Efficient Avoidance of Ellipsoidal Obstacles with Model Predictive Control for Mobile Robots and Vehicles

TL;DR

This work addresses real-time collision avoidance for mobile robots with non-circular footprints by embedding a planar ellipsoidal overlap test into model predictive control (MPC). It represents both the robot and obstacles as ellipsoids $\mathcal{E}_{\textnormal{r}}$ and $\mathcal{E}_{\textnormal{c}}$, and introduces an overlap-like metric based on a parametric family $\mathcal{E}_\lambda$ to form a smooth, efficiently evaluable constraint $f(\\lambda^{\star},\mathcal{E}_{\textnormal{r}},\mathcal{E}_{\textnormal{c}})<0$ within the MPC. The approach is demonstrated on two planar kinematics (omnidirectional and differential-drive) with simulations and hardware experiments, showing real-time feasibility and robustness to pose and model discrepancies. The method yields practical collision avoidance in constrained environments and can be extended to three-dimensional scenarios.

Abstract

In real-world applications of mobile robots, collision avoidance is of critical importance. Typically, global motion planning in constrained environments is addressed through high-level control schemes. However, additionally integrating local collision avoidance into robot motion control offers significant advantages. For instance, it reduces the reliance on heuristics and conservatism that can arise from a two-stage approach separating local collision avoidance and control. Moreover, using model predictive control (MPC), a robot's full potential can be harnessed by considering jointly local collision avoidance, the robot's dynamics, and actuation constraints. In this context, the present paper focuses on obstacle avoidance for wheeled mobile robots, where both the robot's and obstacles' occupied volumes are modeled as ellipsoids. To this end, a computationally efficient overlap test, that works for arbitrary ellipsoids, is conducted and novelly integrated into the MPC framework. We propose a particularly efficient implementation tailored to robots moving in the plane. The functionality of the proposed obstacle-avoiding MPC is demonstrated for two exemplary types of kinematics by means of simulations. A hardware experiment using a real-world wheeled mobile robot shows transferability to reality and real-time applicability. The general computational approach to ellipsoidal obstacle avoidance can also be applied to other robotic systems and vehicles as well as three-dimensional scenarios.

Figures (4)

• Figure 1: Resulting ellipsoid $\mathcal{E}_\lambda$ (red) following from the original ellipsoids $\mathcal{E}_1$ and $\mathcal{E}_2$ (blue) for different values of $\lambda\in(0,1)$ in case of collision (top row) or no collision (bottom row).
• Figure 2: Crucial metrics $K(\lambda)$ and $K(\lambda)q(\lambda)$ for no contact or overlap (left), contact (middle), and overlap (right).
• Figure 3: Simulation results for the omnidirectional mobile robot (top plots) and the differential-drive mobile robot (bottom plots) containing a planar perspective including the obstacles (left plots), the crucial $K(\lambda^\star)q(\lambda^\star)$ metric (middle plots), and the solution times of the OCPs (right plots).
• Figure 4: Hardware results with still images for the omnidirectional mobile robot evading multiple obstacles. The crucial metric is shown on the right for each obstacle.