Optimal control is often used in robotics for planning a trajectory to achieve some desired behavior, as expressed by the cost function. Most works in optimal control focus on finding a single optimal trajectory, which is then typically tracked by another controller. In this work, we instead consider trajectory distribution as the solution of an optimal control problem, resulting in better tracking performance and a more stable controller. A Gaussian distribution is first obtained from an iterative Linear Quadratic Regulator (iLQR) solver. A short horizon Model Predictive Control (MPC) is then used to track this distribution. We show that tracking the distribution is more cost-efficient and robust as compared to tracking the mean or using iLQR feedback control. The proposed method is validated with kinematic control of 7-DoF Panda manipulator and dynamic control of 6-DoF quadcopter in simulation.
Deploying large, complex space structures is of great interest to the modern scientific world as it can provide new capabilities in obtaining scientific, communicative, and observational information. However, many theoretical mission designs contain complexities that must be constrained by the requirements of the launch vehicle, such as volume and mass. To mitigate such constraints, the use of on-orbit additive manufacturing and robotic assembly allows for the flexibility of building large complex structures including telescopes, space stations, and communication satellites. The contribution o…
i2LQR: Iterative LQR for Iterative Tasks in Dynamic Environments
University of California, Berkeley（加州大学伯克利分校）；Xi’an Jiaotong University（西安交通大学）；Shanghai Jiao Tong University（上海交通大学）；University of Minnesota-Twin Cities（明尼苏达大学双城分校）
We present a new walking controller based on 3LP, a 3D model of bipedal walking that is composed of three pendulums to simulate falling, swing and torso dynamics. Taking advantage of linear equations and closed-form solutions of 3LP, the proposed controller projects intermediate states of the biped back to the beginning of the phase for which a discrete LQR controller is designed. After the projection, a proper control policy is generated by this LQR controller and used at the intermediate time. The projection controller reacts to disturbances immediately and compared to the discrete LQR contr…
Lie Group Control Architectures for UAVs: a Comparison of SE2(3)-Based Approaches in Simulation and Hardware
Department of Electrical and Computer Engineering（电气与计算机工程系）；School of Computing（计算学院）；Ingenuity Labs Research Institute（创新实验室研究研究院）；Queen’s University（女王大学）
Vector Institute for Artificial Intelligence（人工智能向量研究所）
In this work we address the problem of performing a repetitive task when we have uncertain observations and dynamics. We formulate this problem as an iterative infinite horizon optimal control problem with output feedback. Previously, this problem was solved for linear time-invariant (LTI) system for the case when noisy full-state measurements are available using a robust iterative learning control framework, which we refer to as robust learning-based model predictive control (RL-MPC). However, this work does not apply to the case when only noisy observations of part of the state are available…
Robotics Institute, Carnegie Mellon University（卡内基梅隆大学机器人研究所）；Department of Computer Science, Cornell University（康奈尔大学计算机科学系）；Aurora Innovation
Iterative learning control (ILC) is a powerful technique for high performance tracking in the presence of modeling errors for optimal control applications. There is extensive prior work showing its empirical effectiveness in applications such as chemical reactors, industrial robots and quadcopters. However, there is little prior theoretical work that explains the effectiveness of ILC even in the presence of large modeling errors, where optimal control methods using the misspecified model (MM) often perform poorly. Our work presents such a theoretical study of the performance of both ILC and MM…
Finite-Sample Closed-Loop Stability of Model Predictive Path Integral Control for Linear Time-Invariant Systems
Department of Mechanical and Nuclear Engineering, Tennessee Technological University（机械与核工程系，田纳西技术大学）；School of Engineering, Department of Electrical and Computer Engineering, Mercer University（工程学院，电气与计算机工程系，梅森大学）
Forecast-Driven MPC for Decentralized Multi-Robot Collision Avoidance
Department of Computer Science（计算机科学系）；Maharishi International University（玛哈里什国际大学）；Electrical Engineering and Computing（电气工程与计算）；University of Zagreb（扎格雷布大学）；Eastern Illinois University（东部伊利诺伊大学）
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）
Generative Models From and For Sampling-Based MPC: A Bootstrapped Approach For Adaptive Contact-Rich Manipulation
Oxford Robotics Institute, University of Oxford, UK（牛津大学机器人研究所）；Robotics and AI Institute (RAI), Boston, USA（机器人与人工智能研究所）；Cornell University, Ithaca, NY, USA（康奈尔大学）
University of California Berkeley（加州大学伯克利分校）；California Institute of Technology（加州理工学院）
Sample-based learning model predictive control (LMPC) strategies have recently attracted attention due to their desirable theoretical properties and their good empirical performance on robotic tasks. However, prior analysis of LMPC controllers for stochastic systems has mainly focused on linear systems in the iterative learning control setting. We present a novel LMPC algorithm, Adjustable Boundary Condition LMPC (ABC-LMPC), which enables rapid adaptation to novel start and goal configurations and theoretically show that the resulting controller guarantees iterative improvement in expectation …
Shenzhen University（深圳大学）；Guangdong Laboratory of Artificial Intelligence and Digital Economy (SZ)（广东省人工智能与数字经济实验室（深圳））
In this paper, a novel switching pushing skill algorithm is proposed to improve the efficiency of planar non-prehensile manipulation, which draws inspiration from human pushing actions and comprises two sub-problems, i.e., discrete decision-making of pushing point and continuous feedback control of pushing action. In order to solve the sub-problems above, a combination of Model Predictive Control (MPC) and Deep Reinforcement Learning (DRL) method is employed. Firstly, the selection of pushing point is modeled as a Markov decision process,and an off-policy DRL method is used by reshaping the re…
The University of Texas at Austin（德克萨斯大学奥斯汀分校）；University of Notre Dame（圣母大学）
Model-based control for robots has increasingly been dependent on optimization-based methods like Differential Dynamic Programming and iterative LQR (iLQR). These methods can form the basis of Model-Predictive Control (MPC), which is commonly used for controlling legged robots. Computing the partial derivatives of the dynamics is often the most expensive part of these algorithms, regardless of whether analytical methods, Finite Difference, Automatic Differentiation (AD), or Chain-Rule accumulation is used. Since the second-order derivatives of dynamics result in tensor computations, they are o…
Robots with Attitude: Singularity-Free Quaternion-Based Model-Predictive Control for Agile Legged Robots
Center for Robotics and Biosystems, Northwestern University（西北大学机器人与生物系统中心）；Robotics Institute, Carnegie Mellon University（卡内基梅隆大学机器人研究所）；Department of Mechanical Engineering, Carnegie Mellon University（卡内基梅隆大学机械工程系）
The Hong Kong University of Science and Technology（香港科技大学）
Developments in cooperative trajectory planning of connected autonomous vehicles (CAVs) have gathered considerable momentum and research attention. Generally, such problems present strong non-linearity and non-convexity, rendering great difficulties in finding the optimal solution. Existing methods typically suffer from low computational efficiency, and this hinders the appropriate applications in large-scale scenarios involving an increasing number of vehicles. To tackle this problem, we propose a novel decentralized iterative linear quadratic regulator (iLQR) algorithm by leveraging the dual…
Hybrid systems are prevalent in robotics. However, ensuring the stability of hybrid systems is challenging due to sophisticated continuous and discrete dynamics. A system with all its system modes stable can still be unstable. Hence special treatments are required at mode switchings to stabilize the system. In this work, we propose a hierarchical, neural network (NN)-based method to control general hybrid systems. For each system mode, we first learn an NN Lyapunov function and an NN controller to ensure the states within the region of attraction (RoA) can be stabilized. Then an RoA NN estimat…
Model predictive control (MPC) is a popular control method that has proved effective for robotics, among other fields. MPC performs re-planning at every time step. Re-planning is done with a limited horizon per computational and real-time constraints and often also for robustness to potential model errors. However, the limited horizon leads to suboptimal performance. In this work, we consider the iterative learning setting, where the same task can be repeated several times, and propose a policy improvement scheme for MPC. The main idea is that between executions we can, offline, run MPC with a…
We present a framework for bi-level trajectory optimization in which a system's dynamics are encoded as the solution to a constrained optimization problem and smooth gradients of this lower-level problem are passed to an upper-level trajectory optimizer. This optimization-based dynamics representation enables constraint handling, additional variables, and non-smooth behavior to be abstracted away from the upper-level optimizer, and allows classical unconstrained optimizers to synthesize trajectories for more complex systems. We provide an interior-point method for efficient evaluation of const…
Munich Electrification（慕尼黑电气化公司）；Arrival（Arrival公司）；The University of Edinburgh（爱丁堡大学）
Accurately modeling robot dynamics is crucial to safe and efficient motion control. In this paper, we develop and apply an iterative learning semi-parametric model, with a neural network, to the task of autonomous racing with a Model Predictive Controller (MPC). We present a novel non-linear semi-parametric dynamics model where we represent the known dynamics with a parametric model, and a neural network captures the unknown dynamics. We show that our model can learn more accurately than a purely parametric model and generalize better than a purely non-parametric model, making it ideal for rea…
Model Predictive Control (MPC) is a state-of-the-art (SOTA) control technique which requires solving hard constrained optimization problems iteratively. For uncertain dynamics, analytical model based robust MPC imposes additional constraints, increasing the hardness of the problem. The problem exacerbates in performance-critical applications, when more compute is required in lesser time. Data-driven regression methods such as Neural Networks have been proposed in the past to approximate system dynamics. However, such models rely on high volumes of labeled data, in the absence of symbolic analy…
The Hong Kong University of Science and Technology (Guangzhou)（香港科技大学（广州））；The Hong Kong University of Science and Technology（香港科技大学）；HKUST Shenzhen-Hong Kong Collaborative Innovation Research Institute（香港科技大学深港协同创新研究院）；National University of Singapore（新加坡国立大学）；University of California, Berkeley（加州大学伯克利分校）
In the context of autonomous driving, the iterative linear quadratic regulator (iLQR) is known to be an efficient approach to deal with the nonlinear vehicle model in motion planning problems. Particularly, the constrained iLQR algorithm has shown noteworthy advantageous outcomes of computation efficiency in achieving motion planning tasks under general constraints of different types. However, the constrained iLQR methodology requires a feasible trajectory at the first iteration as a prerequisite when the logarithmic barrier function is used. Also, the methodology leaves open the possibility f…
Model Predictive Controllers (MPC) are widely used for controlling cyber-physical systems. It is an iterative process of optimizing the prediction of the future states of a robot over a fixed time horizon. MPCs are effective in practice, but because they are computationally expensive and slow, they are not well suited for use in real-time applications. Overcoming the flaw can be accomplished by approximating an MPC's functionality. Neural networks are very good function approximators and are faster compared to an MPC. It can be challenging to apply neural networks to control-based applications…
From Data to Safe Mobile Robot Navigation: An Efficient and Modular Robust MPC Design Pipeline
department of Cognitive Robotics, Delft University of Technology（认知机器人学系，代尔夫特理工大学）；Czech Institute of Informatics, Robotics and Cybernetics, Czech Technical University in Prague（信息学、机器人学与自动化研究所，布拉格技术大学）；Institute for Dynamic Systems and Control, ETH Zürich（动态系统与控制研究所，苏黎世联邦理工学院）
This paper proposes a novel active Simultaneous Localization and Mapping (SLAM) method with continuous trajectory optimization over a stochastic robot dynamics model. The problem is formalized as a stochastic optimal control over the continuous robot kinematic model to minimize a cost function that involves the covariance matrix of the landmark states. We tackle the problem by separately obtaining an open-loop control sequence subject to deterministic dynamics by iterative Covariance Regulation (iCR) and a closed-loop feedback control under stochastic robot and covariance dynamics by Linear Qu…
