Title: Stochastic Motion Planning and Control under Uncertainties

Date: Friday, November 21, 2025

Time: 10:00 am - 12:00 pm ET

Location: Virtual

Zoom Link: https://gatech.zoom.us/j/9553769791

Hongzhe Yu

Robotics Ph.D. Candidate

Daniel Guggenheim School of Aerospace Engineering

Georgia Institute of Technology

https://hzyu17.github.io/hongzheyu.github.io/

Committee:

Dr. Yongxin Chen (Advisor) - Daniel Guggenheim School of Aerospace Engineering, Georgia Institute of Technology

Dr. Panagiotis Tsiotras - Daniel Guggenheim School of Aerospace Engineering, Georgia Institute of Technology

Dr. Aaron Johnson - Department of Mechanical Engineering - Carnegie Mellon University

Dr. Samuel Coogan - School of Electrical and Computer Engineering, Georgia Institute of Technology

Dr. Ye Zhao - George W. Woodruff School of Mechanical Engineering, Georgia Institute of Technology

Abstract:

Robotic systems operating in real-world environments must make decisions under pervasive uncertainties arising from imperfect models, sensor noise, actuator errors, and external disturbances. This dissertation develops a unified probabilistic framework for decision-making, motion planning, and control under uncertainty, grounded in stochastic optimal control and probabilistic inference.

At the core of the formulation is a stochastic optimal control problem for general nonlinear and hybrid dynamical systems with nonconvex cost functions. This formulation encompasses a wide range of robotic tasks while revealing two central challenges: (i) the computational intractability of solving stochastic control problems over high-dimensional trajectory distributions, and (ii) the need for algorithms that achieve both performance optimality and robustness to uncertainty.

To address these challenges, this dissertation introduces several novel methods:

(1) Gaussian Variational Inference Motion Planning (GVIMP), which frames motion planning as a variational inference problem in the space of trajectory distributions, providing a principled approach to approximate stochastic optimal control;

(2) Parallel Gaussian Variational Inference Motion Planning (P-GVIMP), an efficient proximal extension of GVIMP that exploits sparse factor-graph structures and Gaussian Belief Propagation (GBP) for GPU-parallelized gradient computation, enabling scalable planning for nonlinear stochastic systems;

(3) An iterative covariance steering framework based on proximal gradient methods and iterative linearization, providing closed-loop solutions for nonlinear stochastic systems with prescribed uncertainty boundary conditions; and

(4) Two complementary algorithms for hybrid stochastic systems—Hybrid Covariance Steering (H-CS) for linear stochastic flows and Hybrid Path Integral Control (H-PI) for nonlinear flows—both derived from a unified path-distribution control formulation.

Together, these contributions establish a cohesive theoretical and computational foundation that bridges stochastic optimal control, variational inference, and hybrid dynamical systems. The proposed methods are validated across diverse robotic benchmarks, demonstrating robust and efficient motion planning under uncertainty. Future directions include receding-horizon extensions for hybrid systems and learning-based multi-modal variational motion planning.