Real-time analysis for nonlinear model predictive control of autonomous vehicles

A Nonlinear model predictive control (NMPC) for trajectory tracking with the obstacle avoidance of autonomous road vehicles traveling at realistic speeds is presented in this paper, with a focus on the performance of those controllers with respect to the look-ahead horizon of the NMPC. Two different methods of obstacle avoidance are compared and then the NMPC is tested in several simulated but realistic tracking scenarios involving static obstacles on constrained roadways. In order to simplify the vehicle dynamics, a bicycle model is used for the prediction of future vehicle states in the NMPC framework. However, a high-fidelity, nonlinear CarSim vehicle model is used to evaluate the vehicle performance and test the controllers in the simulation results. The CPU time is also analyzed to evaluate these schemes for real-time applications. The results show that the NMPC controller provides satisfactory online tracking performance in a realistic scenario at normal road speeds while still satisfying the real-time constraints. In addition, it is shown that the longer prediction horizons allow for better responses of the controllers, which reduce the deviations while avoiding the obstacles, as compared with shorter horizons.

Nonlinear Model Predictive Control of Food Sterilization Processes

This paper proposes a vision-based obstacle avoidance strategy in a dynamic environment for a fixed-wing unmanned aerial vehicle (UAV). In order to apply a nonlinear model predictive control (NMPC) framework to image-based visual servoing (IBVS), a dynamic model from UAV control input to image features is derived. From this dynamics, a visual information-based obstacle avoidance strategy in an unknown environment is proposed. When a vision system is employed on a UAV, it is easy to lose visibility of the target in the image plane due to its maneuvering. To address this issue, a visibility constraint is considered in the NMPC framework. The advantage of the proposed method is that the constraints (e.g., visibility maintaining, actuator saturation) can be modeled and solved in a unified framework. Numerical simulations on a UAV model show satisfactory results in reference tracking and obstacle avoidance maneuvers with the constraints.

We propose a nonlinear model predictive control (NMPC) framework based on a direct optimal control method that ensures continuous-time constraint satisfaction and accurate evaluation of the running cost, without compromising computational efficiency. We leverage the recently proposed successive convexification framework for trajectory optimization, where: (1) the path constraints and running cost are equivalently reformulated by augmenting the system dynamics, (2) multiple shooting is used for exact discretization, and (3) a convergence-guaranteed sequential convex programming (SCP) algorithm, the prox-linear method, is used to solve the discretized receding-horizon optimal control problems. The resulting NMPC framework is computationally efficient, owing to its support for warm-starting and premature termination of SCP, and its reliance on first-order information only. We demonstrate the effectiveness of the proposed NMPC framework by means of a numerical example with reference-tracking and obstacle avoidance. The implementation is available at https://github.com/UW-ACL/nmpc-ctcs.

Real-time nonlinear model predictive control for optimizing the ammonia coverage ratio of an SCR system based on TC-QPSO

In this article, we devise a nonlinear model predictive control framework for the energy management of nonhybrid hydrostatic drive transmissions. The controller determines the optimal control commands of the actuators by minimising a cost function over a receding horizon. With our approach, the velocity-tracking error is minimised while keeping the fuel economy of the system high. The hydrostatic drive transmission system studied in this article is a typical commercial work machine, that is, there is no energy storage or alternative power source in the system (a nonhybrid hydrostatic drive transmission). We evaluate success with a validated simulation model of the hydrostatic drive transmission of a municipal tractor. In our experiments, a detailed system model is used both in the system simulation and in the prediction phase of the nonlinear model predictive control. The use of a detailed model in the nonlinear model predictive control framework places our design as a benchmark for controlling nonhybrid hydrostatic drive transmissions, when compared to solutions using simplified models or computationally less intensive control methods as in earlier work by the authors. Our nonlinear model predictive control approach enables numerically robust optimisation convergence with the utilised complex nonlinear model. Above all, this is accomplished with stabilising terminal constraints and distinctive terminal cost, both based on an optimal steady-state solution. In addition, a simple method to generate initial guesses for optimisation is introduced. When compared with the performance of a controller based on quasi-static models, our results show notable improvement in velocity tracking while maintaining high fuel economy. Furthermore, our experiments demonstrate that framing energy management as a nonlinear model predictive control provides a flexible and rigorous framework for fast velocity tracking and high energy efficiency. We also compare the results with those of an industrial baseline controller.

A Nonlinear Model Predictive Controller (NMPC) for trajectory tracking of autonomous vehicles is presented in this paper. This controller is tested under several constrained scenarios including static obstacle avoidance and avoidance of obstacles with more complex constraints. In the latter case the real life necessary constraint of remaining on the road while performing the obstacle avoidance manoeuvers is implemented. The resulting controllers are applied and tested in a simulation environment and the required CPU time is analyzed to evaluate the ability to implement these schemes in real-time using both cold and warm starts for the embedded optimization problem. In order to simplify the vehicle dynamics, a bicycle model is used for the prediction of future vehicle states in the NMPC framework. A fully nonlinear CarSim vehicle model is used to evaluate the vehicle performance in the simulations. Results show that the NMPC controller provides satisfactory online tracking performance in a realistic scenario at normal road speeds while still satisfying the real-time constraints.

Online planning of whole-body motions for legged robots is challenging due to the inherent nonlinearity in the robot dynamics. In this work, we propose a nonlinear model predictive control (MPC) framework, the BiConMP which can generate whole body trajectories online by efficiently exploiting the structure of the robot dynamics. BiConMP is used to generate various cyclic gaits on a real quadruped robot and its performance is evaluated on different terrain, countering unforeseen pushes, and transitioning online between different gaits. Furthermore, the ability of BiConMP to generate nontrivial acyclic whole-body dynamic motions on the robot is presented. The same approach is also used to generate various dynamic motions in MPC on a humanoid robot (Talos) and another quadruped robot (AnYmal) in simulation. Finally, an extensive empirical analysis on the effects of planning horizon and frequency on the nonlinear MPC framework is reported and discussed.

Autonomous Unmanned Aerial Vehicles (UAVs) landings on moving aerial platforms present substantial challenges, including real-time feasible path planning and the design of robust control schemes to mitigate disturbances. This paper presents a novel docking strategy for UAVs that integrates dynamic path optimization with a Nonlinear Model Predictive Control (NMPC) framework. The proposed approach initiates with a global planner to generate collision-free, kinodynamically feasible paths, which are subsequently refined using a local planner that employs B-spline formulation alongside gradient-based optimization methods. To enhance control stability, particularly during the landing phase, the NMPC controller is augmented with a dynamic downwash model that compensates for aerodynamic disturbances. Extensive validation in both simulation and real-world experiments demonstrates that the proposed method achieves robust trajectory tracking, reduced landing errors, and improved platform stability. Simulation results show the proposed planner reaches a maximum velocity of 3.49 m/s and an average velocity of 2.07 m/s with a 100% landing success rate. Real-world experiments indicate that with the downwash model, vertical oscillations during landing are reduced by nearly 79% while the overall vertical landing error drops by over 60%.

The article studies the trajectory tracking control problem of underactuated marine vehicles via the nonlinear model predictive control (NMPC) strategy, where practical control and state constraints present. It is a well-known challenging issue that the conventional NMPC is not applicable for underactuated marine vehicles, due to the fact that there does not exist a local static continuous state-feedback controller to stabilize the underactuated dynamics. To resolve this issue, this article proposes to construct an auxiliary time-varying tracking controller to aid terminal constraint design in the NMPC framework, where the time-varying tracking controller borrows the ideas from Lyapunov's direct method and backstepping approach. Based on this, a novel NMPC algorithm is designed to ensure trajectory tracking control of underactuated marine vehicles. Furthermore, a systematic parameter design approach is developed. Under the designed parameters, we show that the tracking error system is input-to-state stable (ISS). Finally, the effectiveness of the designed algorithm is verified by thorough simulation and hardware experiments.

In this work, optimal operation of an Electric Submersible Pump (ESP) lifted oil field is developed by using a Nonlinear Model Predictive Control (NMPC) framework. NMPC is used not only for setpoint tracking but also as an economic optimizer for maximizing profit. Optimal control problem is formulated as a general nonlinear programming (NLP) problem with process constraints. The scope of the NMPC framework is to operate the ESP of each oil well inside its designated operating window by minimizing the cost of the total power consumed by all the ESPs in the field and the cost of operating the separator. In other words, the speed of the ESPs and the production choke valves opening should be optimally chosen for maximizing the profit. At the same time, the capacity of the separator should not be exceeded. The simulation results show that the production choke valves are always 100% opened to maintain optimal fluid flow rate from the reservoir. With no constraints in the top side facility (separator capacity), it is optimal to run the ESP pumps in the upper right corner of the allowed operating window for the ESPs.

In recent years, there has been a large increase in the number of applications for mobile robots ranging from vacuum cleaners to Mars rovers. Depending on the applications, various challenges still need to be addressed related to the control of mobile robots and are being actively researched. We address here the problem of collision avoidance in the presence of dynamic obstacles using the Nonlinear Model Predictive Control (NMPC) framework. We use a scenario-tree formulation for the prediction of different trajectories of the dynamic obstacle and propose two strategies to avoid collisions. We propose a simple strategy to obtain the controlled inputs by solving a nominal NMPC problem by adding different scenarios of predicted obstacle trajectories as constraints. As a second strategy, a less conservative approach under the multi-stage NMPC framework by modeling the recourse in the predictions of the controlled robot is proposed. Both strategies can be applied in real-time and avoid collisions with dynamic obstacles. The non-conservative strategy shows superior performance at the expense of an increased computational effort.

This paper proposes an efficient nonlinear model predictive control (NMPC) framework to solve nonconvex lithium-ion battery trajectory optimization problems for battery management systems (BMS). It is challenging to solve these problems online due to complexity and nonconvexity. To address these challenges, we combine four established techniques from the control literature. First, we represent the single particle model (SPM) using orthogonal projection techniques. Second, we exploit the differential flatness of Fick’s second law of diffusion to capture all of the dynamics in one electrode using a single scalar trajectory of a “flat output” variable. Third, we optimize the above flat output trajectories using pseudospectral methods. Fourth, we employ the NMPC strategy to solve the battery trajectory optimization problem online. The proposed NMPC framework is demonstrated by solving 2 optimal charging problems accounting for physics-based side reaction constraints and is shown to be twice as computationally efficient as pseudospectral online optimization alone.

In this article, we present a quasi-infinite horizon nonlinear model predictive control (MPC) scheme for tracking of generic reference trajectories. This scheme is applicable to nonlinear systems, which are locally incrementally stabilizable. For such systems, we provide a reference generic offline procedure to compute an incrementally stabilizing feedback with a continuously parameterized quadratic quasi-infinite horizon terminal cost. As a result, we get a nonlinear reference tracking MPC scheme with a valid terminal cost for general reachable reference trajectories without increasing the online computational complexity. The practicality of this approach is demonstrated with a benchmark example.

Moving horizon estimation and nonlinear model predictive control for autonomous agricultural vehicles