Infinity-Norm-Based Worst-Case Collision Avoidance Control for Quadrotors

Abstract

In this paper, we propose the infinity-norm based worst-case collision avoidance control system for quadrotors with the collision detector. The associated worst-case collision avoidance is captured via the infinity-norm in \mathbb R <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sup> (equivalently the cube in \mathbb R <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sup> ). With the proposed infinity-norm based collision avoidance approach, the quadrotors are able to avoid any obstacles that cannot be detected by the standard two-norm in \mathbb R <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sup> (the cylinder in \mathbb R <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sup> ). In our proposed collision avoidance method, the obstacle approximation algorithm approximates the true coordinates of obstacles by simple integer values to reduce computational complexity. Then the approximated obstacle is surrounded by infinity-norm based to cover the actual obstacle. Note that the actual obstacle may not be covered with the standard two-norm, which can cause the collision. We then design the collision detector and the Model Predictive Control (MPC) tracker, where the latter generates the optimal trajectory for the quadrotor by cooperating with the proposed collision detector. The optimal trajectory generated by the MPC tracker is regarded as the reference input for the quadrotor without collision, where the quadrotor is controlled by the modified backstepping controller. The proposed approach is validated by performing the hardware-in-the-loop simulations (HILS) and experiments. Specifically, we show the superiority of the proposed infinity-norm based collision avoidance performance, by comparing it with the standard two-norm based approach in various maneuver situations of the quadrotor.