Model-based control of fast parallel robots

A global approach to the problem of model-based control of fast parallel robots is proposed in this work. Fundamental differences between the well-known serial arms and parallel manipulators are first explained. A formalism inspired from Denavit-Hartenberg's makes it possible to parametrize any parallel manipulator by handling it as two tree robots connected through six standard links. Then, it is shown that kinematics and dynamics modeling is greatly simplified when the robot's state is represented both by the variables associated to the actuated joints and the variables specifying the end-effector's position in operational space. The inverse dynamics model of any parallel manipulator can then be put under a standard form called "in the two spaces". A Newton-Euler based algorithm is proposed for the real-time computation of the model in the two spaces its complexity is shown not to be much larger than for serial arms. Through Lagrangian mechanics, the model in the two spaces allows analysis of the robot's dynamics properties, such as passivity. These properties are shown to be equivalent to those of serial arms, except that parallel robots offer good performances only in a restricted workspace in which their Jacobian matrix remains bounded. Various control strategies for the trajectory tracking problem for fast robots are then examined. The advantages of model-based approaches combined with robust feedback laws in operational space are described. It is shown that a control loop in operational space requires less computations than in joint space for a parallel robot. Moreover, such a scheme can be very efficiently be implemented on a multiprocessor control unit that exploits the intrinsically parallel and pipeline structure of the required algorithms. Finally, the proposed approach is applied to the Delta parallel manipulator. A systematic approach leads to the kinematics and dynamics models of this robot, which are expressed under a very compact form. The analysis of the Delta's Jacobian matrix as well as some simulation results reveal the advantages and weak points of this manipulator. The implementation of a model-based control law for the Delta on a control unit with four Transputers is described. Some results obtained on a Delta with a crank belt reduction are presented and discussed.

Improving the accuracy of parallel robots

The main objective of this thesis is the accuracy improvement of parallel robots. Accuracy can be improved either by precise manufacturing and assembly or by calibration of each individual robot using a kinematic model which takes geometric deviations into account. The latter has the advantage of leading to low cost solutions but requires sophisticated modeling of the robot's structure which is usually considerably more complex than the derivation of its nominal model. To substantiate the theoretical tools proposed in this thesis two examples of parallel structures are chosen. One of them is the Delta robot with three translational degrees of freedom whereas the second example is a novel structure called Argos having three rotational degrees of freedom. For experimental verification a mock-up was built for each of the two structures. Four calibration steps, modeling, measurement, identification, and implementation are investigated. Investigations were restricted to static errors due to geometric deviations assuming rigid bodies. First a formula is proposed which allows to calculate the number of independent kinematic parameters required for a complete model of a parallel structure. Then a systematic parameterization is introduced and applied to derive four calibration models, two for each example. Two measurement devices are described which were built to determine the position and orientation (pose) of the end-effectors of the two robots. For the Delta robot two additional set-ups using no external (additional) measurement device are proposed. For parameter identification different methods were tested by simulation. Calibration based on the implicit model is proposed as a standard method to calibrate parallel robots. Another calibration method is introduced, referred to as semiparametric calibration, which leads to low computational effort. Fast solutions of the direct and inverse problems had to be found. For the first time al1 the solutions of the direct problem for the Delta robot were found by means of an algorithm introduced by Husty. In addition a fast numeric algorithm for the Delta's direct problem is proposed. The main contribution of this thesis is the experimental verification of calibration methods to improve the accuracy of parallel robots. Using these calibration methods for the two robots, ARGOS and DELTA, between a three- to a twelve-fold improvement of accuracy was achieved and experimentally verified.

EPFL1996

Modélisation et commande du moteur piézoélectrique à onde progressive

Matteo Bullo

Piezoelectric motors are resonant vibromotors. They represent a new actuator generation in the field of servo-drives. In particular, the travelling wave ultrasonic motor presents a high torque at low speed, a zero speed torque without feeding, low sensitivity to electromagnetic disturbances as well as being a more compact solution if compared to conventional electromagnetic motors. Much researches has been performed by others to determine an analytical model based on the identification of an electromagnetic equivalent circuit or on exploitation of a theoretical model based on numerical approaches, which use finite elements methods. While leading to satisfactory analysis, these modeling methods can hardly be exploited in the design of control algorithms. Indeed, they require considerable processing resources to generate and visualize the results. For this reason, we introduce in this thesis, an analytical model that is easily adaptable to operational applications and control techniques. The proposed analytical model has been validated by comparing measured characteristics with those obtained in simulations, which was possible thanks to the realization of a modular test bench. The travelling wave ultrasonic motor is characterized by strong non-linearity. It also depends highly on the wear state of the materials, which is difficult to model, and on the contact surface between stator and rotor. In addition, the mechanical resonance frequency experiences drift due to the variations of temperature. These considerations of strong non-linearities and parameter sensitivities of the motor represent a challenge for the study and design of an efficient and robust control strategy. We introduce with this thesis a new control approach that guarantees a closed loop response which is independent of the motor operating point. Moreover, the proposed control method allows to avoid the discontinuities typically present with this type of actuator with a very reasonnable hardware requierments. Finally, an important extension in the product range of the piezoelectric actuators is proposed in the last part of this thesis. It acts to develop an fMRI (functional Magnetic Resonance Imaging) compatible haptic interface with one degree of freedom. The use of a robotic interface in conjunction with an fMRI environment would enable neuroscientists to investigate the brain mechanism used to perform tasks with arbitrary dynamics, and could become a critical tool in neuroscience and rehabilitaiton. There is, however, a major problem for robot working within an fMRI environment : conventional actuators and materials interfere with the strong permanent magnetic field and the fast switching magnetic field gradients. Consequently, non-ferromagnetic materials must be used to avoid forces on the device itself, that can compromise its performance and may result in hazardous conditions for the patient or the medical staff. In addition, the materials should be non-conducting to avoid the generation of eddy currents. The travelling wave ultrasonic motor was used because it provides benefits compared to the conventional electromagnetic actuators. Non-ferromagnetic piezoelectric ceramic material is used and as a result motor operation is not affected by the presence of the strong magnetic fields ecountered in the clinical scanners.

EPFL2005

Memory of Motion for Initializing Optimization in Robotics

Teguh Santoso Lembono

Many robotics problems are formulated as optimization problems. However, most optimization solvers in robotics are locally optimal and the performance depends a lot on the initial guess. For challenging problems, the solver will often get stuck at poor local optima without a good initialization. In this thesis, we consider various techniques to provide a good initial guess to the solver based on previous experience. We use the term memory of motion to collectively refer to these techniques. The key idea is to use the existing system models, cost functions, and simulation tools to generate a database of solutions, and then construct a memory of motion model. During online execution, we can then query the initial guess of a given task from the memory of motion. We show that it improves the solver performance in terms of the solution quality, the success rates, and the computation time. We consider two different formulations, i.e., supervised learning and probability density estimation. In the first part, we formulate a regression problem to find the mapping between the task parameters and the solutions. Such a formulation is convenient, as there are a lot of function approximations available, but using them as a black box tool may result in poor predictions. It is especially the case for multimodal problems where there can be several different solutions for a given task and standard function approximators will simply average the different modes. We first propose an ensemble of function approximators that can handle multimodal problems to initialize an optimization-based motion planner. We then investigate the problem of initializing an optimal control solver for legged robot locomotion, where we need to also provide the initial guess of the control sequence. We evaluate the effect of different initialization components on the optimal control solver performance. In the second part, we consider another formulation by first transforming the cost function into an unnormalized Probability Density Function (PDF) and approximating it using various models. This formulation addresses several shortcomings of the supervised learning approaches by using the cost function itself to train or construct the predictive model. It allows us to generate initial guesses that have high probabilities of having low-cost values instead of simply imitating the dataset. We first show that we can obtain a trajectory distribution of an iLQR problem as a Gaussian distribution, and tracking this distribution results in a cost-efficient and robust controller. We then propose a generative adversarial framework to learn the distribution of robot configurations under constraints. Finally, we use tensor methods to approximate the unnormalized PDF. Since it does not rely on gradient information, the method is quite robust in finding the (possibly multiple) global optima or at least the good local optima of various challenging problems including some benchmark optimization functions, inverse kinematics, and motion planning.

EPFL2022