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Multi-Objective Agent-Based Model Predictive Controller for Plug-and-Play Vehicle Control
Jiaming Zhong, Ladan Khoshnevisan, Shucheng Huang, Mohammad Pirani, Yash Vardhan Pant, Amir Khajepour
TL;DR
Vehicle-control systems need flexible coordination of multiple objectives, while integrated MPC and prior AMPC approaches face burdens or limitations with plug-and-play coupled control. The paper develops ADMM-based multi-objective AMPC with three formulations, finding approximate global convergence and improved computational efficiency in simulations and vehicle experiments.
Problem
Plug-and-play vehicle control is difficult for integrated MPC, while prior AMPC does not handle complex coupled objectives with shared agents.
Method
The paper adapts ADMM into multi-objective AMPC and develops three formulations addressing control regularization and linear inequality constraints.
Results
The formulations approximate integrated MPC's global optimum; Local Explicit is most computationally efficient and was validated with improved multi-objective vehicle performance.
Takeaways & Limitations
Multi-objective AMPC offers a practical distributed vehicle-control solution with greater design flexibility and potential computational advantages over integrated MPC.
Abstract
from arXiv · showhide
Functional integration is a growing trend in vehicle control, often involving the coordination of multiple controllers to achieve various objectives simultaneously. The need for flexibility and reliability has led to a "plug-and-play" approach in control system design, which presents challenges for traditional integrated model predictive control (MPC). Agent-based model predictive control (AMPC) has recently emerged as a distributed solution that treats controllers as agents, creating a collaborative framework among them to reach a common goal. However, this approach struggles to manage distributed conflicting objectives when agents are coupled or interdependent. To address this, we propose a novel, practical distributed control scheme called multi-objective AMPC, which adapts the alternating direction method of multipliers (ADMM) into a general control strategy that approximates global optimization while decoupling objectives. We systematically develop three formulations that maintain convergence while addressing control regularization and inequality constraints, applying them to complex vehicle control systems for the first time. The proposed method has been tested on two vehicle control scenarios with a multi-objective topology. Different formulations are compared through simulations, and the most computationally efficient one was implemented on an electric vehicle for real-world evaluations. The results demonstrate that the proposed multi-objective AMPC can converge approximately to the same global optimum as integrated MPC with greater flexibility and the potential to reduce computational costs.
I. INTRODUCTION
Vehicle control increasingly combines multiple controllers and objectives, but integrated MPC can hinder plug-and-play flexibility and incur computational and maintenance burdens. Multi-objective AMPC adapts ADMM to coordinate coupled objective groups while approximating centralized optimization.
- A. Motivation: Integrated MPC can be computationally burdensome and difficult to maintain, motivating distributed architectures for modular vehicle systems.
- A. Motivation: The MACS represents torque-vectoring and differential-braking controllers as connected agents coordinated across objectives such as cruise and stability control.
- C. Contributions: Multi-objective AMPC assigns objectives to corresponding agent groups and iteratively exchanges information to approximate the global optimum while enabling plug-and-play vehicle-control features.
- B. Literature Review: AMPC coordinates controller agents and can converge to centralized MPC, but its single-objective decomposition does not support coupled multi-objective systems with shared agents.
- C. Contributions: The paper proposes three ADMM-tailored formulations, compares them in simulation, and validates multi-objective AMPC on an electric vehicle for real-time control.
- A. Notation: Shared-agent topology is represented by G_j(i), with S_j collecting agents influencing objective O_j and S(i) collecting objectives influenced by agent A(i).
B. Integrated MPC
The integrated MPC reference combines objective costs into a weighted optimization subject to system dynamics and control constraints. Under quadratic costs, linear dynamics, and linear inequalities, the problem is convex and has a global-optimum solution.
- B. Integrated MPC: Integrated MPC constructs a weighted-sum cost over multiple objectives and optimizes it subject to discrete system dynamics and control constraints.
- B. Integrated MPC: The paper focuses on quadratic costs, linear system equations, and linear inequality constraints to improve real-time computational efficiency.
- B. Integrated MPC: Positive-definite tracking penalties and semipositive-definite control penalties define the objective weights, while A_in and b_in parameterize linear inequalities.
- B. Integrated MPC: With these assumptions, the integrated MPC is convex and its solution is the global optimum.
III. MULTI-OBJECTIVE AGENT-BASED MPC
Multi-objective AMPC tailors consensus ADMM to MACSs with shared agents by coordinating local objective optimizations through global and dual updates. The framework provides convergence guarantees while motivating three practical formulations that incorporate cost decomposition and inequality constraints.
- A. Basic Algorithm of Multi-objective AMPC: ADMM coordinates iterative local optimizations through an augmented Lagrangian and is proven to achieve residual, objective, and dual convergence.
- B. Consensus Formulation: The consensus setup uses local costs J_j, Lagrange multipliers γ_j, and positive penalty parameters ρ_j to enforce agreement between local and projected global variables.
- B. Consensus Formulation: The consensus formulation requires local variables to converge to a shared global variable through projected objective-specific variables.
- A. Basic Algorithm of Multi-objective AMPC: For an existing global optimum, ADMM guarantees convergence of the objective value, primal residual, and dual variable to their optimal or saddle-point values.
- A. Basic Algorithm of Multi-objective AMPC: The algorithm alternates local objective updates, projection of the global variable, and dual updates until all objectives satisfy convergence conditions.
- A. Basic Algorithm of Multi-objective AMPC: The basic algorithm does not specify an equivalent distributed decomposition of the integrated cost or include inequality constraints, so three feasible formulations are developed.
B. Formulation 1: Fully Distributed
The Fully Distributed formulation distributes each objective’s state penalty, control regularization, and inequality constraints across local optimizations while coordinating shared agents through exchanged information.
- Each local optimization distributes the state penalty and control regularization associated with its local variable Uj into the local cost Jj.
- Shared agents contribute to multiple objectives, with m(i)=|S(i)| updates for agent A(i), while non-shared agents have m(i)=1.
- Inequality constraints are handled separately in each local optimization using constraint components derived to remain equivalent to the original integrated constraint on Uj.Exchanged actions from agents outside Sj are updated across iterations, causing local inequalities to approach the global inequality.
- The global optimization update can be simplified as an elementwise global average, while dual updates remain unchanged.
- This formulation keeps global and dual updates computationally efficient, but makes each local update relatively complex because control regularization is included at every local node.
C. Formulation 2: Virtual Center Node
The Virtual Center Node formulation centralizes control regularization while distributing state penalties and handling inequality constraints through local optimizations.
- Control-action regularization is handled centrally at a physical or replicated virtual center, while only state penalties are distributed into local costs.
- Local inequality constraints are exchanged through ˜Uj across iterations to approximate the original global inequality constraint.
- The global update applies the regularization directly to the global variable Z rather than to the local variable Uj.
- The regularization penalty R(i) controls the resulting update magnitude: large R(i) drives it near zero, whereas small R(i) leaves it near the unconstrained expression.
- The global update remains efficient through an explicit average, while the local update is simpler than in the Fully Distributed formulation.
D. Formulation 3: Local Explicit
The Local Explicit formulation converts inequality constraints into equality constraints with slack variables, enabling explicit local optimization and centralized constraint handling.
- The main advantage is that local optimization for each objective is solved explicitly through simple matrix operations after inequality constraints become indicator-function penalties.
- The global variable Z is redefined as a slack variable, so its dimension matches the constraint dimension rather than the control-action dimension.
- The indicator penalty assigns infinite cost to negative slack components, making the reformulation equivalent to the original optimization problem.
- The virtual center uses a max operation to enforce the transformed equality constraints and indicator function during the global update.
- Each control variable U(i) must be associated with at least one global constraint variable Z(c), a condition motivated by actuator min-max constraints.
E. Convergence and Parameter Selection
All three formulations retain the ADMM convergence framework, while the penalty parameter ρj affects convergence speed and has formulation-dependent selection guidance.
- The distributed control action approximates the integrated MPC global optimum as the ADMM residuals converge to zero through iterations.
- All three formulations strictly follow ADMM, whose convergence has been established in the literature.
- The penalty parameter ρj affects convergence speed; for the first two formulations, its value is generally selected through practical experience.
- For the Local Explicit formulation, a selection method for ρj is proposed by optimizing an upper bound on the convergence rate.
IV. EXAMPLES ON VEHICLE CONTROL
The vehicle-control examples coordinate multiple wheel-level agents to meet longitudinal and lateral objectives simultaneously. Cruise control combines speed tracking with yaw-rate tracking through shared and externally driven agents.
- A. Cruise Control: Cruise control simultaneously tracks longitudinal speed and yaw rate using four wheel-control agents.The DTR, RTV, FDB, and STR agents respectively provide rear driving torque, rear torque vectoring, front differential braking, and driver steering input.
- A. Cruise Control: The MACS topology assigns DTR to speed tracking, RTV to yaw-rate tracking, and FDB to both objectives, while STR contributes externally to both.The shared FDB agent couples the two objective-specific agent groups.
- A. Cruise Control: The DTR, RTV, and FDB agents have bounded torque actions, while STR supplies estimated lateral tire-force contributions as an external input.DTR ranges from −2000 to 2000, RTV from −500 to 500, and FDB from −1000 to 0.
- A. Cruise Control: Cruise-control states comprise longitudinal speed, lateral speed, and yaw rate, with references determined by speed planning, road friction, and a single-track vehicle model.The target yaw rate is limited by road friction, and the steering angle is treated as a driver input.
B. Holistic Vehicle Stability Control
Holistic vehicle stability control coordinates yaw-rate tracking and wheel-speed tracking for maximum tire capability. Its topology adds a traction-control agent and shares the rear torque-vectoring agent across objectives.
- B. Holistic Vehicle Stability Control: Holistic stability control tracks desired yaw rate and wheel speed for maximum tire capability.The vehicle state includes lateral speed, yaw rate, and the speeds of the two rear wheels.
- B. Holistic Vehicle Stability Control: The TCR agent reduces rear-axle driving torque when rear-wheel slip begins, extending the cruise-control configuration with a slip-management function.This example contains one more agent than cruise control.
- B. Holistic Vehicle Stability Control: The stability-control and wheel-stability objectives share RTV, while FDB serves VSC and TCR serves WSC; STR and DTR enter as external inputs, respectively.The figure defines SVSC = {RTV, FDB} and SWSC = {TCR, RTV}.
- B. Holistic Vehicle Stability Control: The reference wheel speed is set from vehicle speed and a desired longitudinal slip ratio, usually 15%, while the yaw-rate reference remains friction-limited.The reference vector contains the target yaw rate and equal target speeds for both rear wheels.
V. EXPERIMENTAL STUDIES
Experiments compare distributed formulations with integrated MPC in simulations and evaluate the Local Explicit formulation during aggressive lane changes on a real electric vehicle. The results show low torque suboptimality, rapid convergence, and lower computational time than integrated MPC.
- A. Example 1: Cruise Control: Experiments ran in real time at 20 Hz on a four-motor electric vehicle using a laptop-based Matlab implementation and aggressive lane changes on a dedicated test track.The track provided different road frictions and sufficient space for aggressive driving.
- A. Example 1: Cruise Control: The Local Explicit formulation had the best computational efficiency and ran faster than integrated MPC, with torque suboptimality mostly below 5 Nm.The three formulations were compared using suboptimality and time-consumption ratios; all approximated the global optimum.
- A. Example 1: Cruise Control: When yaw-rate tracking was enabled during an aggressive lane change, over-steering was significantly suppressed and yaw stability improved while speed tracking remained smooth.The comparison used tests with only speed tracking enabled versus both objectives enabled under similar speed and steering profiles.
- A. Example 1: Cruise Control: The Local Explicit controller coordinated DTR, RTV, and FDB so rear driving, rear differential, and front independent braking torques jointly served the control objectives.The torque-command results demonstrate cooperation among multiple controllers during the vehicle experiment.
- A. Example 1: Cruise Control: Torque suboptimality was mostly below 20 Nm, iterations stayed below 15, and the time-consumption ratio remained below 1, including the demanding focus period.The focus period required slightly more iterations and a somewhat higher ratio, but the ratio still remained below 1.
B. Example 2: Holistic Vehicle Stability Control
Holistic stability control used multi-objective AMPC to coordinate vehicle stability objectives across two maneuvers. The Local Explicit formulation improved vehicle responses while maintaining approximate convergence and computational efficiency.
- Experiment 1: Straight launch and brake: Wheel speeds stayed near desired values, yaw-rate error decreased, and overall stability improved during straight launch and braking on a low-friction road.The improvement did not sacrifice longitudinal acceleration or deceleration.
- Control-agent coordination: The controller assigned braking and drive-torque adjustments across agents, with FDB braking the front wheels while TCR and RTV coordinated rear-wheel torque.TCR first reduced drive torque to suppress wheel slip, after which RTV adjusted torque for both objectives.
- Experiment 1: Straight launch and brake: Torque suboptimality stayed mostly below 5 Nm, iterations below 15, and time-consumption ratio below 1 in the straight-launch-and-braking experiment.The focus period required slightly more iterations, but its time-consumption ratio remained below 1.
- Experiment 2: Double lane change when acceleration: During double-lane-change acceleration, enabling both objectives reduced yaw-rate error and prevented excessive slip compared with driver-only control.The driver-only test exhibited significant longitudinal wheel slip and over-steering requiring aggressive counter-steering.
- Experiment 2: Double lane change when acceleration: In the double-lane-change experiment, torque suboptimality remained mostly below 5 Nm, iterations stayed below 25, and time-consumption ratio remained below 1.These results support approximate convergence and computational efficiency for the tested maneuver.
- Overall findings: Across the vehicle evaluations, multi-objective AMPC achieved multiple objectives simultaneously, with the Local Explicit formulation showing approximate global convergence and superior computational efficiency.The formulation was selected for experimental comparison because it was more efficient than the other formulations.