Robust online motion planning with reachable sets

Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2013.Cataloged from PDF version of thesis.Includes bibliographical references (p. 51-55).In this thesis we consider the problem of generating motion plans for a nonlinear dynamical system that are guaranteed to succeed despite uncertainty in the environment, parametric model uncertainty, disturbances, and/or errors in state estimation. Furthermore, we consider the case where these plans must be generated online, because constraints such as obstacles in the environment may not be known until they are perceived (with a noisy sensor) at runtime. Previous work on feedback motion planning for nonlinear systems was limited to offline planning due to the computational cost of safety verification. Here we augment the traditional trajectory library approach by designing locally stabilizing controllers for each nominal trajectory in the library and providing guarantees on the resulting closed loop systems. We leverage sums-of-squares programming to design these locally stabilizing controllers by explicitly attempting to minimize the size of the worst case reachable set of the closed-loop system subjected to bounded disturbances and uncertainty. The reachable sets associated with each trajectory in the library can be thought of as "funnels" that the system is guaranteed to remain within. The resulting funnel library is then used to sequentially compose motion plans at runtime while ensuring the safety of the robot. A major advantage of the work presented here is that by explicitly taking into account the effect of uncertainty, the robot can evaluate motion plans based on how vulnerable they are to disturbances. We demonstrate our method on a simulation of a plane flying through a two dimensional forest of polygonal trees with parametric uncertainty and disturbances in the form of a bounded "cross-wind". We further validate our approach by carefully evaluating the guarantees on invariance provided by funnels on two challenging underactuated systems (the "Acrobot" and a small-sized airplane).by Anirudha Majumdar.S.M

SOTER: A Runtime Assurance Framework for Programming Safe Robotics Systems

The recent drive towards achieving greater autonomy and intelligence in robotics has led to high levels of complexity. Autonomous robots increasingly depend on third party off-the-shelf components and complex machine-learning techniques. This trend makes it challenging to provide strong design-time certification of correct operation. To address these challenges, we present SOTER, a robotics programming framework with two key components: (1) a programming language for implementing and testing high-level reactive robotics software and (2) an integrated runtime assurance (RTA) system that helps enable the use of uncertified components, while still providing safety guarantees. SOTER provides language primitives to declaratively construct a RTA module consisting of an advanced, high-performance controller (uncertified), a safe, lower-performance controller (certified), and the desired safety specification. The framework provides a formal guarantee that a well-formed RTA module always satisfies the safety specification, without completely sacrificing performance by using higher performance uncertified components whenever safe. SOTER allows the complex robotics software stack to be constructed as a composition of RTA modules, where each uncertified component is protected using a RTA module. To demonstrate the efficacy of our framework, we consider a real-world case-study of building a safe drone surveillance system. Our experiments both in simulation and on actual drones show that the SOTER-enabled RTA ensures the safety of the system, including when untrusted third-party components have bugs or deviate from the desired behavior

Some Applications of Polynomial Optimization in Operations Research and Real-Time Decision Making

We demonstrate applications of algebraic techniques that optimize and certify polynomial inequalities to problems of interest in the operations research and transportation engineering communities. Three problems are considered: (i) wireless coverage of targeted geographical regions with guaranteed signal quality and minimum transmission power, (ii) computing real-time certificates of collision avoidance for a simple model of an unmanned vehicle (UV) navigating through a cluttered environment, and (iii) designing a nonlinear hovering controller for a quadrotor UV, which has recently been used for load transportation. On our smaller-scale applications, we apply the sum of squares (SOS) relaxation and solve the underlying problems with semidefinite programming. On the larger-scale or real-time applications, we use our recently introduced "SDSOS Optimization" techniques which result in second order cone programs. To the best of our knowledge, this is the first study of real-time applications of sum of squares techniques in optimization and control. No knowledge in dynamics and control is assumed from the reader

Robust Control of Nonlinear Systems with applications to Aerial Manipulation and Self Driving Cars

This work considers the problem of planning and control of robots in an environment with obstacles and external disturbances. The safety of robots is harder to achieve when planning in such uncertain environments. We describe a robust control scheme that combines three key components: system identification, uncertainty propagation, and trajectory optimization. Using this control scheme we tackle three problems. First, we develop a Nonlinear Model Predictive Controller (NMPC) for articulated rigid bodies and apply it to an aerial manipulation system to grasp object mid-air. Next, we tackle the problem of obstacle avoidance under unknown external disturbances. We propose two approaches, the first approach using adaptive NMPC with open- loop uncertainty propagation and the second approach using Tube NMPC. After that, we introduce dynamic models which use Artificial Neural Networks (ANN) and combine them with NMPC to control a ground vehicle and an aerial manipulation system. Finally, we introduce a software framework for integrating the above algorithms to perform complex tasks. The software framework provides users with the ability to design systems that are robust to control and hardware failures where preventive action is taken before-hand. The framework also allows for safe testing of control and task logic in simulation before evaluating on the real robot. The software framework is applied to an aerial manipulation system to perform a package sorting task, and extensive experiments demonstrate the ability of the system to recover from failures. In addition to robust control, we present two related control problems. The first problem pertains to designing an obstacle avoidance controller for an underactuated system that is Lyapunov stable. We extend a standard gyroscopic obstacle avoidance controller to be applicable to an underactuated system. The second problem addresses the navigation of an Unmanned Ground Vehicle (UGV) on an unstructured terrain. We propose using NMPC combined with a high fidelity physics engine to generate a reference trajectory that is dynamically feasible and accounts for unsafe areas in the terrain

Envelope-Aware Flight Management for Loss of Control Prevention Given Rudder Jam

Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/143011/1/1.G000252.pd