Committee Co-Chairs: Ram Vasudevan and Talia Moore

Abstract:
Safe motion planning is essential for deploying autonomous robots in real‑world environments, whether navigating cluttered warehouses, crowded public spaces, or unstructured outdoor settings. To perform reliably in these scenarios, robots must generate plans in real time, offer formal safety guarantees without undue conservatism, handle environmental uncertainty robustly, and tightly integrate visual perception with motion planning so they can react to changes as they occur.

There are several challenges associated with achieving safe autonomous navigation of mobile robots. First, generating dynamically feasible trajectories for high‑dimensional systems is computationally demanding, often requiring significant processing time to produce high‑quality solutions. Many safe motion planners treat these trajectories as high‑level plans (or waypoints) and rely on a lower‑level planner to enforce safety during execution. Consequently, overall performance hinges on the quality of the high‑level plan so suboptimal plans can force frequent replanning or emergency halts. Second, accounting for environmental uncertainty, especially in dynamic settings with uncertain agent motions remains difficult. Planners typically use worst‑case bounds on uncertainty, inflating safety margins and yielding overly conservative behaviors. Third, standard perception pipelines convert images into occupancy grids or decompose the scene into a set of convex primitives to simplify planning. These either discard fine geometric detail which may be useful for downstream task planning, or require significant and expensive preprocessing.

This dissertation proposes a cohesive suite of tools to address each challenge.First I present a collection of novel optimization‑based trajectory generators for high‑dimensional systems, built on the Affine Geometric Heat Flow (AGHF) PDE, which reformulates trajectory optimization as a curve‑shortening process solved by forward‑simulating an ODE system to its extremal curve. By combining pseudospectral collocation with spatial vector algebra, this framework dramatically reduces function evaluations and produces high‑quality, dynamically feasible trajectories in seconds for systems with dozens of degrees of freedom (e.g., 44‑dimensional legged robots) Second, I introduce a risk‑aware planning methodology that rigorously quantifies and bounds uncertainty via chance‑constrained optimization and reachability analysis. This method runs in real-time both in simulation and on hardware, and offers formal safety guarantees while avoiding the excessive conservatism of traditional uncertainty‑aware safe planners. Third, I propose a novel Gaussian splatting representation that allows probabilistic planning in radiance fields. By reformulating radiance field representations into a normalized Gaussian framework, and deriving tight upper bounds on collision probability this approach unifies perception and motion planning: the robot is able to use a single representation to reason about obstacle geometry while maintaining dense visual information that is useful for downstream task planning. Additionally, I present how this method can be applied on both fixed-base and mobile manipulators. Experiments in cluttered scenes and on a real‑world fixed base manipulator demonstrate significant improvements in planning speed and collision avoidance. Together, these contributions move us toward a unified architecture for safe, real‑time motion planning of high‑dimensional robotic systems in uncertain environments while closing the loop between perception and action with robust safety guarantees.

In person and on Zoom.
Zoom passcode: saferobo