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Online Walking Motion Generation with Automatic Footstep Placement

ADVANCED ROBOTICS 2010年第5-6期24卷 719-737页

作者： Herdt, Andrei Diedam, Holger Wieber, Pierre-Brice Dimitrov, Dimitar Mombaur, Katja Diehl, Moritz INRIA Tsukuba Ibaraki 3058568 Japan AIST CNRS Tsukuba Ibaraki 3058568 Japan Heidelberg Univ D-69120 Heidelberg Germany Katholieke Univ Leuven B-3001 Louvain Belgium

The goal of this paper is to demonstrate the capacity of model predictive control (MPC) to generate stable walking motions without the use of predefined footsteps. Building up on well-known MPC schemes for walking motion generation, we show that a minimal modification of these schemes allows designing an online walking motion generator that can track a given reference speed of the robot and decide automatically the footstep placement. Simulation results are proposed on the HRP-2 humanoid robot, showing a significant improvement over previous approaches. (C) Koninklijke Brill NV, Leiden and The Robotics Society of Japan, 2010

关键词： Walking humanoid robot linear model predictive control

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Automatically generated embedded model predictive control: Moving an industrial PC-based MPC to an embedded platform

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OPTIMAL control APPLICATIONS & METHODS 2015年第5期36卷 705-727页

作者： Kufoalor, D. K. M. Aaker, V. Johansen, T. A. Imsland, L. Eikrem, G. O. Norwegian Univ Sci & Technol Dept Engn Cybernet N-7491 Trondheim Norway Statoil ASA FD ER SF Rotvoll Norway Aker Solut ASA Oslo Norway

An embedded model predictive controller (eMPC) based on the linear MPC module in Statoil Estimation and Prediction Tool for Identification and control has been developed, and it is intended to facilitate the MPC application on embedded hardware. The control design approach illustrates a viable way of migrating from an industrial PC-based MPC technology to an embedded platform. This work also provides the transformations and the real-time considerations necessary to achieve a functional high-performance predictive controller on a low-cost embedded hardware, with limited computational resources. The eMPC was implemented for rapid prototyping on the Ethernut 5 open-source hardware, and its performance was tested for a simulated process. The concept was tested using a real MPC application developed for a prototype of a new industrial process that requires an advanced embedded multivariable, constraint handling control solution. The results confirm the viability of the embedded MPC design approach. Copyright (C) 2015 John Wiley & Sons, Ltd.

关键词： embedded real-time model predictive control linear model predictive control automatic custom code generation

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DESIGN OF PATH PLANNING AND TRACKING control OF QUADROTOR

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JOURNAL OF INDUSTRIAL AND MANAGEMENT OPTIMIZATION 2022年第3期18卷 2221-2235页

作者： Gao, Yi Li, Rui Shi, Yingjing Xiao, Li Univ Elect Sci & Technol China Sch Automat Engn Chengdu 611731 Peoples R China

In this paper, we first design a motion planning system based on the Batch Informed Trees (BIT*) algorithm for quadrotor and a linear model predictive control (LMPC) is applied to solve the path tracking problem for a quadrotor. BIT* algorithm is used to plan a barrier-free trajectory quickly in an obstructed environment. Then we apply linear model predictive control for the full state quadrotor system model to track the generated trajectory. Finally, the BIT* algorithm simulation case is presented using RVIZ visual interface and some simulation cases are presented using MATLAB / Simulink. The results demonstrate the capability and the effectiveness of the control strategy in fast path tracking and the quadrotor stability, while the desired performance is achieved.

关键词： linear model predictive control BIT path planning trajectory op-timization path tracking

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Formation control of multiple wheeled mobile robots based on model predictive control

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ROBOTICA 2022年第9期40卷 3178-3213页

作者： Nfaileh, Najla Alipour, Khalil Tarvirdizadeh, Bahram Hadi, Alireza Univ Tehran Fac New Sci & Technol Dept Mech Engn Adv Serv Robots ASR Lab Tehran Iran

This paper considers the problem of formation control for a team of nonholonomic wheeled mobile robots considering obstacle avoidance. A new control algorithm based on the model predictive control (MPC) and the nonlinear dynamics of the system is presented here. The control algorithm is applied to the nonlinear system using two different controllers including linear MPC and nonlinear MPC. The virtual structure formation approach and artificial potential field method are employed to determine the reference trajectories of the robots and to solve the problem of obstacle avoidance. A control algorithm consisting of two parts is proposed to track the trajectories and maintain the team's formation. Two advantages of using MPC techniques are the ability to consider control and state constraints which are of high importance in practical applications. The main contribution of this paper is the design of two robust control systems to disturbance with respect to actuator saturation limits. Simulation results demonstrate the effectiveness and robustness of the proposed control algorithm in trajectory tracking and formation maintenance in the presence of disturbance and actuator limits.

关键词： formation control virtual structure nonholonomic WMR linear model predictive control nonlinear model predictive control obstacle avoidance

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Closed-loop dynamic real-time optimization with stabilizing model predictive control

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AICHE JOURNAL 2021年第10期67卷 e17308-e17308页

作者： Ramesh, Praveen Sundaresan Swartz, Christopher L. E. Mhaskar, Prashant McMaster Univ Dept Chem Engn 1280 Main St West Hamilton ON L8S 4L7 Canada

Dynamic real-time optimization (DRTO) is a supervisory strategy at the upper level of the industrial process automation architecture that computes economically optimal set-point trajectories that are in turn passed on to the lower-level model predictive control (MPC) for tracking. The economically optimal solution, in several process industries, could lead to operating the plant at or around an unstable steady state. The present article accounts for this by developing a closed-loop DRTO (CL-DRTO) formulation that enables handling unstable operating points via an underlying MPC with stability constraints. To this end, a stabilizing MPC that handles trajectory tracking for unstable systems is embedded within the upper-level DRTO. The resulting CL-DRTO problem is reformulated by applying a simultaneous solution approach. The economic benefits realized by the proposed strategy are illustrated through applications to both linearized and nonlinear dynamic models for single-input single-output and multi-input multi-output continuous stirred tank reactor case studies.

关键词： closed-loop dynamic real-time optimization linear model predictive control process economics stability constraints

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Complexity and convergence certification of a block principal pivoting method for box-constrained quadratic programs

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AUTOMATICA 2019年 100卷 29-37页

作者： Cimini, Gionata Bemporad, Alberto ODYS Srl Via Pastrengo 14 I-20159 Milan Italy IMT Sch Adv Studies Lucca Piazza San Francesco 19 I-55100 Lucca Italy

Active-set (AS) methods for quadratic programming (QP) are particularly suitable for real-time optimization, as they provide a high-quality solution in a finite number of iterations. However, they add or remove one constraint at each iteration, which makes them inefficient when the number of constraints and variables grows. Block principal pivoting (BPP) methods perform instead multiple changes in the working set in a single iteration, resulting in a much faster execution time. The infeasible primal-dual method proposed by Kunisch and Rendl (KR) (Kunisch and Rendl, 2003) is a BPP method for box-constrained QP that is particularly attractive when reducing the time for finding an accurate solution is crucial, such as in linear model predictive control (MPC) applications. However, the method is guaranteed to converge only under very restrictive sufficient conditions, and tight bounds on the worst-case complexity are not available. For a given set of box-constrained QP's that depend on a vector of parameters, such as those that arise in linear MPC, this paper proposes an algorithm that computes offline the exact number of iterations and flops needed by the KR method in the worst-case, and the region of the parameter space for which the method converges or is proved to cycle. (C) 2018 Elsevier Ltd. All rights reserved.

关键词： Quadratic programming Active-set methods Block principal pivoting methods linear model predictive control Complexity certification

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Humanoid walking pattern generation based on model predictive control approximated with basis functions

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ADVANCED ROBOTICS 2019年第9期33卷 454-468页

作者： Zhang, Ang Ramirez-Alpizar, Ixchel G. Esclasse, Kevin Giraud Stasse, Olivier Harada, Kensuke Osaka Univ Grad Sch Engn Sci Dept Syst Innovat 1-3 Machikaneyama Cho Toyonaka Osaka 5608531 Japan Univ Toulouse CNRS LAAS Toulouse France

This paper proposes a real-time walking pattern generator (WPG) based on model predictive control (MPC). Since reducing the calculation time is a crucial problem in real-time WPG, we consider introducing basis functions to reduce the number of control input. The control inputs in the MPC are described by a series of basis functions. Compared with the standard discrete-time MPC formulation, the approach with basis functions requires fewer optimization variables at the cost of decreasing precision. In order to find an appropriate trade-off, two basis functions named Laguerre functions and Haar functions, are tested in this paper. MPC with Laguerre functions decreases more computational load while MPC with Haar functions offers a more accurate solution. The approach is not restricted to Laguerre functions or Haar functions, users can select their own basis functions for different applications and preferences.

关键词： Humanoid robot bipedal locomotion linear model predictive control Laguerre orthonormal functions Haar functions

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Integrated Decision control Approach for Cooperative Safety-Critical Payload Transport in a Cluttered Environment

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IEEE TRANSACTIONS ON AEROSPACE AND ELECTRONIC SYSTEMS 2023年第6期59卷 8800-8811页

作者： Rao, Nishanth Sundaram, Suresh Indian Inst Sci Dept Aerosp Engn Artificial Intelligence & Robot Lab Bengaluru 560012 India

In this article, the problem of coordinated transportation of heavy payload by a team of unmanned aerial vehicles (UAVs) in a cluttered environment is addressed. The payload is modeled as a rigid body and is assumed to track a precomputed global flight trajectory from a start point to a goal point. Due to the presence of local dynamic obstacles in the environment, the UAVs must ensure that there is no collision between the payload and these obstacles while ensuring that the payload oscillations are kept minimum. An integrated decision controller (IDC) is proposed that integrates the optimal tracking control law given by a centralized model predictive controller with safety-critical constraints provided by the exponential control barrier functions. The entire payload-UAV system is enclosed by a safe convex hull boundary, and the IDC ensures that no obstacle enters this boundary. To evaluate the performance of the IDC, the results for a numerical simulation as well as a high-fidelity Gazebo simulation are presented. An ablation study is conducted to analyze the robustness of the proposed IDC against practical dubieties like noisy state values, relative obstacle safety margin, and payload mass uncertainty. The proposed method is then compared with a baseline controller qualitatively, emphasizing the use of barrier functions in safety-critical applications. The results clearly show that the IDC achieves both trajectory tracking and obstacle avoidance successfully while restricting the payload oscillations within a safe limit.

关键词： Payloads Collision avoidance Autonomous aerial vehicles Oscillators Aerodynamics Trajectory Heuristic algorithms Cluttered environment cooperative payload transport exponential control barrier functions (ECBF) linear model predictive control multi unmanned aerial vehicle (multi-UAV) system

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Stochastic predictive Energy Management of Power Split Hybrid Electric Bus for Real-World Driving Cycles

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IEEE ACCESS 2018年 6卷 61700-61713页

作者： Shi, Dehua Wang, Shaohua Cai, Yingfeng Chen, Long Jiangsu Univ Automot Engn Res Inst Zhenjiang 212013 Peoples R China Jiangsu Univ Sch Automobile & Traff Engn Zhenjiang 212013 Peoples R China

The energy conversion efficiencies among different sources of power split hybrid electric vehicle rely on the energy management strategy. In this paper, the energy management of a power split hybrid electric bus (HEB) is described as the predictive control problem based on the linear control-oriented model of the HEB. In order to ensure that the engine can output the desired power, the fuzzy PI controller, which can realize the optimal engine speed tracking, is further designed. Two real-world driving cycles are analyzed and formulated to evaluate the vehicle fuel economy under transient practical conditions. On this basis, the driver torque demand and vehicle velocity in the prediction horizon are derived with the stochastic one-step Markov chain. Finally, the hardware-in-the-loop (HIT) simulation platform is built to explore the validity of the controller. Compared with the adaptive equivalent fuel consumption minimization strategy, HIL test results demonstrate the real-time capability and benefits of the proposed approach in optimizing the energy management of HEB.

关键词： Power split energy management linear model predictive control Markov chain fuzzy control hardware in the loop

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Real-time proximal gradient method for embedded linear MPC

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MECHATRONICS 2019年 59卷 1-9页

作者： Van Parys, Ruben Verbandt, Maarten Swevers, Jan Pipeleers, Goele Katholieke Univ Leuven Dept Mech Engn MECO Res Team Leuven Belgium Flanders Make DMMS Corelab Leuven Belgium

This paper presents and experimentally validates an embedded linear model predictive control (MPC) approach that is particularly useful for implementation on resource-constrained embedded hardware. The MPC scheme is based on a real-time implementation of the proximal gradient method (PGM) and generates input signals with guaranteed constraint satisfaction. Given standard linear MPC assumptions, asymptotic stability of the resulting closed loop is proven. Applied to linear systems with simple input constraints, the real-time PGM results in very simple arithmetics that are rapidly executed on resource-constrained hardware. As a proof on concept, the algorithm is demonstrated on two experimental setups in which it is implemented on a micro-controller. These experimental validations and related simulations demonstrate how the proposed real-time PGM allows fast control rates, especially compared to state-of-the-art linear MPC approaches, and this while preserving good closed-loop performance.

关键词： linear model predictive control Proximal gradient method Embedded control

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