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Improved Corner Cutting Constraints for Mixed-Integer Motion Planning of a Differential Drive Micro-Mobility Vehicle

Angelo Caregnato-Neto, Janito Vaqueiro Ferreira

TL;DR

This paper tackles global, collision-free motion planning for differential-drive micro-mobility within structured environments using MILP. It introduces two intersample collision avoidance strategies: an intermediary-point (IP) approach and a novel line-based constraint, both aimed at reducing conservatism while maintaining safety. The MILP formulation integrates orientation discretization, pick-up/delivery sequencing, and the two intersample schemes, and is evaluated via pick-up/delivery scenarios and large-scale Monte Carlo analyses. Results show the novel constraint yields the best average trajectory quality at the cost of longer optimization times, while the IP method offers a middle ground; classical CornerCut remains the least favorable in trajectory quality but fastest to solve, highlighting a trade-off between solution quality and computation time for open-loop planning in micro-mobility.

Abstract

This paper addresses the problem of motion planning for differential drive micro-mobility platforms. This class of vehicle is designed to perform small-distance transportation of passengers and goods in structured environments. Our approach leverages mixed-integer linear programming (MILP) to compute global optimal collision-free trajectories taking into account the kinematics and dynamics of the vehicle. We propose novel constraints for intersample collision avoidance and demonstrate its effectiveness using pick-up and delivery missions and statistical analysis of Monte Carlo simulations. The results show that the novel formulation provides the best trajectories in terms of time expenditure and control effort when compared to two state-of-the-art approaches.

Improved Corner Cutting Constraints for Mixed-Integer Motion Planning of a Differential Drive Micro-Mobility Vehicle

TL;DR

This paper tackles global, collision-free motion planning for differential-drive micro-mobility within structured environments using MILP. It introduces two intersample collision avoidance strategies: an intermediary-point (IP) approach and a novel line-based constraint, both aimed at reducing conservatism while maintaining safety. The MILP formulation integrates orientation discretization, pick-up/delivery sequencing, and the two intersample schemes, and is evaluated via pick-up/delivery scenarios and large-scale Monte Carlo analyses. Results show the novel constraint yields the best average trajectory quality at the cost of longer optimization times, while the IP method offers a middle ground; classical CornerCut remains the least favorable in trajectory quality but fastest to solve, highlighting a trade-off between solution quality and computation time for open-loop planning in micro-mobility.

Abstract

This paper addresses the problem of motion planning for differential drive micro-mobility platforms. This class of vehicle is designed to perform small-distance transportation of passengers and goods in structured environments. Our approach leverages mixed-integer linear programming (MILP) to compute global optimal collision-free trajectories taking into account the kinematics and dynamics of the vehicle. We propose novel constraints for intersample collision avoidance and demonstrate its effectiveness using pick-up and delivery missions and statistical analysis of Monte Carlo simulations. The results show that the novel formulation provides the best trajectories in terms of time expenditure and control effort when compared to two state-of-the-art approaches.
Paper Structure (13 sections, 2 theorems, 22 equations, 4 figures, 1 table)

This paper contains 13 sections, 2 theorems, 22 equations, 4 figures, 1 table.

Table of Contents

  1. INTRODUCTION
  2. Problem statement
  3. Mixed-Integer Motion Planning
  4. Prediction model
  5. Pick-up and delivery of loads
  6. Collision Avoidance and Conventional Intersample Avoidance
  7. Intermediary-point (IP) intersample avoidance
  8. Novel intersample avoidance constraint
  9. Optimization problem
  10. Results
  11. Pick-up and delivery simulation
  12. Statistical analysis
  13. CONCLUSIONS

Key Result

Lemma 1

Let $\mathcal{L}(k)$ be the path of the vehicle connecting its positions $\mathbf{r}(k) \in \mathcal{H}_1$ and $\mathbf{r}(k+1) \in \mathcal{H}_2$, with $\mathcal{H}_1 \subset \mathbb{R}^2$ and $\mathcal{H}_2 \subset \mathbb{R}^2$ being external halfspaces of an obstacle $\mathcal{O}$. If $\exists \

Figures (4)

  • Figure 1: Example of envisioned scenario: three buildings around a grass field. The vehicle transports passengers from a pick-up region $\mathcal{P}$ around the obstacle $\mathcal{O}$ through the drop regions $\mathcal{D}_i$, $i=1,2,3$ in each building.
  • Figure 2: a) The intersample collision problem. b) A potential solution using (\ref{['const:corner_cut_old']}) and c) an example of a more efficient maneuver that violates this constraint.
  • Figure 3: Comparison between trajectories using novel and classical intersample collision avoidance constraints in a micro-mobility motion pĺanning problem.
  • Figure 4: Comparison of optimal cost: a) IP and richardsCornerCut. b) IP and novel method. Comparison of optimization times: c) IP and richardsCornerCut. d) IP and novel method.

Theorems & Definitions (4)

  • Lemma 1
  • proof
  • Theorem 1
  • proof