DRAFT

Mechanical and Civil Engineering Seminar

Thursday, May 19, 2022
10:00am to 12:00pm
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Gates Annex B122
Safe Input Regulation for Robotic Systems
Andrew Singletary, Graduate Student, Mechanical Engineering, Caltech,

Ph.D. Thesis Defense

Abstract: The safety of robotic systems is paramount to their continued emergence into our lives. From collaborative industrial manipulators to drone deliveries to autonomous vehicles, safety is the primary concern when it comes to the continued adoption of these technologies. While a number of techniques can be used to design safe controllers and planners that govern the actions of these robots, few are able to provide the type of safety guarantee needed to bring these technologies into reality.

The goal of this thesis is to provide a framework for regulating, or filtering, existing control inputs before they are applied by the robot, in order to ensure that safety is upheld. To illustrate this, consider one of the primary applications for this method: human-operated robotic platforms. For vehicles, this framework would modify the throttle, braking, and steering commands from a human driver to prevent him from driving off the road or into other cars. However, when the human is operating the vehicle safely, his commands should go unaltered. This illustrates the idea of a minimally invasive safety regulator: one that only engages when absolutely necessary to ensure safety.

Within the last decade, the mathematical framework that allows us to achieve this result, control barrier functions, was introduced. Its adoption among the nonlinear controls community has been rapid, and the method has been used to create controllers that guarantee safety on a large class of systems. Despite this, real-world implementations of control barrier functions are less common, since they require a very accurate model of the system, and they can be difficult to formulate properly. This work provides several major extensions, improvements, and modifications of control barrier functions that allow them to be utilized on a variety of real-world robotic systems.

The first major contribution of this thesis is a set of formulations for safety regulators that do not depend on complete knowledge of the underlying dynamical systems. Three unique formulations are proposed, whose usages depend on the level of knowledge of the underlying system. The resulting performance and safety guarantees are analyzed in real-world applications of quadrotor collision avoidance and fast-food frying with industrial manipulators.

The second major contribution is a set of two safety filtering frameworks that utilize knowledge of the full-order dynamics, but allow for guaranteed safety in the presence of input constraints on high-dimensional systems. Two formulations are given, with one designed for use on microcontrollers with minimal computational resources. Both formulations utilize the knowledge of an existing "backup controller" that attempts to take the system into a small, safe "backup set". This method is demonstrated in simulation on a robotic manipulator and a Segway robot, and on hardware for collision avoidance and geofencing of single and multi-agent racing drones.

The third major contribution is a novel discrete-time formulation of control barrier functions that allow for safety regulation of discrete-time systems. We show how safety constraints can be encoded as temporal logic specifications that are enforced over discrete-time models of the systems and their environments.

The fourth and final major contribution is a unified, multi-rate control framework that guarantees safety at both the high-level, in discrete-time, and the low-level, in continuous-time. A mid-level Model Predictive Controller (MPC) is used to generate reference signals based on the high-level planner, which are tracked by the low-level controller.

Together, these four major contributions result in safe input regulation on a wide variety of robotic systems. Since no single method can reliably enforce safety on such a wide range of systems with different requirements, this thesis provides the smallest collection of methods that applies to the largest classes of systems.

For more information, please contact Mikaela Laite by email at mlaite@caltech.edu or visit https://www.mce.caltech.edu/seminars.