Motion Planning of Uncertain Ordinary Differential Equation Systems

This work presents a novel motion planning framework, rooted in nonlinear programming theory, that treats uncertain fully and under-actuated dynamical systems described by ordinary differential equations. Uncertainty in multibody dynamical systems comes from various sources, such as: system parameters, initial conditions, sensor and actuator noise, and external forcing. Treatment of uncertainty in design is of paramount practical importance because all real-life systems are affected by it, and poor robustness and suboptimal performance result if it’s not accounted for in a given design. In this work uncertainties are modeled using Generalized Polynomial Chaos and are solved quantitatively using a least-square collocation method. The computational efficiency of this approach enables the inclusion of uncertainty statistics in the nonlinear programming optimization process. As such, the proposed framework allows the user to pose, and answer, new design questions related to uncertain dynamical systems. Specifically, the new framework is explained in the context of forward, inverse, and hybrid dynamics formulations. The forward dynamics formulation, applicable to both fully and under-actuated systems, prescribes deterministic actuator inputs which yield uncertain state trajectories. The inverse dynamics formulation is the dual to the forward dynamic, and is only applicable to fully-actuated systems; deterministic state trajectories are prescribed and yield uncertain actuator inputs. The inverse dynamics formulation is more computationally efficient as it requires only algebraic evaluations and completely avoids numerical integration. Finally, the hybrid dynamics formulation is applicable to under-actuated systems where it leverages the benefits of inverse dynamics for actuated joints and forward dynamics for unactuated joints; it prescribes actuated state and unactuated input trajectories which yield uncertain unactuated states and actuated inputs. The benefits of the ability to quantify uncertainty when planning the motion of multibody dynamic systems are illustrated through several case-studies. The resulting designs determine optimal motion plans—subject to deterministic and statistical constraints—for all possible systems within the probability space

Time-Optimal Trajectory Planning with Interaction with the Environment

Optimal motion planning along prescribed paths can be solved with several techniques, but most of them do not take into account the wrenches exerted by the end-effector when in contact with the environment. When a dynamic model of the environment is not available, no consolidated methodology exists to consider the effect of the interaction. Regardless of the specific performance index to optimize, this article proposes a strategy to include external wrenches in the optimal planning algorithm, considering the task specifications. This procedure is instantiated for minimum-time trajectories and validated on a real robot performing an interaction task under admittance control. The results prove that the inclusion of end-effector wrenches affect the planned trajectory, in fact modifying the manipulator's dynamic capability.Comment: \copyright 2022 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other work

Bimanual robot skills: MP encoding, dimensionality reduction and reinforcement learning

In our culture, robots have been in novels and cinema for a long time, but it has been specially in the last two decades when the improvements in hardware - better computational power and components - and advances in Artificial Intelligence (AI), have allowed robots to start sharing spaces with humans. Such situations require, aside from ethical considerations, robots to be able to move with both compliance and precision, and learn at different levels, such as perception, planning, and motion, being the latter the focus of this work. The first issue addressed in this thesis is inverse kinematics for redundant robot manipulators, i.e: positioning the robot joints so as to reach a certain end-effector pose. We opt for iterative solutions based on the inversion of the kinematic Jacobian of a robot, and propose to filter and limit the gains in the spectral domain, while also unifying such approach with a continuous, multipriority scheme. Such inverse kinematics method is then used to derive manipulability in the whole workspace of an antropomorphic arm, and the coordination of two arms is subsequently optimized by finding their best relative positioning. Having solved the kinematic issues, a robot learning within a human environment needs to move compliantly, with limited amount of force, in order not to harm any humans or cause any damage, while being as precise as possible. Therefore, we developed two dynamic models for the same redundant arm we had analysed kinematically: The first based on local models with Gaussian projections, and the second characterizing the most problematic term of the dynamics, namely friction. Such models allowed us to implement feed-forward controllers, where we can actively change the weights in the compliance-precision tradeoff. Moreover, we used such models to predict external forces acting on the robot, without the use of force sensors. Afterwards, we noticed that bimanual robots must coordinate their components (or limbs) and be able to adapt to new situations with ease. Over the last decade, a number of successful applications for learning robot motion tasks have been published. However, due to the complexity of a complete system including all the required elements, most of these applications involve only simple robots with a large number of high-end technology sensors, or consist of very simple and controlled tasks. Using our previous framework for kinematics and control, we relied on two types of movement primitives to encapsulate robot motion. Such movement primitives are very suitable for using reinforcement learning. In particular, we used direct policy search, which uses the motion parametrization as the policy itself. In order to improve the learning speed in real robot applications, we generalized a policy search algorithm to give some importance to samples yielding a bad result, and we paid special attention to the dimensionality of the motion parametrization. We reduced such dimensionality with linear methods, using the rewards obtained through motion repetition and execution. We tested such framework in a bimanual task performed by two antropomorphic arms, such as the folding of garments, showing how a reduced dimensionality can provide qualitative information about robot couplings and help to speed up the learning of tasks when robot motion executions are costly.A la nostra cultura, els robots han estat presents en novel·les i cinema des de fa dècades, però ha sigut especialment en les últimes dues quan les millores en hardware (millors capacitats de còmput) i els avenços en intel·ligència artificial han permès que els robots comencin a compartir espais amb els humans. Aquestes situacions requereixen, a banda de consideracions ètiques, que els robots siguin capaços de moure's tant amb suavitat com amb precisió, i d'aprendre a diferents nivells, com són la percepció, planificació i moviment, essent l'última el centre d'atenció d'aquest treball. El primer problema adreçat en aquesta tesi és la cinemàtica inversa, i.e.: posicionar les articulacions del robot de manera que l'efector final estigui en una certa posició i orientació. Hem estudiat el camp de les solucions iteratives, basades en la inversió del Jacobià cinemàtic d'un robot, i proposem un filtre que limita els guanys en el seu domini espectral, mentre també unifiquem tal mètode dins un esquema multi-prioritat i continu. Aquest mètode per a la cinemàtica inversa és usat a l'hora d'encapsular tota la informació sobre l'espai de treball d'un braç antropomòrfic, i les capacitats de coordinació entre dos braços són optimitzades, tot trobant la seva millor posició relativa en l'espai. Havent resolt les dificultats cinemàtiques, un robot que aprèn en un entorn humà necessita moure's amb suavitat exercint unes forces limitades per tal de no causar danys, mentre es mou amb la màxima precisió possible. Per tant, hem desenvolupat dos models dinàmics per al mateix braç robòtic redundant que havíem analitzat des del punt de vista cinemàtic: El primer basat en models locals amb projeccions de Gaussianes i el segon, caracteritzant el terme més problemàtic i difícil de representar de la dinàmica, la fricció. Aquests models ens van permetre utilitzar controladors coneguts com "feed-forward", on podem canviar activament els guanys buscant l'equilibri precisió-suavitat que més convingui. A més, hem usat aquests models per a inferir les forces externes actuant en el robot, sense la necessitat de sensors de força. Més endavant, ens hem adonat que els robots bimanuals han de coordinar els seus components (braços) i ser capaços d'adaptar-se a noves situacions amb facilitat. Al llarg de l'última dècada, diverses aplicacions per aprendre tasques motores robòtiques amb èxit han estat publicades. No obstant, degut a la complexitat d'un sistema complet que inclogui tots els elements necessaris, la majoria d'aquestes aplicacions consisteixen en robots més aviat simples amb costosos sensors d'última generació, o a resoldre tasques senzilles en un entorn molt controlat. Utilitzant el nostre treball en cinemàtica i control, ens hem basat en dos tipus de primitives de moviment per caracteritzar la motricitat robòtica. Aquestes primitives de moviment són molt adequades per usar aprenentatge per reforç. En particular, hem usat la búsqueda directa de la política, un camp de l'aprenentatge per reforç que usa la parametrització del moviment com la pròpia política. Per tal de millorar la velocitat d'aprenentatge en aplicacions amb robots reals, hem generalitzat un algoritme de búsqueda directa de política per a donar importància a les mostres amb mal resultat, i hem donat especial atenció a la reducció de dimensionalitat en la parametrització dels moviments. Hem reduït la dimensionalitat amb mètodes lineals, utilitzant les recompenses obtingudes EN executar els moviments. Aquests mètodes han estat provats en tasques bimanuals com són plegar roba, usant dos braços antropomòrfics. Els resultats mostren com la reducció de dimensionalitat pot aportar informació qualitativa d'una tasca, i al mateix temps ajuda a aprendre-la més ràpid quan les execucions amb robots reals són costoses

Bimanual robot skills: MP encoding, dimensionality reduction and reinforcement learning

Aplicat embargament des de la data de defensa fins 1/7/2018Premio a la mejor Tesis Doctoral sobre Robótica, Edición 2017, atorgat pel Comité Español de Automática.Finalista del 2018 George Girault PhD Award, from EuRoboticsIn our culture, robots have been in novels and cinema for a long time, but it has been specially in the last two decades when the improvements in hardware - better computational power and components - and advances in Artificial Intelligence (AI), have allowed robots to start sharing spaces with humans. Such situations require, aside from ethical considerations, robots to be able to move with both compliance and precision, and learn at different levels, such as perception, planning, and motion, being the latter the focus of this work. The first issue addressed in this thesis is inverse kinematics for redundant robot manipulators, i.e: positioning the robot joints so as to reach a certain end-effector pose. We opt for iterative solutions based on the inversion of the kinematic Jacobian of a robot, and propose to filter and limit the gains in the spectral domain, while also unifying such approach with a continuous, multipriority scheme. Such inverse kinematics method is then used to derive manipulability in the whole workspace of an antropomorphic arm, and the coordination of two arms is subsequently optimized by finding their best relative positioning. Having solved the kinematic issues, a robot learning within a human environment needs to move compliantly, with limited amount of force, in order not to harm any humans or cause any damage, while being as precise as possible. Therefore, we developed two dynamic models for the same redundant arm we had analysed kinematically: The first based on local models with Gaussian projections, and the second characterizing the most problematic term of the dynamics, namely friction. Such models allowed us to implement feed-forward controllers, where we can actively change the weights in the compliance-precision tradeoff. Moreover, we used such models to predict external forces acting on the robot, without the use of force sensors. Afterwards, we noticed that bimanual robots must coordinate their components (or limbs) and be able to adapt to new situations with ease. Over the last decade, a number of successful applications for learning robot motion tasks have been published. However, due to the complexity of a complete system including all the required elements, most of these applications involve only simple robots with a large number of high-end technology sensors, or consist of very simple and controlled tasks. Using our previous framework for kinematics and control, we relied on two types of movement primitives to encapsulate robot motion. Such movement primitives are very suitable for using reinforcement learning. In particular, we used direct policy search, which uses the motion parametrization as the policy itself. In order to improve the learning speed in real robot applications, we generalized a policy search algorithm to give some importance to samples yielding a bad result, and we paid special attention to the dimensionality of the motion parametrization. We reduced such dimensionality with linear methods, using the rewards obtained through motion repetition and execution. We tested such framework in a bimanual task performed by two antropomorphic arms, such as the folding of garments, showing how a reduced dimensionality can provide qualitative information about robot couplings and help to speed up the learning of tasks when robot motion executions are costly.A la nostra cultura, els robots han estat presents en novel·les i cinema des de fa dècades, però ha sigut especialment en les últimes dues quan les millores en hardware (millors capacitats de còmput) i els avenços en intel·ligència artificial han permès que els robots comencin a compartir espais amb els humans. Aquestes situacions requereixen, a banda de consideracions ètiques, que els robots siguin capaços de moure's tant amb suavitat com amb precisió, i d'aprendre a diferents nivells, com són la percepció, planificació i moviment, essent l'última el centre d'atenció d'aquest treball. El primer problema adreçat en aquesta tesi és la cinemàtica inversa, i.e.: posicionar les articulacions del robot de manera que l'efector final estigui en una certa posició i orientació. Hem estudiat el camp de les solucions iteratives, basades en la inversió del Jacobià cinemàtic d'un robot, i proposem un filtre que limita els guanys en el seu domini espectral, mentre també unifiquem tal mètode dins un esquema multi-prioritat i continu. Aquest mètode per a la cinemàtica inversa és usat a l'hora d'encapsular tota la informació sobre l'espai de treball d'un braç antropomòrfic, i les capacitats de coordinació entre dos braços són optimitzades, tot trobant la seva millor posició relativa en l'espai. Havent resolt les dificultats cinemàtiques, un robot que aprèn en un entorn humà necessita moure's amb suavitat exercint unes forces limitades per tal de no causar danys, mentre es mou amb la màxima precisió possible. Per tant, hem desenvolupat dos models dinàmics per al mateix braç robòtic redundant que havíem analitzat des del punt de vista cinemàtic: El primer basat en models locals amb projeccions de Gaussianes i el segon, caracteritzant el terme més problemàtic i difícil de representar de la dinàmica, la fricció. Aquests models ens van permetre utilitzar controladors coneguts com "feed-forward", on podem canviar activament els guanys buscant l'equilibri precisió-suavitat que més convingui. A més, hem usat aquests models per a inferir les forces externes actuant en el robot, sense la necessitat de sensors de força. Més endavant, ens hem adonat que els robots bimanuals han de coordinar els seus components (braços) i ser capaços d'adaptar-se a noves situacions amb facilitat. Al llarg de l'última dècada, diverses aplicacions per aprendre tasques motores robòtiques amb èxit han estat publicades. No obstant, degut a la complexitat d'un sistema complet que inclogui tots els elements necessaris, la majoria d'aquestes aplicacions consisteixen en robots més aviat simples amb costosos sensors d'última generació, o a resoldre tasques senzilles en un entorn molt controlat. Utilitzant el nostre treball en cinemàtica i control, ens hem basat en dos tipus de primitives de moviment per caracteritzar la motricitat robòtica. Aquestes primitives de moviment són molt adequades per usar aprenentatge per reforç. En particular, hem usat la búsqueda directa de la política, un camp de l'aprenentatge per reforç que usa la parametrització del moviment com la pròpia política. Per tal de millorar la velocitat d'aprenentatge en aplicacions amb robots reals, hem generalitzat un algoritme de búsqueda directa de política per a donar importància a les mostres amb mal resultat, i hem donat especial atenció a la reducció de dimensionalitat en la parametrització dels moviments. Hem reduït la dimensionalitat amb mètodes lineals, utilitzant les recompenses obtingudes EN executar els moviments. Aquests mètodes han estat provats en tasques bimanuals com són plegar roba, usant dos braços antropomòrfics. Els resultats mostren com la reducció de dimensionalitat pot aportar informació qualitativa d'una tasca, i al mateix temps ajuda a aprendre-la més ràpid quan les execucions amb robots reals són costoses.Award-winningPostprint (published version

Planning wrench-feasible motions for cable-driven hexapods

Motion paths of cable-driven hexapods must carefully be planned to ensure that the lengths and tensions of all cables remain within acceptable limits, for a given wrench applied to the platform. The cables cannot go slack-to keep the control of the robot-nor excessively tightto prevent cable breakage-even in the presence of bounded perturbations of the wrench. This paper proposes a path-planning method that accommodates such constraints simultaneously. Given two configurations of the robot, the method attempts to connect them through a path that, at any point, allows the cables to counteract any wrench lying in a predefined uncertainty region. The configuration space, or C-space for short, is placed in correspondence with a smooth manifold, which facilitates the definition of a continuation strategy to search this space systematically from one configuration, until the second configuration is found, or path nonexistence is proved by exhaustion of the search. The force Jacobian is full rank everywhere on the C-space, which implies that the computed paths will naturally avoid crossing the forward singularity locus of the robot. The adjustment of tension limits, moreover, allows to maintain a meaningful clearance relative to such locus. The approach is applicable to compute paths subject to geometric constraints on the platform pose or to synthesize free-flying motions in the full 6-D C-space. Experiments illustrate the performance of the method in a real prototype.Postprint (author's final draft

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

Pressure-Constrained, Reduced-DOF, Interconnected Parallel Manipulators with Applications to Space Suit Design

This dissertation presents the concept of a Morphing Upper Torso, an innovative pressure suit design that incorporates robotic elements to enable a resizable, highly mobile and easy to don/doff spacesuit. The torso is modeled as a system of interconnected, pressure-constrained, reduced-DOF, wire-actuated parallel manipulators, that enable the dimensions of the suit to be reconfigured to match the wearer. The kinematics, dynamics and control of wire-actuated manipulators are derived and simulated, along with the Jacobian transforms, which relate the total twist vector of the system to the vector of actuator velocities. Tools are developed that allow calculation of the workspace for both single and interconnected reduced-DOF robots of this type, using knowledge of the link lengths. The forward kinematics and statics equations are combined and solved to produce the pose of the platforms along with the link tensions. These tools allow analysis of the full Morphing Upper Torso design, in which the back hatch of a rear-entry torso is interconnected with the waist ring, helmet ring and two scye bearings. Half-scale and full-scale experimental models are used along with analytical models to examine the feasibility of this novel space suit concept. The analytical and experimental results demonstrate that the torso could be expanded to facilitate donning and doffing, and then contracted to match different wearer's body dimensions. Using the system of interconnected parallel manipulators, suit components can be accurately repositioned to different desired configurations. The demonstrated feasibility of the Morphing Upper Torso concept makes it an exciting candidate for inclusion in a future planetary suit architecture