Modeling error or external disturbances can severely degrade the performance of Model Predictive Control (MPC) in real-world scenarios. Robust MPC (RMPC) addresses this limitation by optimizing over feedback policies but at the expense of increased computational complexity. Tube MPC is an approximate solution strategy in which a robust controller, designed offline, keeps the system in an invariant tube around a desired nominal trajectory, generated online. Naturally, this decomposition is suboptimal, especially for systems with changing objectives or operating conditions. In addition, many tube MPC approaches are unable to capture state-dependent uncertainty due to the complexity of calculating invariant tubes, resulting in overly-conservative approximations. This work presents the Dynamic Tube MPC (DTMPC) framework for nonlinear systems where both the tube geometry and open-loop trajectory are optimized simultaneously. By using boundary layer sliding control, the tube geometry can be expressed as a simple relation between control parameters and uncertainty bound; enabling the tube geometry dynamics to be added to the nominal MPC optimization with minimal increase in computational complexity. In addition, DTMPC is able to leverage state-dependent uncertainty to reduce conservativeness and improve optimization feasibility. DTMPC is demonstrated to robustly perform obstacle avoidance and modify the tube geometry in response to obstacle proximity.
A number of works have been published on the stability, feasibility, and performance of linear tube MPC @cite_10 @cite_13 @cite_8 . While this is an effective strategy to achieve robustness, decoupling the nominal MPC problem and controller design is suboptimal. Rakovi @cite_17 showed that the region of attraction can be enlarged by parameterizing the problem with the open-loop trajectory and tube size. The authors presented the homothetic tube MPC (HTMPC) algorithm that treated the state and control tubes as homothetic copies of a fixed cross-section shape, enabling the problem to be parameterized by the tube’s centers (i.e., open-loop trajectory) and a cross-section scaling factor. The work was extended to tubes with varying shapes, known as elastic tube MPC (ETMPC), but at the expense of computational complexity @cite_12 . Both HTMPC and ETMPC possess strong theoretical properties and have the potential to significantly improve performance but a nonlinear extension has yet to be developed.
@cite_8 @cite_10 @cite_13 @cite_12 @cite_17
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This paper introduces elastic tube model predictive control (MPC) synthesis. The proposed framework is a natural generalization of the rigid and homothetic tube MPC design methods. The cross-sections of the employed state and control tubes are allowed to change more elastically, while the local component of the tubes control policy is permitted to take a more general form. The related stabilizing terminal conditions are also adequately generalized in order to take advantage of more flexible tubes and tubes control policy parameterizations. These novel features result in an improved tube MPC at the cost of a manageable increase in computational complexity. In this paper, we present a novel constraint tightening approach for nonlinear robust model predictive control (MPC). This approach uses a simple constructive constraint tightening based on growing tubes. Contrary to other approaches, we require no complex offline computations to obtain a stabilizing control law. Instead, we consider the notion of incremental stabilizability and design tubes based on an estimate of the achievable exponential decay rate. In addition, we show how this tightening can be used as an ad-hoc modification to improve the robustness of MPC without terminal constraints. We study the system theoretic properties of the resulting closed-loop system, including bounds on the region of attraction and the minimal robust positively invariant (RPI) set. Within an MPC framework without terminal constraints, the proposed constraint tightening leads to a nonlinear robust controller without complex design procedures, which makes it appealing for practical applications. This paper focuses on the design of a tube-based Model Predictive Control law for the control of constrained mobile robots in off-road conditions with longitudinal slip while ensuring robustness and stability. A time-varying trajectory tracking error model is used, where uncertainties are assumed to be bounded and additive. The robust tube-based MPC is compared with other motion control techniques through simulation and physical experiments. These tests show the satisfactory behavior of the presented control strategy. The robust model predictive control for constrained linear discrete time systems is solved through the development of a homothetic tube model predictive control synthesis method. The method employs several novel features including a more general parameterization of the state and control tubes based on homothety and invariance, a more flexible form of the terminal constraint set and a relaxation of the controlled dynamics of the sets that define the state and control tubes. Under natural assumptions, the proposed method is computationally efficient and it induces strong system theoretic properties. Concentric tube robots are tentacle-like medical robots that can bend around anatomical obstacles to access hard-to-reach clinical targets. The component tubes of these robots can be swapped prior to performing a task in order to customize the robot's behavior and reachable workspace. Optimizing a robot's design by appropriately selecting tube pa- rameters can improve the robot's effectiveness on a procedure- and patient-specific basis. In this paper, we present an algorithm that generates sets of concentric tube robot designs that can collectively maximize the reachable percentage of a given goal region in the human body. Our algorithm combines a search in the design space of a concentric tube robot using a global optimization method with a sampling-based motion planner in the robot's configuration space in order to find sets of designs that enable motions to goal regions while avoiding contact with anatomical obstacles. We demonstrate the effectiveness of our algorithm in a simulated scenario based on lung anatomy. I. INTRODUCTION Concentric tube robots are tentacle-like medical robots that can potentially enable safer minimally invasive interventions at many sites in the human body, including the lungs, the skull base, and the heart (1). These robots are composed of nested nitinol tubes that each are precurved, typically with a straight segment followed by a curved segment. To perform a task, the robot axially rotates and translates each tube relative to one another, causing the entire device's shape to change. Concentric tube robots act like shape-changing robotic needles that can curve around anatomical obstacles (e.g., bones, blood vessels, critical nerves, etc.) to reach clinical targets not easily accessed using traditional straight medical instruments. The curvilinear shapes achievable by concentric tube robots are highly dependent on the component tubes' physi- cal specifications. The design of the concentric tubes, includ- ing the tubes' lengths and precurvatures, affects the robot's workspace and the space of the robot's attainable shapes. Consequently, the design of the concentric tubes determines the set of clinical targets that the robot can safely reach. Even with the shape-changing capabilities of a concentric tube robot (as shown in Fig. 2), due to kinematic constraints Concentric tube robots are a novel continuum robot technology that is well suited to minimally invasive surgeries inside small body cavities such as the heart. These robots are constructed of concentrically combined pre-curved elastic tubes to form 3D curves. Each telescopic section of the robot is either of fixed or variable curvature. One advantage of this approach is that the component tube curvatures, lengths and stiffnesses can easily be fabricated to be procedure- and patient-specific. This paper proposes an optimization framework for solving the robot design problem. Given a 3D description of the constraining anatomy, the number of fixed and variable curvature robot sections and a tip workspace description, the algorithm solves for the robot design that possesses the desired workspace, remains inside the anatomical constraints and minimizes the curvature and length of all sections. The approach is illustrated in the context of beating-heart closure of atrial septal defects. This paper addresses the trajectory tracking problem of an autonomous tractor-trailer system by using a decentralized control approach. A fully decentralized model predictive controller is designed in which interactions between subsystems are neglected and assumed to be perturbations to each other. In order to have a robust design, a tube-based approach is proposed to handle the differences between the nominal model and real system. Nonlinear moving horizon estimation is used for the state and parameter estimation after each new measurement, and the estimated values are fed to robust tube-based decentralized nonlinear model predictive controller. The proposed control scheme is capable of driving the tractor-trailer system to any desired trajectory ensuring high control accuracy and robustness against neglected subsystem interactions and environmental disturbances. The experimental results show an accurate trajectory tracking performance on a bumpy grass field. This report describes the calculation of the reach sets and tubes for linear control systems with time-varying coefficients and hard bounds on the controls through tight external and internal ellipsoidal approximations. These approximating tubes touch the reach tubes from outside and inside respectively at every point of their boundary so that the surface of the reach tube is totally covered by curves that belong to the approximating tubes. The proposed approximation scheme induces a very small computational burden compared with other methods of reach set calculation. In particular such approximations may be expressed through ordinary differential equations with coefficients given in explicit analytical form. This yields exact parametric representation of reach tubes through families of external and internal ellipsoidal tubes. The proposed techniques, combined with calculation of external and internal approximations for intersections of ellipsoids, provide an approach to reachability problems for hybrid systems. This paper presents a novel approach for weakly-supervised action localization, i.e., that does not require per-frame spatial annotations for training. We first introduce an effective method for extracting human tubes by combining a state-of-the-art human detector with a tracking-by-detection approach. Our tube extraction leverages the large amount of annotated humans available today and outperforms the state of the art by an order of magnitude: with less than 5 tubes per video, we obtain a recall of 95 on the UCF-Sports and J-HMDB datasets. Given these human tubes, we perform weakly-supervised selection based on multi-fold Multiple Instance Learning (MIL) with improved dense trajectories and achieve excellent results. We obtain a mAP of 84 on UCF-Sports, 54 on J-HMDB and 45 on UCF-101, which outperforms the state of the art for weakly-supervised action localization and is close to the performance of the best fully-supervised approaches. The second contribution of this paper is a new realistic dataset for action localization, named DALY (Daily Action Localization in YouTube). It contains high quality temporal and spatial annotations for 10 actions in 31 hours of videos (3.3M frames), which is an order of magnitude larger than standard action localization datasets. On the DALY dataset, our tubes have a spatial recall of 82 , but the detection task is extremely challenging, we obtain 10.8 mAP. Concentric tube robots are catheter-sized continuum robots that are well suited for minimally invasive surgery inside confined body cavities. These robots are constructed from sets of precurved superelastic tubes and are capable of assuming complex 3-D curves. The family of 3-D curves that the robot can assume depends on the number, curvatures, lengths, and stiffnesses of the tubes in its tube set. The robot design problem involves solving for a tube set that will produce the family of curves necessary to perform a surgical procedure. At a minimum, these curves must enable the robot to smoothly extend into the body and to manipulate tools over the desired surgical workspace while respecting anatomical constraints. This paper introduces an optimization framework that utilizes procedure- or patient-specific image-based anatomical models along with surgical workspace requirements to generate robot tube set designs. The algorithm searches for designs that minimize robot length and curvature and for which all paths required for the procedure consist of stable robot configurations. Two mechanics-based kinematic models are used. Initial designs are sought using a model assuming torsional rigidity. These designs are then refined using a torsionally compliant model. The approach is illustrated with clinically relevant examples from neurosurgery and intracardiac surgery. This paper addresses the attraction domain of model-based predictive control (MPC) for nonlinear systems with control input and state constraints. Based on a stability condition of nonlinear MPC, a method to determine the terminal weighting term in the performance index and the terminal stabilising control law to maximise the domain of attraction of the nonlinear MPC is proposed. The problem of maximisation of the attraction region is recast as a well-defined optimisation problem. By an LMI based optimisation approach, the terminal weighting item and fictitious terminal stabilising control law axe optimised to enlarge the attraction domain and hence the feasibility domain of the nonlinear MPC method. The proposed method is illustrated by a numerical example and favourably compared with existing results. Model-free policy learning has enabled robust performance of complex tasks with relatively simple algorithms. However, this simplicity comes at the cost of requiring an Oracle and arguably very poor sample complexity. This renders such methods unsuitable for physical systems. Variants of model-based methods address this problem through the use of simulators, however, this gives rise to the problem of policy transfer from simulated to the physical system. Model mismatch due to systematic parameter shift and unmodelled dynamics error may cause sub-optimal or unsafe behavior upon direct transfer. We introduce the Adaptive Policy Transfer for Stochastic Dynamics (ADAPT) algorithm that achieves provably safe and robust, dynamically-feasible zero-shot transfer of RL-policies to new domains with dynamics error. ADAPT combines the strengths of offline policy learning in a black-box source simulator with online tube-based MPC to attenuate bounded model mismatch between the source and target dynamics. ADAPT allows online transfer of policy, trained solely in a simulation offline, to a family of unknown targets without fine-tuning. We also formally show that (i) ADAPT guarantees state and control safety through state-action tubes under the assumption of Lipschitz continuity of the divergence in dynamics and, (ii) ADAPT results in a bounded loss of reward accumulation relative to a policy trained and evaluated in the source environment. We evaluate ADAPT on 2 continuous, non-holonomic simulated dynamical systems with 4 different disturbance models, and find that ADAPT performs between 50 -300 better on mean reward accrual than direct policy transfer. Concentric tube continuum robots provide an infinite-dimensional design space, consisting of individual tube space curves and other tube parameters. Even when design choices are made to restrict the design space to a small number of discrete parameters, ad hoc selection of parameter values to achieve coverage of a desired volume, in the presence of geometric workspace constraints, is essentially impossible - even for experienced researchers. General design algorithms proposed to date have focused on reaching a discrete set of specific points, and have made non-physical approximations in the robot model (most significantly assuming infinite torsional rigidity), to speed up model computation. In this paper, we extend prior algorithms to use more accurate models and incorporate volume-based objectives. These extensions are illustrated in a case study on the design of a concentric tube robot for endonasal pituitary surgery. We show that volume-based design optimization increases the reachable percentage of the surgical workspace by an average of approximately 50 , in comparison to various sets of manually selected design parameters. We conclude that volume-based objectives should be included in future multi-objective design optimization procedures for concentric tube continuum robots. Using only the existence and uniqueness of trajectories for a generic dynamic system with inputs, we define and examine eight types of forward and backward reachability constructs. If the input is treated in a worst-case fashion, any forward or backward reach set or tube can be used for safety analysis, but if the input is treated in a best-case fashion only the backward reach tube always provides the correct results. Fortunately, forward and backward algorithms can be exchanged if well-posed reverse time trajectories can be defined. Unfortunately, backward reachability constructs are more likely to suffer from numerical stability issues, especially in systems with significant contraction--the very systems where forward simulation and reachability are most effective. We focus on a replanning scenario for quadrotors where considering time efficiency, non-static initial state and dynamical feasibility is of great significance. We propose a real-time B-spline based kinodynamic (RBK) search algorithm, which transforms a position-only shortest path search (such as A * and Dijkstra) into an efficient kinodynamic search, by exploring the properties of B-spline parameterization. The RBK search is greedy and produces a dynamically feasible time-parameterized trajectory efficiently, which facilitates non-static initial state of the quadrotor. To cope with the limitation of the greedy search and the discretization induced by a grid structure, we adopt an elastic optimization (EO) approach as a post-optimization process, to refine the control point placement provided by the RBK search. The EO approach finds the optimal control point placement inside an expanded elastic tube which represents the free space, by solving a Quadratically Constrained Quadratic Programming (QCQP) problem. We design a receding horizon replanner based on the local control property of B-spline. A systematic comparison of our method against two state-of-the-art methods is provided. We integrate our replanning system with a monocular vision-based quadrotor and validate our performance onboard. In this paper, a model predictive control (MPC) approach for controlling an active front steering system in an autonomous vehicle is presented. At each time step, a trajectory is assumed to be known over a finite horizon, and an MPC controller computes the front steering angle in order to follow the trajectory on slippery roads at the highest possible entry speed. We present two approaches with different computational complexities. In the first approach, we formulate the MPC problem by using a nonlinear vehicle model. The second approach is based on successive online linearization of the vehicle model. Discussions on computational complexity and performance of the two schemes are presented. The effectiveness of the proposed MPC formulation is demonstrated by simulation and experimental tests up to 21 m s on icy roads We describe here a mathematical model of the adaptive dynamics of a transport network of the true slime mold Physarum polycephalum, an amoeboid organism that exhibits path-finding behavior in a maze. This organism possesses a network of tubular elements, by means of which nutrients and signals circulate through the plasmodium. When the organism is put in a maze, the network changes its shape to connect two exits by the shortest path. This process of path-finding is attributed to an underlying physiological mechanism: a tube thickens as the flux through it increases. The experimental evidence for this is, however, only qualitative. We constructed a mathematical model of the general form of the tube dynamics. Our model contains a key parameter corresponding to the extent of the feedback regulation between the thickness of a tube and the flux through it. We demonstrate the dependence of the behavior of the model on this parameter. We introduce an approach for spatio-temporal human action localization using sparse spatial supervision. Our method leverages the large amount of annotated humans available today and extracts human tubes by combining a state-of-the-art human detector with a tracking-by-detection approach. Given these high-quality human tubes and temporal supervision, we select positive and negative tubes with very sparse spatial supervision, i.e., only one spatially annotated frame per instance. The selected tubes allow us to effectively learn a spatio-temporal action detector based on dense trajectories or CNNs. We conduct experiments on existing action localization benchmarks: UCF-Sports, J-HMDB and UCF-101. Our results show that our approach, despite using sparse spatial supervision, performs on par with methods using full supervision, i.e., one bounding box annotation per frame. To further validate our method, we introduce DALY (Daily Action Localization in YouTube), a dataset for realistic action localization in space and time. It contains high quality temporal and spatial annotations for 3.6k instances of 10 actions in 31 hours of videos (3.3M frames). It is an order of magnitude larger than existing datasets, with more diversity in appearance and long untrimmed videos. We introduce a method for task-oriented design of concentric tube robots, which are tentacle-like robots with the potential to enable new minimally invasive surgical procedures. Our objective is to create a robot design on a patient-specific and surgery-specific basis to enable the robot to reach multiple clinically relevant sites while avoiding anatomical obstacles. Our method uses a mechanically accurate model of concentric tube robot kinematics that considers a robot's time-varying shape throughout the performance of a task. Our method combines a search over a robot's design space with sampling-based motion planning over its configuration space to compute a design under which the robot can feasibly perform a specified task without damaging surrounding tissues. To accelerate the algorithm, we leverage design coherence, the observation that collision-free configuration spaces of robots of similar designs are similar. If a solution exists, our method is guaranteed, as time is allowed to increase, to find a design and corresponding feasible motion plan. We provide examples illustrating the importance of using mechanically accurate models during design and motion planning and demonstrating our method's effectiveness in a medically motivated simulated scenario involving navigation through the lung. The solution of a particular Hamilton-Jacobi (HJ) partial differential equation (PDE) provides an implicit representation of reach sets and tubes for continuous systems with nonlinear dynamics and can treat inputs in either worst-case or best-case fashion; however, it can rarely be determined analytically and its numerical approximation typically requires computational resources that grow exponentially with the state space dimension. In this paper we describe a new formulation - also based on HJ PDEs - for reach sets and tubes of systems where some states are terminal integrators: states whose evolution can be written as an integration over time of the other states. The key contribution of this new mixed implicit explicit (MIE) scheme is that its computational cost is linear in the number of terminal integrators, although still exponential in the dimension of the rest of the state space. Application of the new scheme to four examples of varying dimension provides empirical evidence of its considerable improvement in computational speed.