Robust online motion planning with reachable sets

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).

Department dc:contributor.department

Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science.

Grantor dc:publisher

Massachusetts Institute of Technology

Year dc:date.issued

2013

Author dc:creator

• Majumdar, Anirudha

Advisor dc:contributor.advisor

• Russ Tedrake.

• Electrical Engineering and Computer Science.

Statement dc:rights

• M.I.T. theses are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. See provided URL for inquiries about permission.

Licence dc:rights.uri

• http://dspace.mit.edu/handle/1721.1/7582

Language dc:language.iso

eng

Handle dc:identifier.uri

http://hdl.handle.net/1721.1/82404

OAI identifier oai:identifier

oai:dspace.mit.edu:1721.1/82404