dual-envelope-mpc-vehicle-drift

name: dual-envelope-mpc-vehicle-drift description: "Dual-envelope constrained nonlinear MPC for autonomous vehicle drifting control. Methods for constructing stability envelopes in phase plane, model predictive control with envelope constraints, and handling bounded steering/yaw-moment control for distributed drive EVs. Triggers: vehicle drifting control, MPC envelope constraint, autonomous drifting, distributed drive EV, yaw moment control, saddle point stability, phase plane envelope."

Dual-Envelope Constrained NMPC for Vehicle Drifting

Model predictive control framework for autonomous drifting with stability envelope constraints.

Overview

Paper: "Dual-Envelope Constrained Nonlinear MPC for Distributed Drive Electric Vehicles Drifting Under Bounded Steering and Direct Yaw-Moment Control" (arXiv: 2604.07342v1, April 2026)

Key contribution: Extended dual envelope framework that accounts for control input coupling, enabling smoother drift convergence and improved tracking.

Vehicle Dynamics Model

Distributed Drive Configuration

• Independent torque control for each wheel
• Direct yaw moment generation via torque distribution
• Superior yaw control compared to conventional vehicles

Drift State Variables

Tire Model

Nonlinear tire model captures:

• Force saturation at high slip angles
• Road adhesion coefficient effects
• Combined slip effects

Saddle Point Analysis

Phase Plane Construction

Build stability boundaries in (β, r) phase plane:

1. Identify drift equilibrium (saddle point)
2. Construct stability boundaries from equilibrium analysis
3. Account for control input effects on saddle location

Control Input Coupling Effects

Critical insight: Control inputs reshape phase plane:

• Steering angle shifts saddle point location
• Yaw moment modifies stability boundaries
• Open-loop envelopes may be invalid for closed-loop control

Saddle Point Coordinate Model

# Account for all relevant parameters
saddle_point = {
    'road_adhesion': μ,       # Road friction coefficient
    'velocity': v,            # Longitudinal velocity
    'steering': δ_f,          # Front wheel steering angle
    'yaw_moment': M_z,        # Additional yaw moment
}

Dual Envelope Framework

Outer Envelope

Purpose: Define recoverable set under bounded control inputs

Characteristics:

• States reachable from drift equilibrium
• Constrained by steering angle limits
• Constrained by yaw moment limits
• Defines maximum drift extent

Inner Envelope

Purpose: Characterize non-drifting stability region

Characteristics:

• States with unsaturated tire forces
• Normal driving stability region
• Transition boundary to drift regime

Envelope Construction

Phase Plane → Envelope Boundaries:
1. Analyze convergence tendency toward saddle points
2. Apply steering angle bounds
3. Apply yaw moment bounds
4. Compute reachable state sets
5. Define inner/outer envelope boundaries

NMPC Controller Design

Control Objective

Track reference trajectory while maintaining drift stability:

• Maintain desired drift angle
• Track velocity reference
• Control yaw rate
• Respect envelope boundaries

Constraint Implementation

# NMPC constraints
constraints = {
    'state_envelope': inner < β < outer,  # Slip angle bounds
    'yaw_envelope': r_min < r < r_max,    # Yaw rate bounds
    'steering_limit': |δ_f| < δ_max,      # Steering angle limit
    'yaw_moment_limit': |M_z| < M_z_max,  # Yaw moment limit
}

Optimization Problem

minimize: tracking_error + control_effort
subject to: envelope_constraints + input_limits + dynamics

Performance Results

Hardware-in-the-Loop Experiments

Compared NMPC with envelope constraints vs. unconstrained NMPC:

Benefits

• Smaller convergence toward drift saddle point
• Reduced tracking errors across all state variables
• Robust to friction mismatch - Handles road condition changes

Implementation Guidance

Controller Tuning

Key parameters:

1. Envelope boundary margins
2. Control horizon length
3. Prediction step size
4. Weighting matrices for cost function

Real-time Considerations

• Optimize solver for real-time execution
• Use warm-starting for successive solves
• Pre-compute envelope boundaries offline

Reference

• Paper: arXiv:2604.07342v1
• PDF: https://arxiv.org/pdf/2604.07342v1
• Category: eess.SY (Systems and Control)