Method and apparatus for configuration control of redundant robots

A method and apparatus to control a robot or manipulator configuration over the entire motion based on augmentation of the manipulator forward kinematics is disclosed. A set of kinematic functions is defined in Cartesian or joint space to reflect the desirable configuration that will be achieved in addition to the specified end-effector motion. The user-defined kinematic functions and the end-effector Cartesian coordinates are combined to form a set of task-related configuration variables as generalized coordinates for the manipulator. A task-based adaptive scheme is then utilized to directly control the configuration variables so as to achieve tracking of some desired reference trajectories throughout the robot motion. This accomplishes the basic task of desired end-effector motion, while utilizing the redundancy to achieve any additional task through the desired time variation of the kinematic functions. The present invention can also be used for optimization of any kinematic objective function, or for satisfaction of a set of kinematic inequality constraints, as in an obstacle avoidance problem. In contrast to pseudoinverse-based methods, the configuration control scheme ensures cyclic motion of the manipulator, which is an essential requirement for repetitive operations. The control law is simple and computationally very fast, and does not require either the complex manipulator dynamic model or the complicated inverse kinematic transformation. The configuration control scheme can alternatively be implemented in joint space

Self-motion control of kinematically redundant robot manipulators

Thesis (Master)--Izmir Institute of Technology, Mechanical Engineering, Izmir, 2012Includes bibliographical references (leaves: 88-92)Text in English; Abstract: Turkish and Englishxvi,92 leavesRedundancy in general provides space for optimization in robotics. Redundancy can be defined as sensor/actuator redundancy or kinematic redundancy. The redundancy considered in this thesis is the kinematic redundancy where the total degrees-of-freedom of the robot is more than the total degrees-of-freedom required for the task to be executed. This provides infinite number of solutions to perform the same task, thus, various subtasks can be carried out during the main-task execution. This work utilizes the property of self-motion for kinematically redundant robot manipulators by designing the general subtask controller that controls the joint motion in the null-space of the Jacobian matrix. The general subtask controller is implemented for various subtasks in this thesis. Minimizing the total joint motion, singularity avoidance, posture optimization for static impact force objectives, which include maximizing/minimizing the static impact force magnitude, and static and moving obstacle (point to point) collision avoidance are the subtasks considered in this thesis. New control architecture is developed to accomplish both the main-task and the previously mentioned subtasks. In this architecture, objective function for each subtask is formed. Then, the gradient of the objective function is used in the subtask controller to execute subtask objective while tracking a given end-effector trajectory. The tracking of the end-effector is called main-task. The SCHUNK LWA4-Arm robot arm with seven degrees-of-freedom is developed first in SolidWorks® as a computer-aided-design (CAD) model. Then, the CAD model is converted to MATLAB® Simulink model using SimMechanics CAD translator to be used in the simulation tests of the controller. Kinematics and dynamics equations of the robot are derived to be used in the controllers. Simulation test results are presented for the kinematically redundant robot manipulator operating in 3D space carrying out the main-task and the selected subtasks for this study. The simulation test results indicate that the developed controller’s performance is successful for all the main-task and subtask objectives

Null-Space Minimization of Center of Gravity Displacementof a Redundant Aerial Manipulator

Displacements of the base during trajectory tracking are a common issue in the control of aerial manipulators. These are caused by reaction torques transferred to the base due to the manipulator motion and, in particular, to the motion of its center of gravity. We present a novel approach to reduce base displacements of a kinematically redundant aerial manipulator by using null-space projection in the inverse kinematic control. A secondary objective function minimizes the horizontal displacement of the manipulator center of gravity. We test this algorithm on different trajectories for both three and four degrees of freedom (DOF) manipulators in a simulation environment. The results comparing our algorithm with inverse kinematic control without the null-space projection show up to an 80% reduction in the end-effector position error and an average of about 56% reduction in maximum base displacement. The simulation implementation also runs faster than in real-time in our code implementation. We provide a workspace analysis based on multiple stopping criteria such as excessive base displacement, joint velocities and end-effector position error for the 3 and 4 DOF manipulators. As expected, the 4 DOF manipulator has a larger workspace

Kinematic equations for control of the redundant eight-degree-of-freedom advanced research manipulator 2

The forward position and velocity kinematics for the redundant eight-degree-of-freedom Advanced Research Manipulator 2 (ARM2) are presented. Inverse position and velocity kinematic solutions are also presented. The approach in this paper is to specify two of the unknowns and solve for the remaining six unknowns. Two unknowns can be specified with two restrictions. First, the elbow joint angle and rate cannot be specified because they are known from the end-effector position and velocity. Second, one unknown must be specified from the four-jointed wrist, and the second from joints that translate the wrist, elbow joint excluded. There are eight solutions to the inverse position problem. The inverse velocity solution is unique, assuming the Jacobian matrix is not singular. A discussion of singularities is based on specifying two joint rates and analyzing the reduced Jacobian matrix. When this matrix is singular, the generalized inverse may be used as an alternate solution. Computer simulations were developed to verify the equations. Examples demonstrate agreement between forward and inverse solutions

Optimal redundancy control for robot manipulators

Optimal control for kinematically redundant robots is addressed for two different optimization problems. In the first optimization problem, we consider the minimization of the transfer time along a given Cartesian path for a redundant robot. This problem can be solved in two steps, by separating the generation of a joint path associated to the Cartesian path from the exact minimization of motion time under kinematic/dynamic bounds along the obtained parametrized joint path. In this thesis, multiple sub-optimal solutions can be found, depending on how redundancy is locally resolved in the joint space within the first step. A solution method that works at the acceleration level is proposed, by using weighted pseudoinversion, optimizing an inertia-related criterion, and including null-space damping. The obtained results demonstrate consistently good behaviors and definitely faster motion times in comparison with related methods proposed in the literature. The motion time obtained with the proposed method is close to the global time-optimal solution along the same Cartesian path. Furthermore, a reasonable tracking control performance is obtained on the experimental executed motions. In the second optimization problem, we consider the known phenomenon of torque oscillations and motion instabilities that occur in redundant robots during the execution of sufficiently long Cartesian trajectories when the joint torque is instantaneously minimized. In the framework of on-line local redundancy resolution methods, we propose basic variations of the minimum torque scheme to address this issue. Either the joint torque norm is minimized over two successive discrete-time samples using a short preview window, or we minimize the norm of the difference with respect to a desired momentum-damping joint torque, or the two schemes are combined together. The resulting local control methods are all formulated as well-posed linear-quadratic problems, and their closed-form solutions generate also low joint velocities while addressing the primary torque optimization objectives. Stable and consistent behaviors are obtained along short or long Cartesian position trajectories. For the two addressed optimization problems in this thesis, the results are obtained using three different robot systems, namely a 3R planar arm, a 6R Universal Robots UR10, and a 7R KUKA LWR robot

Singularity Avoidance for Cart-Mounted Hand-Guided Collaborative Robots: A Variational Approach

Most collaborative robots (cobots) can be taught by hand guiding: essentially, by manually jogging the robot, an operator teaches some configurations to be employed as via points. Based on those via points, Cartesian end-effector trajectories such as straight lines, circular arcs or splines are then constructed. Such methods can, in principle, be employed for cart-mounted cobots (i.e., when the jogging involves one or two linear axes, besides the cobot axes). However, in some applications, the sole imposition of via points in Cartesian space is not sufficient. On the contrary, albeit the overall system is redundant, (i) the via points must be reached at the taught joint configurations, and (ii) the undesirable singularity (and near-singularity) conditions must be avoided. The naive approach, consisting of setting the cart trajectory beforehand (for instance, by imposing a linear-in-time motion law that crosses the taught cart configurations), satisfies the first need, but does not guarantee the satisfaction of the second. Here, we propose an approach consisting of (i) a novel strategy for decoupling the planning of the cart trajectory and that of the robot joints, and (ii) a novel variational technique for computing the former in a singularity-aware fashion, ensuring the avoidance of a class of workspace singularity and near-singularity configurations

Robot coordination using task-priority and sliding-mode techniques

In this work, an approach based on task-priority redundancy resolution and sliding mode ideas is proposed for robot coordination. In particular, equality and inequality constraints representing the coordination of the multi-robot system are considered as mandatory (for instance, rigid-body manipulation constraints to distance between the end-effectors of several robot arms, or other inequality constraints guaranteeing safe operation of a robotic swarm or confining the robot's workspace to avoid collision and joint limits). Besides the mandatory constraints, other constraints with lower priority are considered for the tracking of the workspace reference and to achieve secondary goals. Thus, lower-priority constraints are satisfied only in the null space of the higherpriority ones. The fulfillment of the constraints is achieved using geometric invariance and sliding mode control theory. The validity and effectiveness of the proposed approach is substantiated by 2D and 3D simulation results using two 3R planar robots and two 6R PUMA-762 robots, respectively.This work was supported in part by research under Project DPI2011-27845-C02-01 of the Spanish Government and Projects ANPCyT PICT-2011-0888, CONICET PIP 112-2011-00361 and UNLP 1164 in Argentina.Gracia Calandin, LI.; Sala Piqueras, A.; Garelli, F. (2014). Robot coordination using task-priority and sliding-mode techniques. Robotics and Computer-Integrated Manufacturing. 30(1):74-89. https://doi.org/10.1016/j.rcim.2013.08.003S748930

Minimum Jerk Trajectory Planning for Trajectory Constrained Redundant Robots

In this dissertation, we develop an efficient method of generating minimal jerk trajectories for redundant robots in trajectory following problems. We show that high jerk is a local phenomenon, and therefore focus on optimizing regions of high jerk that occur when using traditional trajectory generation methods. The optimal trajectory is shown to be located on the foliation of self-motion manifolds, and this property is exploited to express the problem as a minimal dimension Bolza optimal control problem. A numerical algorithm based on ideas from pseudo-spectral optimization methods is proposed and applied to two example planar robot structures with two redundant degrees of freedom. When compared with existing trajectory generation methods, the proposed algorithm reduces the integral jerk of the examples by 75% and 13%. Peak jerk is reduced by 98% and 33%. Finally a real time controller is proposed to accurately track the planned trajectory given real-time measurements of the tool-tip\u27s following error

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