Funnel libraries for real-time robust feedback motion planning

Abstract

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. 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, the resulting hardware demonstrations on a fixed-wing airplane constitute one of the first examples of provably safe and robust control for robotic systems with complex nonlinear dynamics that need to plan in realtime in environments with complex geometric constraints.The key computational engine we leverage is sums-of-squares (SOS) programming. While SOS programming allows us to apply our approach to systems of relatively high dimensionality (up to approximately 10-15 dimensional state spaces), scaling our approach to higher dimensional systems such as humanoid robots requires a different set of computational tools. In this thesis, we demonstrate how DSOS and SDSOS programming, which are recently introduced alternatives to SOS programming, can be employed to achieve this improved scalability and handle control systems with as many as 30-50 state dimensions. My conversations with him on measure theory, functional analysis, and algebraic topology were extremely enriching and provided me with a set of technical tools that will no doubt be very valuable going forwards. I am grateful to Hongkai for giving me the chance to explore problems in grasping and manipulation with him. Hongkai's incredible capacity to work long hours have been an inspiration throughout my time as a graduate student and have pushed me to work that extra bit longer myself. I have lost count of the number of times a quick late night conversation with him has helped solve a problem that I was stuck on.I would also like to thank the other members of the Robot Locomotion Group for inspiration, advice, help, and entertainment during my time here. It has been an honor to work with people who will no doubt lead our field in years to come. Ian Manchester, Zack Jackowski, Michael Levashov, John Roberts,...

Generalized Cylinders for Learning, Reproduction, Generalization, and Refinement of Robot Skills

“…The real-time motion planning approach proposed by Majumdar and Tedrake approximates a boundary around a trajectory, which is visualized as a funnel [20]. The generated funnels illustrate a similar representation to our approach, however, we do not require extensive off-line computation.…”

Robust Sampling Based Model Predictive Control with Sparse Objective Information

“…This can be a problematic paradigm when operating noisy systems near their dynamic limits, since failure may occur if a planned path is not feasible or if disturbances push the trajectory off the initially planned path. Within the motion planning literature, our work is most closely related to [14], which also endeavors to control a system state by keeping it within a tube. However, this method restricts behavior to a finite library of pre-generated maneuvers, and requires both the initial library generation and a stabilizing feedback controller to be pre-specified.…”

High‐speed autonomous obstacle avoidance with pushbroom stereo

“…Verification of controllers can guarantee safe transitions by ensuring that the next controller is capable of stabilizing the ending state of the previous controller . In recent work, Majumdar has shown a full working system that uses these guarantees to aggressively avoid obstacles …”