Point-to-Cloud NMPC with Smooth Avoidance Constraints

TL;DR

This paper introduces a nonlinear model predictive control method with smooth avoidance constraints for set-point tracking, ensuring reliable obstacle avoidance even in complex environments.

Contribution

It presents a novel smooth point-to-cloud distance metric integrated into NMPC, enabling differentiable safety constraints and improved feasibility with artificial variables.

Findings

Demonstrates accurate tracking of set-points in an aerial robot

Achieves smooth obstacle avoidance in complex environments

Ensures numerically well-conditioned gradients for safety constraints

Abstract

This paper proposes a finite-horizon optimal control strategy for set-point tracking using a nonlinear model predictive control framework with integrated avoidance capabilities. The formulation employs a smooth point-to-cloud distance metric that ensures continuously differentiable and numerically well-conditioned gradients, even in the presence of regions with complex and nonconvex geometries. This smoothness allows safety constraints to be formulated consistently and differentiably through control barrier functions, resulting in a reliable avoidance behavior for the closed-loop system. Additionally, stationary artificial variables are introduced in the optimal control problem to preserve feasibility under changing set-points. The proposed approach is validated through numerical experiments of an aerial robot, demonstrating accurate tracking and smooth obstacle avoidance in complex environments.