Mixed-Integer MPC-Based Motion Planning Using Hybrid Zonotopes with Tight Relaxations

TL;DR

This paper introduces a hybrid zonotope-based mixed-integer MPC approach for autonomous vehicle motion planning, enabling efficient, real-time obstacle avoidance and risk-aware planning with tight relaxations and reduced computational complexity.

Contribution

The paper develops a novel hybrid zonotope representation for non-convex constraints, leading to tight relaxations and faster mixed-integer quadratic programming solutions in AV motion planning.

Findings

Solver is an order of magnitude faster than commercial alternatives.

Tight convex relaxations are achieved for certain hybrid zonotope representations.

Method enables real-time embedded hardware implementation.

Abstract

Autonomous vehicle (AV) motion planning problems often involve non-convex constraints, which present a major barrier to applying model predictive control (MPC) in real time on embedded hardware. This paper presents an approach for efficiently solving mixed-integer MPC motion planning problems using a hybrid zonotope representation of the obstacle-free space. The MPC optimization problem is formulated as a multi-stage mixed-integer quadratic program (MIQP) using a hybrid zonotope representation of the non-convex constraints. Risk-aware planning is supported by assigning costs to different regions of the obstacle-free space within the MPC cost function. A multi-stage MIQP solver is presented that exploits the structure of the hybrid zonotope constraints. For some hybrid zonotope representations, it is shown that the convex relaxation is tight, i.e., equal to the convex hull. In conjunction with logical constraints derived from the AV motion planning context, this property is leveraged to generate tight quadratic program (QP) sub-problems within a branch-and-bound mixed-integer solver. The hybrid zonotope structure is further leveraged to reduce the number of matrix factorizations that need to be computed within the QP sub-problems. Simulation studies are presented for obstacle-avoidance and risk-aware motion planning problems using polytopic maps and occupancy grids. In most cases, the proposed solver finds the optimal solution an order of magnitude faster than a state-of-the-art commercial solver. Processor-in-the-loop studies demonstrate the utility of the solver for real-time implementations on embedded hardware.