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

Direct Policy Optimization using Deterministic Sampling and Collocation

We present an approach for approximately solving discrete-time stochastic optimal-control problems by combining direct trajectory optimization, deterministic sampling, and policy optimization. Our feedback motion-planning algorithm uses a quasi-Newton method to simultaneously optimize a reference trajectory, a set of deterministically chosen sample trajectories, and a parameterized policy. We demonstrate that this approach exactly recovers LQR policies in the case of linear dynamics, quadratic objective, and Gaussian disturbances. We also demonstrate the algorithm on several nonlinear, underactuated robotic systems to highlight its performance and ability to handle control limits, safely avoid obstacles, and generate robust plans in the presence of unmodeled dynamics.Comment: revisions for RA-L 202

Spacecraft/Rover Hybrids for the Exploration of Small Solar System Bodies

This study investigated a mission architecture that allows the systematic and affordable in-situ exploration of small solar system bodies, such as asteroids, comets, and Martian moons (Figure 1). The architecture relies on the novel concept of spacecraft/rover hybrids,which are surface mobility platforms capable of achieving large surface coverage (by attitude controlled hops, akin to spacecraft flight), fine mobility (by tumbling), and coarse instrument pointing (by changing orientation relative to the ground) in the low-gravity environments(micro-g to milli-g) of small bodies. The actuation of the hybrids relies on spinning three internal flywheels. Using a combination of torques, the three flywheel motors can produce a reaction torque in any orientation without additional moving parts. This mobility concept allows all subsystems to be packaged in one sealed enclosure and enables the platforms to be minimalistic. The hybrids would be deployed from a mother spacecraft, which would act as a communication relay to Earth and would aid the in-situ assets with tasks such as localization and navigation (Figure 1). The hybrids are expected to be more capable and affordable than wheeled or legged rovers, due to their multiple modes of mobility (both hopping and tumbling), and have simpler environmental sealing and thermal management (since all components are sealed in one enclosure, assuming non-deployable science instruments). In summary, this NIAC Phase II study has significantly increased the TRL (Technology Readiness Level) of the mobility and autonomy subsystems of spacecraft/rover hybrids, and characterized system engineering aspects in the context of a reference mission to Phobos. Future studies should focus on improving the robustness of the autonomy module and further refine system engineering aspects, in view of opportunities for technology infusion