# Continuous Implicit SDF Based Any-shape Robot Trajectory Optimization

**Authors:** Tingrui Zhang, Jingping Wang, Chao Xu, Alan Gao, Fei Gao  
**arXiv:** [2303.01330](https://arxiv.org/abs/2303.01330)  
**Date:** 2023-03-02  
**Summary page:** https://www.summarizepaper.com/en/arxiv-id/2303.01330v1/

## Key points

- The paper explores the use of implicit functions in optimizing trajectories for arbitrarily shaped robots.
- Authors address limitations of existing approaches that oversimplify robot geometry or incur significant overhead in maintaining additional information like the Signed Distance Field (SDF).
- They propose considering the robot as an implicit function with its surface boundary represented by the zero-level set of its SDF.
- Introduce another implicit function to efficiently evaluate collisions using continuity in space-time.
- A tailored trajectory optimization pipeline is proposed for this approach.
- Effectiveness of the method is demonstrated through simulations and real-world experiments for complex robots.
- The research contributes significantly to advancing robot trajectory optimization techniques by bridging the gap between conservative planning and computationally intensive methods.

## Summary

The paper titled "Continuous Implicit SDF Based Any-shape Robot Trajectory Optimization" by Tingrui Zhang, Jingping Wang, Chao Xu, Alan Gao, and Fei Gao explores the use of implicit functions in optimizing trajectories for arbitrarily shaped robots. The authors address limitations of existing approaches that oversimplify robot geometry or incur significant overhead in maintaining additional information like the Signed Distance Field (SDF). To overcome these challenges, they propose considering the robot as an implicit function with its surface boundary represented by the zero-level set of its SDF. Additionally, they introduce another implicit function to efficiently evaluate collisions using continuity in space-time. A tailored trajectory optimization pipeline is also proposed for this approach. Through simulations and real-world experiments, the effectiveness of this novel method is demonstrated in optimizing trajectories for complex robots. By bridging the gap between conservative planning and computationally intensive methods, this research contributes significantly to advancing robot trajectory optimization techniques.