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Non-Conservative Obstacle Avoidance for Multi-Body Systems Leveraging Convex Hulls and Predicted Closest Points

Lotte Rassaerts, Eke Suichies, Bram van de Vrande, Marco Alonso, Bas Meere, Michelle Chong, Elena Torta

TL;DR

A novel approach that integrates future closest point predictions into the distance constraints of a collision avoidance controller, leveraging convex hulls with closest point distance calculations, demonstrates improved distance prediction accuracy, smoother trajectories, and safer navigation near obstacles.

Abstract

This paper introduces a novel approach that integrates future closest point predictions into the distance constraints of a collision avoidance controller, leveraging convex hulls with closest point distance calculations. By addressing abrupt shifts in closest points, this method effectively reduces collision risks and enhances controller performance. Applied to an Image Guided Therapy robot and validated through simulations and user experiments, the framework demonstrates improved distance prediction accuracy, smoother trajectories, and safer navigation near obstacles.

Non-Conservative Obstacle Avoidance for Multi-Body Systems Leveraging Convex Hulls and Predicted Closest Points

TL;DR

A novel approach that integrates future closest point predictions into the distance constraints of a collision avoidance controller, leveraging convex hulls with closest point distance calculations, demonstrates improved distance prediction accuracy, smoother trajectories, and safer navigation near obstacles.

Abstract

This paper introduces a novel approach that integrates future closest point predictions into the distance constraints of a collision avoidance controller, leveraging convex hulls with closest point distance calculations. By addressing abrupt shifts in closest points, this method effectively reduces collision risks and enhances controller performance. Applied to an Image Guided Therapy robot and validated through simulations and user experiments, the framework demonstrates improved distance prediction accuracy, smoother trajectories, and safer navigation near obstacles.

Paper Structure

This paper contains 15 sections, 16 equations, 8 figures, 3 tables, 3 algorithms.

Table of Contents

  1. Introduction
  2. Related Work
  3. Preliminaries
  4. Problem Formulation
  5. System and Collision Model
  6. Model Predictive Control Framework
  7. Challenges in Distance Prediction
  8. Objective
  9. Methodology
  10. Future Closest Point Formulation
  11. Point Smoothing
  12. Experimental Validation
  13. Simulations with Artificial Inputs
  14. Virtual Reality Inputs
  15. Conclusion

Figures (8)

  • Figure 1: The IGT robot with its rotational joints $q_1$, $q_2$ and $q_3$, the end-effector position and the link names.
  • Figure 2: Geometric representations of the system (orange) with the end-effector (gray box). (a) Frontal system with 8 spheres and (b) with 13 convex hulls $P_j$.
  • Figure 3: Distance prediction in MPC. (a) With spheres. (b) With convex hulls, where an abrupt change in the closest point may occur due to a rotation $\theta$.
  • Figure 4: Illustration of determining future closest points in Alg. \ref{['alg:JP']}. (a) Future closest point in global coordinates (line \ref{['lst:line:gjk1']}). (b) Transform to local coordinates (line \ref{['lst:line:CLPl2']}). (c) Transform back to global coordinates for the current configuration $\boldsymbol{x}(k)$ (line \ref{['lst:line:CLPw']}). (d) Determine current distance (line \ref{['lst:line:gjk3']}).
  • Figure 5: Switching of the closest points between two configurations: a dispersed position and almost the same position, causing oscillatory movement $\theta$ of the system.
  • ...and 3 more figures