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Motion Planning on Visual Manifolds

M Seetha Ramaiah

TL;DR

The thesis proposes Visual Configuration Space (VCS) as a vision-based alternative to explicit configuration spaces for robot motion planning, enabling learning of body structure from images via manifold learning and planning on a Visual Roadmap (VRM). It demonstrates that planning paths over a graph embedded in the image space can handle static and dynamic obstacles without detailed geometry, using Isomap and other NLDR methods to reveal the low-dimensional structure underlying high-dimensional visual data. The work extends the VCS framework to model body schema, infant-like visuomotor learning, and avatar head-motion animation, highlighting the versatility of visually grounded representations for planning, perception, and synthetic motion generation. Key contributions include the Visual Roadmap methodology, collision detection via image overlap and RLE, and demonstrations on planar and spatial robots, as well as a vision-based approach to head animation, all built upon manifold learning foundations. The approach offers a robust, less geometry-dependent alternative with practical implications for real-time planning in changing environments and immersive virtual environments, while acknowledging conservatism in obstacle approximation and the need for multi-modal fusion for stronger robustness.

Abstract

In this thesis, we propose an alternative characterization of the notion of Configuration Space, which we call Visual Configuration Space (VCS). This new characterization allows an embodied agent (e.g., a robot) to discover its own body structure and plan obstacle-free motions in its peripersonal space using a set of its own images in random poses. Here, we do not assume any knowledge of geometry of the agent, obstacles or the environment. We demonstrate the usefulness of VCS in (a) building and working with geometry-free models for robot motion planning, (b) explaining how a human baby might learn to reach objects in its peripersonal space through motor babbling, and (c) automatically generating natural looking head motion animations for digital avatars in virtual environments. This work is based on the formalism of manifolds and manifold learning using the agent's images and hence we call it Motion Planning on Visual Manifolds.

Motion Planning on Visual Manifolds

TL;DR

The thesis proposes Visual Configuration Space (VCS) as a vision-based alternative to explicit configuration spaces for robot motion planning, enabling learning of body structure from images via manifold learning and planning on a Visual Roadmap (VRM). It demonstrates that planning paths over a graph embedded in the image space can handle static and dynamic obstacles without detailed geometry, using Isomap and other NLDR methods to reveal the low-dimensional structure underlying high-dimensional visual data. The work extends the VCS framework to model body schema, infant-like visuomotor learning, and avatar head-motion animation, highlighting the versatility of visually grounded representations for planning, perception, and synthetic motion generation. Key contributions include the Visual Roadmap methodology, collision detection via image overlap and RLE, and demonstrations on planar and spatial robots, as well as a vision-based approach to head animation, all built upon manifold learning foundations. The approach offers a robust, less geometry-dependent alternative with practical implications for real-time planning in changing environments and immersive virtual environments, while acknowledging conservatism in obstacle approximation and the need for multi-modal fusion for stronger robustness.

Abstract

In this thesis, we propose an alternative characterization of the notion of Configuration Space, which we call Visual Configuration Space (VCS). This new characterization allows an embodied agent (e.g., a robot) to discover its own body structure and plan obstacle-free motions in its peripersonal space using a set of its own images in random poses. Here, we do not assume any knowledge of geometry of the agent, obstacles or the environment. We demonstrate the usefulness of VCS in (a) building and working with geometry-free models for robot motion planning, (b) explaining how a human baby might learn to reach objects in its peripersonal space through motor babbling, and (c) automatically generating natural looking head motion animations for digital avatars in virtual environments. This work is based on the formalism of manifolds and manifold learning using the agent's images and hence we call it Motion Planning on Visual Manifolds.
Paper Structure (79 sections, 5 theorems, 15 equations, 50 figures, 4 tables, 4 algorithms)

This paper contains 79 sections, 5 theorems, 15 equations, 50 figures, 4 tables, 4 algorithms.

Table of Contents

  1. Introduction and Preliminaries
  2. Motion Planning
  3. Motion Planning: Examples
  4. Traditional Approach to Robot Motion Planning
  5. Configuration Space
  6. Configuration Space: Examples
  7. Free Configuration Space
  8. Free Space Computation: Example
  9. Path Planning in Free C-Space
  10. Complexity of the Traditional Approaches
  11. An Inspiration from Human Cognition
  12. Main Claims of This Thesis
  13. Configuration Manifold
  14. Manifolds
  15. Examples of Manifolds
  16. ...and 64 more sections

Key Result

Theorem 1

For a visually distinguishable SMPR, whenever $\mathcal{Q}$ is a manifold, $\mathcal{I}$ is a manifold of the same dimension.

Figures (50)

  • Figure 1: A circular mobile robot in a planar workspace with obstacles. The goal is to generate a sequence of motion instructions for the robot to move from the source position to the destination position without hitting obstacles.
  • Figure 2: A 2-link planar arm in a planar workspace with obstacles (white objects). The goal is to guide the arm to change its configuration from the source pose to the destination pose, through a continuous motion without hitting obstacles.
  • Figure 3: Configuration space of a circular mobile robot, with the position of the center being used as its configuration, excludes the points (the dark part in the right half of the figure) which cannot be the center of the robot in the workspace. Correspondence between the workspace and the configuration space representations of the robot is shown by the dotted lines. In this case, the workspace and the configuration space, both have an $\mathbb{R}^2$ topology.
  • Figure 4: Configuration space of a 2-link robotic arm, with the joint angle vector $(\theta_1, \theta_2)$ being used as its configuration, is a torus which can be cut and flattened into a plane. The robot's configuration is shown as a point on the torus and in the plane. Because of the circular topology of each joint angle, each pair of opposite edges of the plane is actually the same line. This illustration is based on a figure from choset-05_robot-motion-theory.
  • Figure 5: An obstacle in the workspace vs. in the configuration space for a circular mobile robot. The geometry of the robot and obstacle play a crucial role in computing the free C-space. Center of the robot cannot be inside the dotted region in the workspace, for any configuration of the robot, and hence the shape of a rectangular obstacle in the workspace takes the form of a bigger rounded rectangle in the C-space as shown on the right side. Some corresponding configurations are shown in the free workspace and in the free C-space.
  • ...and 45 more figures

Theorems & Definitions (20)

  • Definition 3.1
  • Definition 3.2
  • Theorem 1
  • Lemma 3.1
  • Lemma 3.2
  • Theorem 2
  • Definition 1.1
  • Example 1.1
  • Definition 1.2
  • Example 1.2
  • ...and 10 more