Model Predictive Path-Following Control Research Articles

An improved Bi-RRT*-based path planning algorithm with adaptive search strategy assignment mechanism for ultra-low-altitude penetration of fixed-wing aircraft

The ultra-low-altitude penetration with complex three-dimensional terrain environment usually requires the path planning algorithm to be computationally efficient to generate feasible optimized flight paths in a limited period of time. This paper investigates an improved bidirectional rapidly-exploring random tree* (RRT*) path planning algorithm with adaptive search strategy assignment mechanism to accelerate the exploration speed. The greedy optimization method and the three-dimensional Dubins method are utilized to reduce redundant nodes and optimize the flight path to satisfy the kinematic constraints of the fixed-wing aircraft. The model predictive control method is then employed to design the path-following controller, in which multiple types of constraints can be addressed. To demonstrate the superior planning efficiency of the proposed adaptive-alternating-exploration RRT* method, the existing widely-used path planning algorithms are used as benchmarks in the simulation studies. Simulation results show that the path planning time can be significantly reduced by up to 90% with the proposed adaptive-alternating-exploration RRT* method, simultaneously with optimized path length. Moreover, the designed model predictive path-following controller succeeds to track the planned collision-free path with maximum tracking errors of less than 2 meters. The effectiveness of the path planning algorithm and the designed controller is thoroughly demonstrated.

Model predictive path-following control for truck–trailer systems with specific guidance points — design and experimental validation

This article presents an experimental validation of a model predictive path-following control algorithm (PF-MPC ) applied to a truck–trailer system, encompassing both forward and backward motions. The proposed controller is designed to precisely follow a predefined path generated by a path planner, with a designated guidance point positioned on either the truck or the trailer. The algorithm’s performance is assessed through implementation and validation on a model-scaled truck–trailer system, where MPC, state estimation, and low-level control are executed on a microcontroller (MCU ). The experimental results demonstrate the effectiveness of the proposed control approach in achieving highly accurate path-following performance, even when operating in the challenging context of unstable backward motion, and with the involvement of up to two trailers. Moreover, the successful implementation of the algorithm on a microcontroller underscores its suitability for real-time control applications. The results of this study collectively highlight the promising potential of the proposed control algorithm for practical utilization in autonomous driving systems.

Model Predictive Path-Following Control for UGVs with Curvature Inaccuracy: A Disturbance Rejection Approach Combining Speed Regulation

Model Predictive Path-Following Control for UGVs with Curvature Inaccuracy: A Disturbance Rejection Approach Combining Speed Regulation

Model predictive path-following controller for Generalised N-Trailer vehicles with noisy sensors and disturbances

Generalised N-Trailer (GNT) vehicles, commonly used in agriculture, mining, and industry, consist of a tractor pulling multiple passive trailers. This paper presents a nonlinear moving horizon estimator (NMHE) and nonlinear model predictive controller (NMPC) for GNT robotic vehicles. The NMHE accurately estimates the vehicle’s state under challenging conditions such as noisy measurements, disturbances, and different soil conditions, without relying on assumptions about disturbances, making it more effective than techniques like the Extended Kalman Filter (EKF). Similarly, the NMPC successfully steers the GNT along a predefined path with lower control effort compared to existing algorithms, thanks to smoother tractor manoeuvres that minimise energy in the objective function. Moreover, unlike other methods, this approach computes the tractors’ velocities instead of those of the last trailer, eliminating the need for kinematic inversion and making it suitable for various vehicle configurations. Efficient solvers for the NMHE and NMPC problems were generated using two different open-source frameworks. The proposed framework was evaluated through challenging simulated studies and field experiments. Additional resources, including code implementation and field experiment videos, can be found at https://drive.google.com/drive/folders/1n-qVWJA40cZn-WiDpwXhhF9AdK54LTfX?usp=sharing.

Model Predictive Path Following Control without terminal constraints for holonomic mobile robots

In this paper, a model predictive path following control (MPFC) for holonomic mobile robots is considered. The MPFC is aimed to control a mobile robot to follow a geometric path, where the time evolution of the path parameterization is not fixed a priori. Instead, the time evolution is considered as an extra degree of freedom of the controller. Contrary to previous works, in this study, the closed-loop asymptotic stability of holonomic mobile robots under MPFC without terminal constraints or costs is rigorously proven and a stabilizing-horizon length is calculated. The analysis is based on verifying the cost-controllability assumption by deriving an upper bound of the MPFC value function with a finite prediction horizon. Then, using this bound, the length of a stabilizing prediction horizon is calculated. The analysis is performed in the discrete time settings and theoretical results are verified with numerical simulations as well as implementations on an actual mobile robot.

Simultaneous Feasible Local Planning and Path-Following Control for Autonomous Driving

In this paper, a new approach for lane change and double-lane change planning and following for autonomous driving is proposed. Herein, we introduce a novel technique, based on exponential functions, to generate online and feasible lane change maneuvers; these maneuvers satisfy the constraints on the maximum allowable curvature a given vehicle can handle. In addition, a simultaneous local path planning and path-following control framework is adapted. The framework utilizes a multi-threading architecture to run the local planner module concurrently with the control module. The planning module generates parametric reference paths based on the proposed lane change and double-lane change maneuvers. The control module is based on a Model Predictive Path-following Control (MPFC) scheme, which achieves the path following objective while satisfying vehicle’s state and control limits. To validate the proposed framework, several real-time simulation scenarios are designed and tested on CARLA soft real-time vehicle simulator. The results show the effectiveness of the proposed framework in generating and smoothly following lane change maneuvers.

Nonlinear Model Predictive Path Following Controller with Obstacle Avoidance

In the control systems community, path-following refers to the problem of tracking an output reference curve. This work presents a novel model predictive path-following control formulation for nonlinear systems with constraints, extended with an obstacle avoidance strategy. The method proposed in this work simultaneously provides an optimizing solution for both, path-following and obstacle avoidance tasks in a single optimization problem, using Nonlinear Model Predictive Control (NMPC). The main idea consists in extending the existing NMPC controllers by the introduction of an additional auxiliary trajectory that maintains the feasibility of the successive optimization problems even when the reference curve is unfeasible, possibly discontinuous, relaxing assumptions required in previous works. The obstacle avoidance is fulfilled by introducing additional terms in the value functional, rather than imposing state space constraints, with the aim of maintaining the convexity of the state and output spaces. Simulations results considering an autonomous vehicle subject to input and state constraints are carried out to illustrate the performance of the proposed control strategy.

Learning-Based Predictive Path Following Control for Nonlinear Systems Under Uncertain Disturbances

Accurate path following is challenging for autonomous robots operating in uncertain environments. Adaptive and predictive control strategies are crucial for a nonlinear robotic system to achieve high-performance path following control. In this paper, we propose a novel learning-based predictive control scheme that couples a high-level model predictive path following controller (MPFC) with a low-level learning-based feedback linearization controller (LB-FBLC) for nonlinear systems under uncertain disturbances. The low-level LB-FBLC utilizes Gaussian Processes to learn the uncertain environmental disturbances online and tracks the reference state accurately with a probabilistic stability guarantee. Meanwhile, the high-level MPFC exploits the linearized system model augmented with a virtual linear path dynamics model to optimize the evolution of path reference targets, and provides the reference states and controls for the low-level LB-FBLC. Simulation results illustrate the effectiveness of the proposed control strategy on a quadrotor path following task under unknown wind disturbances.

Nonlinear Model Predictive Path-Following Controller for a Small-Scale Autonomous Bulldozer for Accurate Placement of Materials and Debris of Masonry in Construction Contexts

This paper presents a nonlinear model predictive control (NMPC) scheme for the medium-level control of a small-scale autonomous bulldozer to accurately and safely displace crushed materials of masonry in construction contexts. For this purpose, the controller is required to minimize the error between the achieved and required paths; additionally, the control actions must be smooth for minimizing the mistreatment of equipment, which is intended to operate in the long term, as it is usual in industrial-grade solutions. The proposed NMPC based path-follower can adequately handle the platform's constraints and usual perturbations. In terms of state estimation, a map-based localizer is implemented via an extended Kalman filter (EKF) based on the platform nominal process model and light detecting and ranging (LiDAR) and inertial measurement unit (IMU) sensors measurements. The localizer provides estimates of the platform's pose, necessary for the MPC controller's state feedback. An actual experiment on a modified UGV (Clearpaths Husky A-200) is performed to validate the performance of the proposed control scheme. The UGV is retrofitted with a blade (for pushing material) and appropriate sensors for the necessary perception tasks. Experimental results indicate that the proposed control scheme is robust and suitable for safely pushing the crushed materials, presenting appropriately low deviation from the nominal path and requiring reasonably low processing time.

Model Predictive Path-Following Control of Snake Robots Using an Averaged Model

We propose a new simplified model for the control design of snake robots and apply it to a path-following control design using model predictive control (MPC). While MPC has an advantage in that inequality constraints can be explicitly considered in control design, most of the previous simplified models are still too complex to apply to MPC since the models include joint angles as time-varying parameters. Thus, we exclude joint angles using the averaging method to construct a simpler model. Another feature of the proposed model is that it can be derived from the original complex model without parameter identification using simulation data and without assuming straight-line movements. In addition to inequality constraints on joint angles and the frequency of joint motions, we impose constraints on the change rates of these variables in our MPC design since the averaged model is derived by assuming that these variables slowly change. Furthermore, we introduce a soft constraint to decrease the effects of approximation error of the simplified model on the control performance. The effectiveness of the control system is verified in both simulations and experiments.

A predictive path-following controller for multi-steered articulated vehicles

Stabilizing multi-steered articulated vehicles in backward motion is a complex task for any human driver. Unless the vehicle is accurately steered, its structurally unstable joint-angle kinematics during reverse maneuvers can cause the vehicle segments to fold and enter a jack-knife state. In this work, a model predictive path-following controller is proposed enabling automatic low-speed steering control of multi-steered articulated vehicles, comprising a car-like tractor and an arbitrary number of trailers with passive or active steering. The proposed path-following controller is tailored to follow nominal paths that contains full state and control-input information, and is designed to satisfy various physical constraints on the vehicle states as well as saturations and rate limitations on the tractor’s curvature and the trailer steering angles. The performance of the proposed model predictive path-following controller is evaluated in a set of simulations for a multi-steered 2-trailer with a car-like tractor where the last trailer has steerable wheels.

Nonlinear Model Predictive Path-Following Control for Highly Automated Driving

Abstract Within the scope of highly automated driving, steering a vehicle autonomously along a pre-specified geometric reference path is an important control task. In this article we present an implementation of model predictive path-following control for a modified VW Golf VII series vehicle. This approach allows the assignment of the reference motion and the computation of inputs to track the reference simultaneously at the runtime of the controller, while respecting actuator and state constraints. In contrast to trajectory tracking, the time evolution along the path is not fixed a priori. It can be seen as a degree of freedom to be determined by the controller. This allows the controller to adapt the vehicle speed to the respective driving situation according to the modeled physical limits of the vehicle. Therefore, a combined longitudinal and lateral vehicle dynamic model is derived firstly. Finally, experimental results are presented for a test scenario to demonstrate the abilities of the approach.

Sample Efficient Learning of Path Following and Obstacle Avoidance Behavior for Quadrotors

In this paper we propose an algorithm for the training of neural network control policies for quadrotors. The learned control policy computes control commands directly from sensor inputs and is hence computationally efficient. An imitation learning algorithm produces a policy that reproduces the behavior of a path following control algorithm with collision avoidance. Due to the generalization ability of neural networks, the resulting policy performs local collision avoidance of unseen obstacles while following a global reference path. The algorithm uses a time-free model predictive path-following controller as a supervisor. The controller generates demonstrations by following few example paths. This enables an easy to implement learning algorithm that is robust to errors of the model used in the model predictive controller. The policy is trained on the real quadrotor, which requires collision-free exploration around the example path. An adapted version of the supervisor is used to enable exploration. Thus, the policy can be trained from a relatively small number of examples on the real quadrotor, making the training sample efficient.

Predictive Path Following of Mobile Robots without Terminal Stabilizing Constraints

This paper considers model predictive path-following control for differentially driven mobile robots and state-space paths. In contrast to previous works, we analyze stability of model predictive path-following control without stabilizing terminal constraints or terminal costs. To this end, we verify cost controllability assumptions and compute bounds on the stabilizing horizon length. Finally, we draw upon simulations to verify our stability results.

Implementation of Nonlinear Model Predictive Path-Following Control for an Industrial Robot

Many robotic applications, such as milling, gluing, or high precision measurements, require the exact following of a pre-defined geometric path. In this paper, we investigate the real-time feasible implementation of model predictive path-following control for an industrial robot. We consider constrained output path following with and without reference speed assignment. We present results from an implementation of the proposed model predictive path-following controller on a KUKA LWR IV robot.

Model Predictive Path-Following Control for Airborne Wind Energy Systems

A nonlinear path following model predictive control scheme with application to a kite based airborne wind energy system is presented. A novel terminal constraint is introduced to guarantee closed-loop stability and convergence of the vehicle to geometric paths of desired shapes. Convergence conditions are investigated and the efficacy of the approach is demonstrated via numerical simulations for desired path shapes under nominal and perturbed conditions.

Real-time Nonlinear Model Predictive Path-Following Control of a Laboratory Tower Crane

A path-following controller is developed and applied to a laboratory tower crane. The control task is to move a load along a predefined geometric path. The time evolution along the path is not fixed but left as a degree of freedom to be determined by the controller. In order to be able to account for system constraints, a model predictive control scheme is adopted with special focus on real-time feasibility with small sampling times. The resulting controller is applied to a laboratory-scale tower crane and validated through simulation studies and measurement results.

Adaptive nonlinear model predictive path-following control for a fixed-wing unmanned aerial vehicle

This paper presents an adaptive Nonlinear Model Predictive Control (NMPC) for the path tracking control of a fixed-wing unmanned aircraft. The objective is to minimize the mean and maximum error between the reference trajectory and the UAV. Navigating in a cluttered environment requires accurate tracking. However linear controllers cannot provide good tracking performance due to nonlinearities that arise in the system dynamics and physical limitations such as actuator saturation and state constraints. NMPC provides an alternative since it can combine multiple objectives and constraints which minimize the objective function. However, computational complexity is a major barrier to the real time implementation of the NMPC. An indirect approach which uses gradient descent methods can speed up the optimization but it is dicult to specify a proper termination condition of the optimization. If a decreasing cost metric is used, it can cause control input oscillations. We propose a new optimization termination metric which can remove the control input oscillations. This can be achieved by adding the actuator slew limit to the optimization termination requirement in addition to the cost monotonocity. In addition, we propose an adaptive NMPC which varies the control horizon according to the path curvature profile for tight tracking. Simulation results show that the proposed optimization algorithm can remove control input oscillations and track the trajectory more accurately than the conventional fixed horizon NMPC.