedal robots. This paper aims to extend the HZD methods to address walking, ambling and trotting behaviors on a quadrupedal robot. We present a framework that systematically generates a wide range of optimal trajectories and then provably stabilizes them for the full-order, nonlinear and hybrid dynamical models of quadrupedal locomotion. The gait planning is addressed through a scalable nonlinear programming using direct collocation and HZD. The controller synthesis for the exponential stability is then achieved through the Poincaré sections analysis. In particular, we employ an iterative optimization algorithm involving linear and bilinear matrix inequalities (LMIs and BMIs) to design HZD-based controllers that guarantee the exponential stability of the fixed points for the Poincaré return map. The power of the framework is demonstrated through gait generation and HZD-based controller synthesis for an advanced quadruped robot, ---Vision 60, with 36 state variables and 12 control inputs. The numerical simulations as well as real world experiments confirm the validity of the proposed framework.

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arXiv2019

Safe Policy Synthesis in Multi-Agent POMDPs via Discrete-Time Barrier Functions

A multi-agent partially observable Markov decision process (MPOMDP) is a modeling paradigm used for high-level planning of heterogeneous autonomous agents subject to uncertainty and partial observation. Despite their modeling efficiency, MPOMDPs have not received significant attention in safety-critical settings. In this paper, we use barrier functions to design policies for MPOMDPs that ensure safety. Notably, our method does not rely on discretization of the belief space, or finite memory. To this end, we formulate sufficient and necessary conditions for the safety of a given set based on discrete-time barrier functions (DTBFs) and we demonstrate that our formulation also allows for Boolean compositions of DTBFs for representing more complicated safe sets. We show that the proposed method can be implemented online by a sequence of one-step greedy algorithms as a standalone safe controller or as a safety-filter given a nominal planning policy. We illustrate the efficiency of the proposed methodology based on DTBFs using a high-fidelity simulation of heterogeneous robots.

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arXiv2019

Dynamic Walking with Compliance on a Cassie Bipedal Robot

The control of bipedal robotic walking remains a challenging problem in the domains of computation and experiment, due to the multi-body dynamics and various sources of uncertainty. In recent years, there has been a rising trend towards model reduction and the design of intuitive controllers to overcome the gap between assumed model and reality. Despite its viability in practical implementation, this local representation of true dynamics naturally indicate limited scalibility towards more dynamical behaviors. With the goal of moving towards increasingly dynamic behaviors, we leverage the detailed full body dynamics to generate controllers for the robotic system which utilizes compliant elements in the passive dynamics. In this process, we present a feasible computation method that yields walking trajectories for a highly complex robotic system. Direct implementation of these results on physical hardware is also performed with minimal tuning and heuristics. We validate the suggested method by applying a consistent control scheme across simulation, optimization and experiment, the result is that the bipedal robot Cassie walks over a variety of indoor and outdoor terrains reliably.

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arXiv2019

Hierarchical and Safe Motion Control for Cooperative Locomotion of Robotic Guide Dogs and Humans: A Hybrid Systems Approach

This paper presents a hierarchical control strategy based on hybrid systems theory, nonlinear control, and safety-critical systems to enable cooperative locomotion of robotic guide dogs and visually impaired people. We address high-dimensional and complex hybrid dynamical models that represent collaborative locomotion. At the high level of the control scheme, local and nonlinear baseline controllers, based on the virtual constraints approach, are designed to induce exponentially stable dynamic gaits. The baseline controller for the leash is assumed to be a nonlinear controller that keeps the human in a safe distance from the dog while following it. At the lower level, a real-time quadratic programming (QP) is solved for modifying the baseline controllers of the robot as well as the leash to avoid obstacles. In particular, the QP framework is set up based on control barrier functions (CBFs) to compute optimal control inputs that guarantee safety while being close to the baseline controllers. The stability of the complex periodic gaits is investigated through the Poincare return map. To demonstrate the power of the analytical foundation, the control algorithms are transferred into an extensive numerical simulation of a complex model that represents cooperative locomotion of a quadrupedal robot, referred to as Vision 60, and a human model. The complex model has 16 continuous-time domains with 60 state variables and 20 control inputs.

math.OC↗

arXiv2019

Control Barrier Functions: Theory and Applications

This paper provides an introduction and overview of recent work on control barrier functions and their use to verify and enforce safety properties in the context of (optimization based) safety-critical controllers. We survey the main technical results and discuss applications to several domains including robotic systems.

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arXiv2019

A Control Lyapunov Perspective on Episodic Learning via Projection to State Stability

The goal of this paper is to understand the impact of learning on control synthesis from a Lyapunov function perspective. In particular, rather than consider uncertainties in the full system dynamics, we employ Control Lyapunov Functions (CLFs) as low-dimensional projections. To understand and characterize the uncertainty that these projected dynamics introduce in the system, we introduce a new notion: Projection to State Stability (PSS). PSS can be viewed as a variant of Input to State Stability defined on projected dynamics, and enables characterizing robustness of a CLF with respect to the data used to learn system uncertainties. We use PSS to bound uncertainty in affine control, and demonstrate that a practical episodic learning approach can use PSS to characterize uncertainty in the CLF for robust control synthesis.

eess.SY↗

arXiv2019

Episodic Learning with Control Lyapunov Functions for Uncertain Robotic Systems

Many modern nonlinear control methods aim to endow systems with guaranteed properties, such as stability or safety, and have been successfully applied to the domain of robotics. However, model uncertainty remains a persistent challenge, weakening theoretical guarantees and causing implementation failures on physical systems. This paper develops a machine learning framework centered around Control Lyapunov Functions (CLFs) to adapt to parametric uncertainty and unmodeled dynamics in general robotic systems. Our proposed method proceeds by iteratively updating estimates of Lyapunov function derivatives and improving controllers, ultimately yielding a stabilizing quadratic program model-based controller. We validate our approach on a planar Segway simulation, demonstrating substantial performance improvements by iteratively refining on a base model-free controller.

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arXiv2018

Dynamic Walking on Slippery Surfaces: Demonstrating Stable Bipedal Gaits with Planned Ground Slippage

Dynamic bipedal robot locomotion has achieved remarkable success due in part to recent advances in trajectory generation and nonlinear control for stabilization. A key assumption utilized in both theory and experiments is that the robot's stance foot always makes no-slip contact with the ground, including at impacts. This assumption breaks down on slippery low-friction surfaces, as commonly encountered in outdoor terrains, leading to failure and loss of stability. In this work, we extend the theoretical analysis and trajectory optimization to account for stick-slip transitions at point foot contact using Coulomb's friction law. Using AMBER-3M planar biped robot as an experimental platform, we demonstrate for the first time a slippery walking gait which can be stabilized successfully both on a lubricated surface and on a rough no-slip surface. We also study the influence of foot slippage on reducing the mechanical cost of transport, and compare energy efficiency in both numerical simulations and experimental measurements.

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