Funnel libraries for real-time robust feedback motion planning

By Anirudha Majumdar, Russ Tedrake. 2016

405 citations recorded by the source corpus.

We consider the problem of generating motion plans for a robot that are guaranteed to succeed despite uncertainty in the environment, parametric model uncertainty, and disturbances. Furthermore, we consider scenarios where these plans must be generated in real time, because constraints such as obstacles in the environment may not be known until they are perceived (with a noisy sensor) at runtime. Our approach is to pre-compute a library of “funnels” along different maneuvers of the system that the state is guaranteed to remain within (despite bounded disturbances) when the feedback controller corresponding to the maneuver is executed. We leverage powerful computational machinery from convex optimization (sums-of-squares programming in particular) to compute these funnels. 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 and validate our method using extensive hardware experiments on a small fixed-wing airplane avoiding obstacles at high speed (~12 mph), along with thorough simulation experiments of ground vehicle and quadrotor models navigating through cluttered environments. To our knowledge, these demonstrations constitute one of the first examples of provably safe and robust control for robotic systems with complex nonlinear dynamics that need to plan in real time in environments with complex geometric constraints.

Subfields: Computer Vision and Pattern Recognition, Control and Systems Engineering

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Citations in the corpus

Uncertainty-Aware Reinforcement Learning for Collision Avoidance (2017, background): “Methods based on reachability provide appealing theoretical guarantees, but cannot cope with rich sensory input and are often difﬁcult to scale to high-dimensional systems [23, 17, 10].”
Generalized Cylinders for Learning, Reproduction, Generalization, and Refinement of Robot Skills (2017, methodology): “The real-time motion planning approach proposed by Majumdar and Tedrake approximates a boundary around a trajectory, which is visualized as a funnel [20].”
Neural Lyapunov Control (2020, methodology): “A large body of work in control uses SOS representations and SDP optimization in the search for Lyapunov functions [14, 22, 9, 15, 20].”
Hamilton-Jacobi reachability: A brief overview and recent advances (2017, background): “barrier certificates [33] or funnels [34], [35] with Lyapunov properties.”
Trajectory-Based Skill Learning Using Generalized Cylinders (2018, methodology): “Several other techniques utilize models with characteristics similar to generalized cylinders (Quinlan and Khatib, 1993; Majumdar and Tedrake, 2016).”