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Constrained Bimanual Planning with Analytic Inverse Kinematics

Thomas Cohn, Seiji Shaw, Max Simchowitz, Russ Tedrake

TL;DR

This work leverages an analytic solution to the inverse kinematics problem to parametrize the configuration space, resulting in a lower-dimensional representation where the set of valid configurations has positive measure.

Abstract

In order for a bimanual robot to manipulate an object that is held by both hands, it must construct motion plans such that the transformation between its end effectors remains fixed. This amounts to complicated nonlinear equality constraints in the configuration space, which are difficult for trajectory optimizers. In addition, the set of feasible configurations becomes a measure zero set, which presents a challenge to sampling-based motion planners. We leverage an analytic solution to the inverse kinematics problem to parametrize the configuration space, resulting in a lower-dimensional representation where the set of valid configurations has positive measure. We describe how to use this parametrization with existing motion planning algorithms, including sampling-based approaches, trajectory optimizers, and techniques that plan through convex inner-approximations of collision-free space.

Constrained Bimanual Planning with Analytic Inverse Kinematics

TL;DR

This work leverages an analytic solution to the inverse kinematics problem to parametrize the configuration space, resulting in a lower-dimensional representation where the set of valid configurations has positive measure.

Abstract

In order for a bimanual robot to manipulate an object that is held by both hands, it must construct motion plans such that the transformation between its end effectors remains fixed. This amounts to complicated nonlinear equality constraints in the configuration space, which are difficult for trajectory optimizers. In addition, the set of feasible configurations becomes a measure zero set, which presents a challenge to sampling-based motion planners. We leverage an analytic solution to the inverse kinematics problem to parametrize the configuration space, resulting in a lower-dimensional representation where the set of valid configurations has positive measure. We describe how to use this parametrization with existing motion planning algorithms, including sampling-based approaches, trajectory optimizers, and techniques that plan through convex inner-approximations of collision-free space.
Paper Structure (13 sections, 8 equations, 4 figures, 2 tables, 1 algorithm)

This paper contains 13 sections, 8 equations, 4 figures, 2 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Related Work
  3. Methodology
  4. Topology of Inverse Kinematics
  5. Parametrizing the Kinematically Constrained Space
  6. Reformulating the Motion Planning Problem
  7. Motion Planning with the Parametrization
  8. Sampling-Based Planning
  9. Trajectory Optimization
  10. Graph of Convex Sets
  11. Constructing Convex Valid Sets
  12. Results
  13. Discussion

Figures (4)

  • Figure 1: Hardware setup for our experiments. The two arms must work together to move an objects between the shelves, avoiding collisions and respecting the kinematic constraint.
  • Figure 2: A high level description of our parametrization. The controlled arm can move freely, and analytic IK is used to position the subordinate arm so as to maintain a fixed transformation between the end-effectors.
  • Figure 3: Continuous (left) and discrete (right) self-motions of a 7DoF arm. The continuous self-motion yields an additional degree of freedom for the planner to consider, whereas the discrete self-motion is not utilized.
  • Figure 4: Robot configurations sampled from various IRIS regions.