# QCQP-Tunneling: Ellipsoidal Constrained Agent Navigation

## TL;DR

This paper introduces ECAN, a convex-QCQP based path planning algorithm that constructs ellipsoidal tunnels for agents navigating unknown environments, ensuring collision avoidance without shape constraints.

## Contribution

The paper proposes a novel convex-QCQP based method for online path planning using ellipsoidal tunnels, extending to agents and obstacles of arbitrary shape and size.

## Key findings

- Successfully plans collision-free paths in unknown environments.
- Extends the framework from point-mass to finite-sized agents and obstacles.
- Demonstrates effectiveness in 2D and 3D environments.

## Abstract

This paper presents a convex-QCQP based novel path planning algorithm named ellipsoidal constrained agent navigation (ECAN), for a challenging problem of online path planning in completely unknown and unseen continuous environments. ECAN plans path for the agent by making a tunnel of overlapping ellipsoids, in an online fashion, through the environment. Convex constraints in the ellipsoid-formation step circumvent collision with the obstacles. The problem of online-tunneling is solved as a convex-QCQP. This paper assumes no constraints on shape of the agent and the obstacles. However, to make the approach clearer, this paper first introduces the framework for a point-mass agent with point-size obstacles. After explaining the underlying principle in drawing an ellipsoid tunnel, the framework is extended to the agent and obstacles having finite area (2d space) and finite-volume (3d-space).