In this paper, we use a nonlinear hierarchical model predictive control (MPC) to stabilize the Segway robot. We also use hardware in the loop (HIL) simulation in order to model the delay response of the wheels' motor and verify the control algorithm. In Two-Wheeled Personal Transportation Robots (TWPTR), changing the center of mass location and value, the nonlinearity of the equations, and the dynamics of the system are topics complicating the control problem. A nonlinear MPC predicts the dynamics of the system and solves the control problem efficiently, but requires the exact information of the system models. Since model uncertainties are unavoidable, the time-delay control (TDC) method is used to cancel the unknown dynamics and unexpected disturbances. When the TDC method is applied, the results show that the maximum required torque for engines is reduced by 7%. And the maximum displacement of the robot has dropped by 44% around the balance axis. In other words, robot stability has increased by 78%. Due to the cost of implementing control in practice, this research runs the HIL simulation for the first time. The use of this simulation helps in implementing the control algorithms without approximation, and also the system response can be discussed in a more realistic way.
To be able to measure relevant data for transport infrastructure monitoring and to obtain maintenance indicators in a crowd sensing-based fashion, a set of requirements (both from hardware and software points of view) needs to be satisfied. Heterogeneity of smartphones and various uncertainties associated with the mainstream \textit{off-the-shelf} hardware combined with the fact that inexperienced participants will take an active part in the data collection process necessitates that the system accounts for dynamicity, uncertainty, unreliability, and heterogeneity of the environment, participan…
To effectively control large-scale distributed systems online, model predictive control (MPC) has to swiftly solve the underlying high-dimensional optimization. There are multiple techniques applied to accelerate the solving process in the literature, mainly attributed to software-based algorithmic advancements and hardware-assisted computation enhancements. However, those methods focus on arithmetic accelerations and overlook the benefits of the underlying system's structure. In particular, the existing decoupled software-hardware algorithm design that naively parallelizes the arithmetic oper…
We present a delay-compensating control method that transforms exponentially stabilizing controllers for an undelayed system into a sample-based predictive controller with numerical integration. Our method handles both first-order and transport delays in actuators and trades-off numerical accuracy with computation delay to guaranteed stability under hardware limitations. Through hybrid stability analysis and numerical simulation, we demonstrate the efficacy of our method from both theoretical and simulation perspectives.
This paper considers a cooperative cruise control problem from a predictive control perspective. Online decision-making is used to be executed during the driving process based on the information obtained from the network. We formalize a synchronization problem approach from a predictive control theory using bargaining games to find an operating agreement between the vehicles. Finally, we test these results in an emulation environment in a hardware-in-the-loop system.
Model predictive control (MPC) has become a hot cake technology for various applications due to its ability to handle multi-input multi-output systems with physical constraints. The optimization solvers require considerable time, limiting their embedded implementation for real-time control. To overcome the bottleneck of traditional quadratic programming (QP) solvers, this paper proposes a robust penalty method (RPM) to solve an optimization problem in a linear MPC. The main idea of RPM is to solve an unconstrained QP problem using Broyden Fletcher Goldfarb Shannon (BFGS) algorithm. The beauty …
This paper considers the control of uncertain systems that are operated under limited resource factors, such as battery life or hardware longevity. We consider here resource-aware self-triggered control techniques that schedule system operation non-uniformly in time in order to balance performance against resource consumption. When running in an uncertain environment, unknown disturbances may deteriorate system performance by acting adversarially against the planned event triggering schedule. In this work, we propose a resource-aware stochastic predictive control scheme to tackle this challeng…
The modular open-source framework GRAMPC-D for model predictive control of distributed systems is presented in this paper. The modular concept allows to solve optimal control problems (OCP) in a centralized and distributed fashion using the same problem description. It is tailored to computational efficiency with the focus on embedded hardware. The distributed solution is based on the Alternating Direction Method of Multipliers (ADMM) and uses the concept of neighbor approximation to enhance convergence speed. The presented framework can be accessed through Cpp and Python and also supports plu…
The paper deals with the design of an improved model predictive control scheme for achieving station-keeping in a quasi Halo orbit around the $L_2$ point in the Earth-Moon system. The improvement is obtained thanks to a multi-rate sampled-data trajectory planner that allows for simplifying the optimization problem of the model predictive controller while guaranteeing feasibility and convergence to the desired orbit. The multi-rate planner is designed based on a simplified model of the dynamics under a preliminary nonlinear regulation feedback. The proposed control scheme is shown to outperform…
Whole-Body Model-Predictive Control of Legged Robots with MuJoCo
Department Aeronautics and Astronautics, Massachusetts Institute of Technology（航空宇航与工程力学系，麻省理工学院）；Google DeepMind（谷歌DeepMind）；Department of Electrical and Computer Engineering, Carnegie Mellon University（电气与计算机工程系，卡内基梅隆大学）；Robotics Institute, Carnegie Mellon University（机器人研究所，卡内基梅隆大学）
Model predictive Path-Following Control (MPFC) is a viable option for motion systems in many application domains. However, despite considerable progress on tailored numerical methods for predictive control, the real-time implementation of predictive control and MPFC on small-scale autonomous platforms with low-cost embedded hardware remains challenging. While usual stabilizing MPC formulations lead to static feedback laws, the MPFC feedback turns out to be dynamic as the path parameter acts as an internal controller variable. In this paper, we leverage deep learning to implement predictive pat…
We present the design, implementation and experimental validation of a supervisory predictive control approach for an electrical heating system featuring a phase change slurry as heat storage and transfer medium. The controller optimizes the energy flows that are used as set points for the heat generation and energy distribution components. The optimization handles the thermal and electrical subsystems simultaneously and is able to switch between different objectives. We show the control can be implemented on low-cost embedded hardware and validate it with an experimental test bed comprising a…
Distributed model predictive control (DMPC) is often used to tackle path planning for unmanned aerial vehicle (UAV) swarms. However, it requires considerable computations on-board the UAV, leading to increased weight and power consumption. In this work, we propose to offload path planning computations to multiple ground-based computation units. As simultaneously communicating and recomputing all trajectories is not feasible for a large swarm with tight timing requirements, we develop a novel event-triggered DMPC that selects a subset of most relevant UAV trajectories to be replanned. The resul…
GATO: GPU-Accelerated and Batched Trajectory Optimization for Scalable Edge Model Predictive Control
School of Engineering and Applied Science, Columbia University（哥伦比亚大学工程与应用科学学院）；University of Michigan（密歇根大学）；Barnard College, Columbia University and Dartmouth College（哥伦比亚大学巴纳德学院和达特茅斯学院）
Code Generation and Conic Constraints for Model-Predictive Control on Microcontrollers with Conic-TinyMPC
School of Engineering and Applied Science, Columbia University（哥伦比亚大学工程与应用科学学院）；Carnegie Mellon University（卡内基梅隆大学）；Massachusetts Institute of Technology（麻省理工学院）；Barnard College, Columbia University and Dartmouth College（哥伦比亚大学巴纳德学院和达特茅斯学院）
In automotive power electronics, distortion and electromagnetic interference (EMI) generated by the switching action of power semiconductors can be a significant challenge for the design of a compact, lightweight vehicle. As semiconductor switching frequencies increase, e.g., through the introduction of new materials, such as gallium nitride and silicon carbide, this problem becomes more severe. We present a control scheme for an automotive dc-to-dc converter that reduces the EMI generated by shaping switching distortion predictively at the run time. The multistep model-predictive control sche…
ETH Zürich（苏黎世联邦理工学院）；California Institute of Technology（加州理工学院）
The theoretical unification of Nonlinear Model Predictive Control (NMPC) with Control Lyapunov Functions (CLFs) provides a framework for achieving optimal control performance while ensuring stability guarantees. In this paper we present the first real-time realization of a unified NMPC and CLF controller on a robotic system with limited computational resources. These limitations motivate a set of approaches for efficiently incorporating CLF stability constraints into a general NMPC formulation. We evaluate the performance of the proposed methods compared to baseline CLF and NMPC controllers wi…
This article presents the real-time implementation of the model predictive control for tracking formulation to control a two-wheeled inverted pendulum robot. This formulation offers several advantages over standard MPC formulations at the expense of the addition of a small number of decision variables, which complicates the inner structure of the matrices of the optimization problem. We implement a sparse solver, based on an extension of the alternating direction method of multipliers, in the system's embedded hardware. The results indicate that the solver is suitable for controlling a real sy…
University of Toronto（多伦多大学）；University of Tartu（塔尔图大学）
This paper proposes a Model Predictive Control (MPC) algorithm for target tracking amongst static and dynamic obstacles. Our main contribution lies in improving the computational tractability and reliability of the underlying non-convex trajectory optimization. The result is an MPC algorithm that runs real-time on laptops and embedded hardware devices such as Jetson TX2. Our approach relies on novel reformulations for the tracking, collision, and occlusion constraints that induce a multi-convex structure in the resulting trajectory optimization. We exploit these mathematical structures using t…
We present a general approach for controlling robotic systems that make and break contact with their environments. Contact-implicit model predictive control (CI-MPC) generalizes linear MPC to contact-rich settings by utilizing a bi-level planning formulation with lower-level contact dynamics formulated as time-varying linear complementarity problems (LCPs) computed using strategic Taylor approximations about a reference trajectory. These dynamics enable the upper-level planning problem to reason about contact timing and forces, and generate entirely new contact-mode sequences online. To achiev…
In this paper we propose a novel decision making architecture for Robust Model Predictive Path Integral control (RMPPI) and investigate its performance guarantees and applicability to off-road navigation. Key building blocks of the proposed architecture are an augmented state space representation of the system consisting of nominal and actual dynamics, a placeholder for different types of tracking controllers, a safety logic for nominal state propagation, and an importance sampling scheme that takes into account the capabilities of the underlying tracking control. Using these ingredients, we d…
In control applications there is often a compromise that needs to be made with regards to the complexity and performance of the controller and the computational resources that are available. For instance, the typical hardware platform in embedded control applications is a microcontroller with limited memory and processing power, and for battery powered applications the control system can account for a significant portion of the energy consumption. We propose a controller architecture in which the computational cost is explicitly optimized along with the control objective. This is achieved by a…
