Mandy Xie

Ph.D. student in Computer Science, Georgia Institute of Technology

Email

I am now a third year Ph.D. student in computer science, co-advised by professor Frank Dellaert and professor Harish Ravichandar at Georgia Institute of Technology. Prior to enrolling in computer science, I completed my master's program in Aerospace Engineering at Georgia Tech, and received my bachelor degree in Mechanical Engineering from Huazhong University of Science and Technology, Wuhan, China.

My current research interests cover various topics in robotics, including but not limited to robot motion planning, motion generation, and reactive motion policy learning. I am interested in learning motion policies from demonstrations and leveraging structured motion policy classes such as Riemannian Motion Policy and Geometric Fabrics to improve data efficiency.


Research Projects


Geometric Fabrics: Generalizing Classical Mechanics to Capture the Physics of Behavior


Classical mechanical systems are central to controller design in energy shaping methods of geometric control. However, their expressivity is limited by position-only metrics and the intimate link between metric and geometry. Recent work on Riemannian Motion Policies (RMPs) has shown that shedding these restrictions results in powerful design tools, but at the expense of theoretical stability guarantees. In this work, we generalize classical mechanics to what we call geometric fabrics, whose expressivity and theory enable the design of systems that outperform RMPs in practice. Geometric fabrics strictly generalize classical mechanics forming a new physics of behavior by first generalizing them to Finsler geometries and then explicitly bending them to shape their behavior while maintaining stability. We develop the theory of fabrics and present both a collection of controlled experiments examining their theoretical properties and a set of robot system experiments showing improved performance over a well-engineered and hardened implementation of RMPs, our current state-of-the-art in controller design.


Paper:

[1] K. Wyk*, M. Xie*, A. Li, M. A. Rana, B. Peele, Q. Wan, I. Akinola, B. Sundaralingam, D. Fox, B. Boots, N. Ratliff. Geometric Fabrics: Generalizing Classical Mechanics to Capture the Physics of Behavior. [PDF]


Geometric Fabrics for the Acceleration-based Design of Robotic Motion


In this project, we study the pragmatic design and construction of geometric fabrics for shaping a robot's task-independent nominal behavior, capturing behavioral components such as obstacle avoidance, joint limit avoidance, redundancy resolution, global navigation heuristics, etc. Geometric fabrics constitute the most concrete incarnation of a new mathematical formulation for reactive behavior called optimization fabrics. Fabrics generalize recent work on Riemannian Motion Policies (RMPs); they add provable stability guarantees and improve design consistency while promoting the intuitive acceleration-based principles of modular design that make RMPs successful. We describe a suite of mathematical modeling tools that practitioners can employ in practice and demonstrate both how to mitigate system complexity by constructing behaviors layer-wise and how to employ these tools to design robust, strongly-generalizing, policies that solve practical problems one would expect to find in industry applications. Our system exhibits intelligent global navigation behaviors expressed entirely as provably stable fabrics with zero planning or state machine governance.


Paper:

[1] M. Xie*, K. Wyk*, A. Li, M. A. Rana, Q. Wan, D. Fox, B. Boots, N. Ratliff. Geometric Fabrics for the Acceleration-based Design of Robotic Motion. [PDF]


Imitation Learning via Simultaneous Optimization of Policies and Auxiliary Trajectories


Imitation learning (IL) is a frequently used approach for data-efficient policy learning. Many IL methods, such as Dataset Aggregation (DAgger), combat challenges like distributional shift by interacting with oracular experts. Unfortunately, assuming access to oracular experts is often unrealistic in practice; data used in IL frequently comes from offline processes such as lead-through or teleoperation. In this paper, we present a novel imitation learning technique called Collocation for Demonstration Encoding (CoDE) that operates on only a fixed set of trajectory demonstrations. We circumvent challenges with methods like back-propagation-through-time by introducing an auxiliary trajectory network, which takes inspiration from collocation techniques in optimal control. Our method generalizes well and more accurately reproduces the demonstrated behavior with fewer guiding trajectories when compared to standard behavioral cloning methods. We present simulation results on a 7-degree-of-freedom (DoF) robotic manipulator that learns to exhibit lifting, target-reaching, and obstacle avoidance behaviors.


Paper:

[1] M. Xie, A. Li, K. Wyk, F. Dellaert, B. Boots, N. Ratliff. Imitation Learning via Simultaneous Optimization of Policies and Auxiliary Trajectoriess. [PDF]


Solve Manipulator Dynamics Problems using Factor Graphs


Manipulator dynamics is one of the most fundamental problems in robotics, and it is considered to be a well studied problem. Various different algorithms have been developed to solve each type of dynamics problems, including inverse, forward and hybrid dynamics problems. However, they are not easily explained in a unified and intuitive way. In this project, our goal is to develop a unified method which solves all types of dynamics problems for robotic manipulators with either open kinematic chains or closed kinematic loops based on factor graphs.


Paper:

[1] M. Xie and F. Dellaert. A unified method for solving inverse, forward, and hybrid manipulator dynamics using factor graphs. [PDF]


Solve Kinodynamic Motion Planning Problems using Factor Graphs.


In this project, we introduce dynamics factor graphs as a graphical framework to solve dynamics problems and kinodynamic motion planning problems with full consideration of whole-body dynamics and contacts. A factor graph representation of dynamics problems provides an insightful visualization of their mathematical structure and can be used in conjunction with sparse nonlinear optimizers to solve challenging, highdimensional optimization problems in robotics. We can easily formulate kinodynamic motion planning as a trajectory optimization problem with factor graphs. We demonstrate the flexibility and descriptive power of dynamics factor graphs by applying them to control various dynamical systems, ranging from a simple cart pole to a 12-DoF quadrupedal robot.


Paper:

[1] M. Xie, A. Escontrela, and F. Dellaert. A Factor-Graph Approach for Optimization Problems with Dynamics Constraints. [PDF]


Modeling and Simulation for Soft Robotic Arms using Finite Element Method based on Factor Graphs


Soft robots have contunuum solid bodies that is capable of deforming in an infinite number of ways, however, such property presents a formidable challenge to modeling and analysis. Many attempts have been made to establish a general modeling method for soft robots, and finite element method is one of the most popular methods, which has been widely used for both rigid and soft robots. The FEM model can capture all the deformation information, and can represent the robot dynamics accurately. However, using such models is very difficult in a real-time system of control due to the heavy computation involved in solving FEM models. In this project, we are interested in developing FEM models with factor graphs, and taking advantages of the intuitive representation and efficient computation of factor graphs in solving either linear or nonlinear systems.