LQR-trees: Feedback Motion Planning via Sums-of-Squares Verification

By Russ Tedrake, Ian R. Manchester, Mark M. Tobenkin, John W. Roberts. 2010

520 citations recorded by the source corpus.

Subfields: Computational Theory and Mathematics, Computer Vision and Pattern Recognition, Control and Systems Engineering

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Citations in the corpus

Certified Defenses against Adversarial Examples (2018, methodology): “In robotics, certificates of stability are routinely used both for safety verification (Lygeros et al., 1999; Mitchell et al., 2005) and controller synthesis (Başar & Bernhard, 2008; Tedrake et al., 2010).”
Verifiable Reinforcement Learning via Policy Extraction (2018, methodology): “Second, we focus on verifying stability locally around 0; there has been work extending the approach we use by “patching together” different regions of attraction [32].”
Sampling-based algorithms for optimal motion planning (2011, background): “These algorithms proved to be very effective for motion planning in high-dimensional spaces, and attracted significant attention over the last decade, including very recent work (see, e.g., Stilman et al. 2007; Berenson et al. 2008; Yershova and LaValle 2008; Prentice and Roy 2009; Koyuncu et al. 20”
Invariant Funnels around Trajectories using Sum-of-Squares Programming (2010, methodology): “This work is motivated by new algorithms for nonlinear control design wherein the controller is constructed from a tree of ﬁnite-time trajectories, each locally stabilized and all leading to a certain goal point (see Tedrake et al. (2010)).”
Hamilton-Jacobi reachability: A brief overview and recent advances (2017, methodology): “In addition, methods that utilize semideﬁnite programming to search for Lyapunov functions can be used to verify safety [31], [32].”
Intelligent Autonomous Things on the Battlefield (2019, unknown): “…advances in planning have allowed us to sidestep the challenge of thinking through all of the compounding choices by substituting enumeration with sampling and relying on the mechanisms of probability to give us a path to convergence and optimality (Karaman and Frazzoli, 2011; Tedrake et. al.”
Models, feedback control, and open problems of 3D bipedal robotic walking (2014, methodology): “Important initial work in hybrid systems is available in [203, 110].”
A Review of Robot Learning for Manipulation: Challenges, Representations, and Algorithms (2019, background): “LQRbased controllers have also been chained together as LQRtrees, allowing coverage of a larger, more complex space [379].”