Chance-Constrained Trajectory Optimization for Safe Exploration and Learning of Nonlinear Systems

Learning-based control algorithms require data collection with abundant supervision for training. Safe exploration algorithms ensure the safety of this data collection process even when only partial knowledge is available. We present a new approach for optimal motion planning with safe exploration that integrates chance-constrained stochastic optimal control with dynamics learning and feedback control. We derive an iterative convex optimization algorithm that solves an \underline{Info}rmation-cost \underline{S}tochastic \underline{N}onlinear \underline{O}ptimal \underline{C}ontrol problem (Info-SNOC). The optimization objective encodes both optimal performance and exploration for learning, and the safety is incorporated as distributionally robust chance constraints. The dynamics are predicted from a robust regression model that is learned from data. The Info-SNOC algorithm is used to compute a sub-optimal pool of safe motion plans that aid in exploration for learning unknown residual dynamics under safety constraints. A stable feedback controller is used to execute the motion plan and collect data for model learning. We prove the safety of rollout from our exploration method and reduction in uncertainty over epochs, thereby guaranteeing the consistency of our learning method. We validate the effectiveness of Info-SNOC by designing and implementing a pool of safe trajectories for a planar robot. We demonstrate that our approach has higher success rate in ensuring safety when compared to a deterministic trajectory optimization approach.Comment: Submitted to RA-L 2020, review-

Applied Interval Analysis with Examples in Parameter and State Estimation, Robust Control and Robotics

http://www.springer.com/engineering/computational+intelligence+and+complexity/book/978-1-4471-1067-5This book is about guaranteed numerical methods based on interval analysis for approximating sets, and about the application of these methods to vast classes of engineering problems. Guaranteed means here that inner and outer approximations of the sets of interest are obtained, which can be made as precise as desired, at the cost of increasing the computational effort. It thus becomes possible to achieve tasks still thought by many to be out of the reach of numerical methods, such as finding all solutions of sets of non-linear equations and inequality or all global optimizers of possibly multi-modal criteria. The basic methodology is explained as simply as possible, in a concrete and readily applicable way, with a large number of figures and illustrative examples. Some of the techniques reported appear in book format for the first time. The ability of the approach advocated here to solve non-trivial engineering problems is demonstrated through examples drawn from the fields of parameter and state estimation, robust control and robotics. Enough detail is provided to allow readers with other applications in mind to grasp their significance. An in-depth treatment of implementation issues facilitates the understanding and use of freely available software that makes interval computation about as easy as computation with floating-point numbers. The reader is even given the basic information needed to build his or her own C++ interval library

Towards Robust Methods for Indoor Localization using Interval Data

International audienceIndoor localization has gained an increase in interest recently because of the wide range of services it may provide by using data from the Internet of Things. Notwithstanding the large variety of techniques available, indoor localization methods usually show insufficient accuracy and robustness performance because of the noisy nature of the raw data used. In this paper, we investigate ways to work explicitly with range of data, i.e., interval data, instead of point data in the localization algorithms, thus providing a set-theoretic method that needs no probabilistic assumption. We will review state-of-the-art infrastructure-based localization methods that work with interval data. Then, we will show how to extend the existing infrastructure-less localization techniques to allow explicit computation with interval data. The preliminary evaluation of our new method shows that it provides smoother and more consistent localization estimates than state-of-the-art methods

A New Approach to Time-Optimal Path Parameterization based on Reachability Analysis

Time-Optimal Path Parameterization (TOPP) is a well-studied problem in robotics and has a wide range of applications. There are two main families of methods to address TOPP: Numerical Integration (NI) and Convex Optimization (CO). NI-based methods are fast but difficult to implement and suffer from robustness issues, while CO-based approaches are more robust but at the same time significantly slower. Here we propose a new approach to TOPP based on Reachability Analysis (RA). The key insight is to recursively compute reachable and controllable sets at discretized positions on the path by solving small Linear Programs (LPs). The resulting algorithm is faster than NI-based methods and as robust as CO-based ones (100% success rate), as confirmed by extensive numerical evaluations. Moreover, the proposed approach offers unique additional benefits: Admissible Velocity Propagation and robustness to parametric uncertainty can be derived from it in a simple and natural way.Comment: 15 pages, 9 figure

Chance-Constrained Trajectory Optimization for Safe Exploration and Learning of Nonlinear Systems

Learning-based control algorithms require data collection with abundant supervision for training. Safe exploration algorithms ensure the safety of this data collection process even when only partial knowledge is available. We present a new approach for optimal motion planning with safe exploration that integrates chance-constrained stochastic optimal control with dynamics learning and feedback control. We derive an iterative convex optimization algorithm that solves an Information-cost Stochastic Nonlinear Optimal Control problem (Info-SNOC). The optimization objective encodes control cost for performance and exploration cost for learning, and the safety is incorporated as distributionally robust chance constraints. The dynamics are predicted from a robust regression model that is learned from data. The Info-SNOC algorithm is used to compute a sub-optimal pool of safe motion plans that aid in exploration for learning unknown residual dynamics under safety constraints. A stable feedback controller is used to execute the motion plan and collect data for model learning. We prove the safety of rollout from our exploration method and reduction in uncertainty over epochs, thereby guaranteeing the consistency of our learning method. We validate the effectiveness of Info-SNOC by designing and implementing a pool of safe trajectories for a planar robot. We demonstrate that our approach has higher success rate in ensuring safety when compared to a deterministic trajectory optimization approach

Anchor-Based Localization Using Distributed Interval Contractors

This paper presents a new method to solve anchor-based distributed localization problems. This method is based on a generic algorithm using interval contractors. In the theoretical part, we detail a new formalism for distributed contractors. This formalism is used to demonstrate that our distributed algorithm converges to the same fixed point than the centralized algorithm. Then, we use this distributed algorithm to solve an anchor-based distributed localization problem in a Wireless Sensor Network (WSN)