Kinodynamic planning and control of closed-chain robotic systems

Aplicat embargament des de la data de defensa fins el dia 1/6/2022This work proposes a methodology for kinodynamic planning and trajectory control in robots with closed kinematic chains. The ability to plan trajectories is key in a robotic system, as it provides a means to convert high-level task commands¾like “move to that location'', or “throw the object at such a speed''¾into low-level controls to be followed by the actuators. In contrast to purely kinematic planners, which only generate collision-free paths in configuration space, kinodynamic planners compute state-space trajectories that also account for the dynamics and force limits of the robot. In doing so, the resulting motions are more realistic and exploit gravity, inertia, and centripetal forces to the benefit of the task. Existing kinodynamic planners are fairly general and can deal with complex problems, but they require the state coordinates to be independent. Therefore, they are hard to apply to robots with loop-closure constraints whose state space is not globally parameterizable. These constraints define a nonlinear manifold on which the trajectories must be confined, and they appear in many systems, like parallel robots, cooperative arms manipulating an object, or systems that keep multiple contacts with the environment. In this work, we propose three steps to generate optimal trajectories for such systems. In a first step, we determine a trajectory that avoids the collisions with obstacles and satisfies all kinodynamic constraints of the robot, including loop-closure constraints, the equations of motion, or any limits on the velocities or on the motor and constraint forces. This is achieved with a sampling-based planner that constructs local charts of the state space numerically, and with an efficient steering method based on linear quadratic regulators. In a second step, the trajectory is optimized according to a cost function of interest. To this end we introduce two new collocation methods for trajectory optimization. While current methods easily violate the kinematic constraints, those we propose satisfy these constraints along the obtained trajectories. During the execution of a task, however, the trajectory may be affected by unforeseen disturbances or model errors. That is why, in a third step, we propose two trajectory control methods for closed-chain robots. The first method enjoys global stability, but it can only control trajectories that avoid forward singularities. The second method, in contrast, has local stability, but allows these singularities to be traversed robustly. The combination of these three steps expands the range of systems in which motion planning can be successfully applied.Aquest treball proposa una metodologia per a la planificació cinetodinàmica i el control de trajectòries en robots amb cadenes cinemàtiques tancades. La capacitat de planificar trajectòries és clau en un robot, ja que permet traduir instruccions d'alt nivell com ara ¿mou-te cap aquella posició'' o ¿llença l'objecte amb aquesta velocitat'' en senyals de referència que puguin ser seguits pels actuadors. En comparació amb els planificadors purament cinemàtics, que només generen camins lliures de col·lisions a l'espai de configuracions, els planificadors cinetodinàmics obtenen trajectòries a l'espai d'estats que són compatibles amb les restriccions dinàmiques i els límits de força del robot. Els moviments que en resulten són més realistes i aprofiten la gravetat, la inèrcia i les forces centrípetes en benefici de la tasca que es vol realitzar. Els planificadors cinetodinàmics actuals són força generals i poden resoldre problemes complexos, però assumeixen que les coordenades d'estat són independents. Per tant, no es poden aplicar a robots amb restriccions de clausura cinemàtica en els quals l'espai d'estats no admeti una parametrització global. Aquestes restriccions defineixen una varietat diferencial sobre la qual cal mantenir les trajectòries, i apareixen en sistemes com ara els robots paral·lels, els braços que manipulen objectes coordinadament o els sistemes amb extremitats en contacte amb l'entorn. En aquest treball, proposem tres passos per generar trajectòries òptimes per a aquests sistemes. En un primer pas, determinem una trajectòria que evita les col·lisions amb els obstacles i satisfà totes les restriccions cinetodinàmiques, incloses les de clausura cinemàtica, les equacions del moviment o els límits en les velocitats i en les forces d'actuació o d'enllaç. Això s'aconsegueix mitjançant un planificador basat en mostratge aleatori que utilitza cartes locals construïdes numèricament, i amb un mètode eficient de navegació local basat en reguladors quadràtics lineals. En un segon pas, la trajectòria s'optimitza segons una funció de cost donada. A tal efecte, introduïm dos nous mètodes de col·locació per a l'optimització de trajectòries. Mentre els mètodes existents violen fàcilment les restriccions cinemàtiques, els que proposem satisfan aquestes restriccions al llarg de les trajectòries obtingudes. Durant l'execució de la tasca, tanmateix, la trajectòria pot veure's afectada per pertorbacions imprevistes o per errors deguts a incerteses en el model dinàmic. És per això que, en un tercer pas, proposem dos mètodes de control de trajectòries per robots amb cadenes tancades. El primer mètode gaudeix d'estabilitat global, però només permet controlar trajectòries que no travessin singularitats directes del robot. El segon mètode, en canvi, té estabilitat local, però permet travessar aquestes singularitats de manera robusta. La combinació d'aquests tres passos amplia el ventall de sistemes en els quals es pot aplicar amb èxit la planificació cinetodinàmica.Postprint (published version

A randomized kinodynamic planner for closed-chain robotic systems

Kinodynamic RRT planners are effective tools for finding feasible trajectories in many classes of robotic systems. However, they are hard to apply to systems with closed-kinematic chains, like parallel robots, cooperating arms manipulating an object, or legged robots keeping their feet in contact with the environ- ment. The state space of such systems is an implicitly-defined manifold, which complicates the design of the sampling and steering procedures, and leads to trajectories that drift away from the manifold when standard integration methods are used. To address these issues, this report presents a kinodynamic RRT planner that constructs an atlas of the state space incrementally, and uses this atlas to both generate ran- dom states, and to dynamically steer the system towards such states. The steering method is based on computing linear quadratic regulators from the atlas charts, which greatly increases the planner efficiency in comparison to the standard method that simulates random actions. The atlas also allows the integration of the equations of motion as a differential equation on the state space manifold, which eliminates any drift from such manifold and thus results in accurate trajectories. To the best of our knowledge, this is the first kinodynamic planner that explicitly takes closed kinematic chains into account. We illustrate the performance of the approach in significantly complex tasks, including planar and spatial robots that have to lift or throw a load at a given velocity using torque-limited actuators.Peer ReviewedPreprin

Modeling, Control and Estimation of Reconfigurable Cable Driven Parallel Robots

The motivation for this thesis was to develop a cable-driven parallel robot (CDPR) as part of a two-part robotic device for concrete 3D printing. This research addresses specific research questions in this domain, chiefly, to present advantages offered by the addition of kinematic redundancies to CDPRs. Due to the natural actuation redundancy present in a fully constrained CDPR, the addition of internal mobility offers complex challenges in modeling and control that are not often encountered in literature. This work presents a systematic analysis of modeling such kinematic redundancies through the application of reciprocal screw theory (RST) and Lie algebra while further introducing specific challenges and drawbacks presented by cable driven actuators. It further re-contextualizes well-known performance indices such as manipulability, wrench closure quality, and the available wrench set for application with reconfigurable CDPRs. The existence of both internal redundancy and static redundancy in the joint space offers a large subspace of valid solutions that can be condensed through the selection of appropriate objective priorities, constraints or cost functions. Traditional approaches to such redundancy resolution necessitate computationally expensive numerical optimization. The control of both kinematic and actuation redundancies requires cascaded control frameworks that cannot easily be applied towards real-time control. The selected cost functions for numerical optimization of rCDPRs can be globally (and sometimes locally) non-convex. In this work we present two applied examples of redundancy resolution control that are unique to rCDPRs. In the first example, we maximize the directional wrench ability at the end-effector while minimizing the joint torque requirement by utilizing the fitness of the available wrench set as a constraint over wrench feasibility. The second example focuses on directional stiffness maximization at the end-effector through a variable stiffness module (VSM) that partially decouples the tension and stiffness. The VSM introduces an additional degrees of freedom to the system in order to manipulate both reconfigurability and cable stiffness independently. The controllers in the above examples were designed with kinematic models, but most CDPRs are highly dynamic systems which can require challenging feedback control frameworks. An approach to real-time dynamic control was implemented in this thesis by incorporating a learning-based frameworks through deep reinforcement learning. Three approaches to rCDPR training were attempted utilizing model-free TD3 networks. Robustness and safety are critical features for robot development. One of the main causes of robot failure in CDPRs is due to cable breakage. This not only causes dangerous dynamic oscillations in the workspace, but also leads to total robot failure if the controllability (due to lack of cables) is lost. Fortunately, rCDPRs can be utilized towards failure tolerant control for task recovery. The kinematically redundant joints can be utilized to help recover the lost degrees of freedom due to cable failure. This work applies a Multi-Model Adaptive Estimation (MMAE) framework to enable online and automatic objective reprioritization and actuator retasking. The likelihood of cable failure(s) from the estimator informs the mixing of the control inputs from a bank of feedforward controllers. In traditional rigid body robots, safety procedures generally involve a standard emergency stop procedure such as actuator locking. Due to the flexibility of cable links, the dynamic oscillations of the end-effector due to cable failure must be actively dampened. This work incorporates a Linear Quadratic Regulator (LQR) based feedback stabilizer into the failure tolerant control framework that works to stabilize the non-linear system and dampen out these oscillations. This research contributes to a growing, but hitherto niche body of work in reconfigurable cable driven parallel manipulators. Some outcomes of the multiple engineering design, control and estimation challenges addressed in this research warrant further exploration and study that are beyond the scope of this thesis. This thesis concludes with a thorough discussion of the advantages and limitations of the presented work and avenues for further research that may be of interest to continuing scholars in the community

Design Optimization, Analysis, and Control of Walking Robots

Passive dynamic walking refers to the dynamical behavior of mechanical devices that are able to naturally walk down a shallow slope in a stable manner, without using actuation or sensing of any kind. Such devices can attain motions that are remarkably human-like by purely exploiting their natural dynamics. This suggests that passive dynamic walking machines can be used to model and study human locomotion; however, there are two major limitations: they can be difficult to design, and they cannot walk on level ground or uphill without some kind of actuation. This thesis presents a mechanism design optimization framework that allows the designer to find the best design parameters based on the chosen performance metric(s). The optimization is formulated as a convex problem, where its solutions are globally optimal and can be obtained efficiently. To enable locomotion on level ground and uphill, this thesis studies a robot based on a passive walker: the rimless wheel with an actuated torso. We design and validate two control policies for the robot through the use of scalable methodology based on tools from mathematical analysis, optimization theory, linear algebra, differential equations, and control theory

Enhancing VTOL Multirotor Performance With a Passive Rotor Tilting Mechanism

This article discusses the benefits of introducing a simple passive mechanism to enable rotor tilting in Vertical Take-Off and Landing (VTOL) multirotor vehicles. Such a system is evaluated in relevant Urban Air Mobility (UAM) passenger transport scenarios such as hovering in wind conditions and overcoming rotor failures. While conventional parallel axis multirotors are underactuated systems, the proposed mechanism makes the vehicle fully actuated in SE(3), which implies independent cabin position and orientation control. An accurate vehicle simulator with realistic parameters is presented to compare in simulation the proposed architecture with a conventional underactuated VTOL vehicle that shares the same physical properties. In order to make fair comparisons, controllers are obtained solving an optimization problem in which the cost function of both systems is chosen to be equivalent. In particular, the control laws are Linear-Quadratic Regulators (LQR), which are derived by linearizing the systems around hover. It is shown through extensive simulation that the introduction of a passive rotor tilting mechanism based on universal joints improves performance metrics such as vehicle stability, power consumption, passenger comfort and position tracking precision in nominal flight conditions and it does not compromise vehicle safety in rotor failure situations

Advanced Strategies for Robot Manipulators

Amongst the robotic systems, robot manipulators have proven themselves to be of increasing importance and are widely adopted to substitute for human in repetitive and/or hazardous tasks. Modern manipulators are designed complicatedly and need to do more precise, crucial and critical tasks. So, the simple traditional control methods cannot be efficient, and advanced control strategies with considering special constraints are needed to establish. In spite of the fact that groundbreaking researches have been carried out in this realm until now, there are still many novel aspects which have to be explored

Programming by Demonstration on Riemannian Manifolds

This thesis presents a Riemannian approach to Programming by Demonstration (PbD). It generalizes an existing PbD method from Euclidean manifolds to Riemannian manifolds. In this abstract, we review the objectives, methods and contributions of the presented approach. OBJECTIVES PbD aims at providing a user-friendly method for skill transfer between human and robot. It enables a user to teach a robot new tasks using few demonstrations. In order to surpass simple record-and-replay, methods for PbD need to \u2018understand\u2019 what to imitate; they need to extract the functional goals of a task from the demonstration data. This is typically achieved through the application of statisticalmethods. The variety of data encountered in robotics is large. Typical manipulation tasks involve position, orientation, stiffness, force and torque data. These data are not solely Euclidean. Instead, they originate from a variety of manifolds, curved spaces that are only locally Euclidean. Elementary operations, such as summation, are not defined on manifolds. Consequently, standard statistical methods are not well suited to analyze demonstration data that originate fromnon-Euclidean manifolds. In order to effectively extract what-to-imitate, methods for PbD should take into account the underlying geometry of the demonstration manifold; they should be geometry-aware. Successful task execution does not solely depend on the control of individual task variables. By controlling variables individually, a task might fail when one is perturbed and the others do not respond. Task execution also relies on couplings among task variables. These couplings describe functional relations which are often called synergies. In order to understand what-to-imitate, PbDmethods should be able to extract and encode synergies; they should be synergetic. In unstructured environments, it is unlikely that tasks are found in the same scenario twice. The circumstances under which a task is executed\u2014the task context\u2014are more likely to differ each time it is executed. Task context does not only vary during task execution, it also varies while learning and recognizing tasks. To be effective, a robot should be able to learn, recognize and synthesize skills in a variety of familiar and unfamiliar contexts; this can be achieved when its skill representation is context-adaptive. THE RIEMANNIAN APPROACH In this thesis, we present a skill representation that is geometry-aware, synergetic and context-adaptive. The presented method is probabilistic; it assumes that demonstrations are samples from an unknown probability distribution. This distribution is approximated using a Riemannian GaussianMixtureModel (GMM). Instead of using the \u2018standard\u2019 Euclidean Gaussian, we rely on the Riemannian Gaussian\u2014 a distribution akin the Gaussian, but defined on a Riemannian manifold. A Riev mannian manifold is a manifold\u2014a curved space which is locally Euclidean\u2014that provides a notion of distance. This notion is essential for statistical methods as such methods rely on a distance measure. Examples of Riemannian manifolds in robotics are: the Euclidean spacewhich is used for spatial data, forces or torques; the spherical manifolds, which can be used for orientation data defined as unit quaternions; and Symmetric Positive Definite (SPD) manifolds, which can be used to represent stiffness and manipulability. The Riemannian Gaussian is intrinsically geometry-aware. Its definition is based on the geometry of the manifold, and therefore takes into account the manifold curvature. In robotics, the manifold structure is often known beforehand. In the case of PbD, it follows from the structure of the demonstration data. Like the Gaussian distribution, the Riemannian Gaussian is defined by a mean and covariance. The covariance describes the variance and correlation among the state variables. These can be interpreted as local functional couplings among state variables: synergies. This makes the Riemannian Gaussian synergetic. Furthermore, information encoded in multiple Riemannian Gaussians can be fused using the Riemannian product of Gaussians. This feature allows us to construct a probabilistic context-adaptive task representation. CONTRIBUTIONS In particular, this thesis presents a generalization of existing methods of PbD, namely GMM-GMR and TP-GMM. This generalization involves the definition ofMaximum Likelihood Estimate (MLE), Gaussian conditioning and Gaussian product for the Riemannian Gaussian, and the definition of ExpectationMaximization (EM) and GaussianMixture Regression (GMR) for the Riemannian GMM. In this generalization, we contributed by proposing to use parallel transport for Gaussian conditioning. Furthermore, we presented a unified approach to solve the aforementioned operations using aGauss-Newton algorithm. We demonstrated how synergies, encoded in a Riemannian Gaussian, can be transformed into synergetic control policies using standard methods for LinearQuadratic Regulator (LQR). This is achieved by formulating the LQR problem in a (Euclidean) tangent space of the Riemannian manifold. Finally, we demonstrated how the contextadaptive Task-Parameterized Gaussian Mixture Model (TP-GMM) can be used for context inference\u2014the ability to extract context from demonstration data of known tasks. Our approach is the first attempt of context inference in the light of TP-GMM. Although effective, we showed that it requires further improvements in terms of speed and reliability. The efficacy of the Riemannian approach is demonstrated in a variety of scenarios. In shared control, the Riemannian Gaussian is used to represent control intentions of a human operator and an assistive system. Doing so, the properties of the Gaussian can be employed to mix their control intentions. This yields shared-control systems that continuously re-evaluate and assign control authority based on input confidence. The context-adaptive TP-GMMis demonstrated in a Pick & Place task with changing pick and place locations, a box-taping task with changing box sizes, and a trajectory tracking task typically found in industr

PID and LQR controllers applied to the inverse dynamics of a 3-DOF Manipulator / Controladores PID e LQR aplicados à dinâmica inversa de um Manipulador 3-GDL

The application in the industrial manipulator robots has grown over the years making production systems increasingly efficient. Within this context, the need for efficient controllers is required to perform the control of these manipulators. In this work the PID controller (Proportional-Integral-Derivative) and LQR (Linear Quadratic Regulator) is presented from the inverse dynamics model of a RPP (Rotational - Prismatic - Prismatic) cylindrical manipulator. The inverse dynamic model which is modeled on Simulink together with a cascaded PID controller is presented. The PID and LQR results are also presented for joint independent and joint dependent control, i.e a controlled PID is used for each joint, controlling the trajectories and speeds at the same time. This paper has as main contributions the development of the manipulator dynamics model and the design of the LQR and PID controllers applied to the inverse dynamics model, which makes the system simpler to control

Design of Super Twisting Integral Sliding Mode Control for Industrial Robot Manipulator

In the present work, integral sliding mode based continuous control algorithm is extended to multi input multi output system. The typical integral sliding mode control (ISMC) contains nominal control with discontinuous feedback control due to which overall control becomes discontinuous in nature. The proposed controller is a fusion of two continuous terms and one of which is able to handle, estimate and reject the disturbance successfully. A proposed robust ISMC technique is applied for industrial robot manipulators which utilizes interactive manipulation activity. Here, robust position tracking control obtained via ISMC principle for two link IRM scheme influenced by parametric uncertainties and external disturbances. The proposed ISMC design replaces the discontinuous part by continuous control, which super twisting control is able to handle the disturbance rejection completely. The effectiveness of the proposed control technique is tested under uncertain conditions and comparison study with other controllers has been done. The simulation result shows that the tracking error is effectively minimized by the proposed technique in presence of uncertain conditions