Adaptive Control of Arm Movement based on Cerebellar Model

This study is an attempt to take advantage of a cerebellar model to control a biomimetic arm. Aware that a variety of cerebellar models with different levels of details has been developed, we focused on a high-level model called MOSAIC. This model is thought to be able to describe the cerebellar functionality without getting into the details of the neural circuitry. To understand where this model exactly fits, we glanced over the biology of the cerebellum and a few alternative models. Certainly, the arm control loop is composed of other components. We reviewed those elements with emphasis on modeling for our simulation. Among these models, the arm and the muscle system received the most attention. The musculoskeletal model tested independently and by means of optimization techniques, a human-like control of arm through muscle activations achieved. We have discussed how MOSAIC can solve a control problem and what drawbacks it has. Consequently, toward making a practical use of MOSAIC model, several ideas developed and tested. In this process, we borrowed concepts and methods from the control theory. Specifically, known schemes of adaptive control of a manipulator, linearization and approximation were utilized. Our final experiment dealt with a modified/adjusted MOSAIC model to adaptively control the arm. We call this model ORF-MOSAIC (Organized by Receptive Fields MOdular Selection And Identification for Control). With as few as 16 modules, we were able to control the arm in a workspace of 30 x 30 cm. The system was able to adapt to an external field as well as handling new objects despite delays. The discussion section suggests that there are similarities between microzones in the cerebellum and the modules of this new model

Ball-and-finger system: modeling and optimal trajectories

A rigid-body model of a finger interacting with a trackball is considered. The proposed system is a suitable candidate for studying trajectory generation when interaction plays an important role, such as in assembly and manipulation tasks. The mathematical model consists of a ball with a spherical joint constraint, a finger with three degrees of freedom, and the Coulomb friction model. From first principles, we derive a hybrid, high-index differential-algebraic equation for modeling the system dynamics, which is used for both simulation and finding optimal trajectories. For this problem, task planning, path planning, and trajectory generation are strongly interrelated, which makes using an integrated approach to trajectory generation inevitable. Moreover, the trajectory generation algorithm has to handle a number of important features, e.g., unilateral and non-holonomic constraints

Online Minimum-Jerk Trajectory Generation

Robotic trajectory generation is reformulated as a controller design problem. For minimum-jerk trajectories, an optimal controller using the Hamilton-Jacobi-Bellman equation is derived. The controller instantaneously updates the trajectory in a closed-loop system as a result of the changes in the reference signal. The resulting trajectories coincide with piece-wise fifth-order polynomial trajectories for piece-wise constant target states. Since having hard constraints on the final time poses certain robustness issues, a smooth transition between the finite-horizon and an infinite-horizon problem is developed. This enables to switch softly to a tracking mode when a moving target is reached

An Analytic Solution to Fixed-Time Point-to-Point Trajectory Planning

We derive an analytic solution to the problem of fixed-time trajectory generation with a quadratic cost function under velocity and acceleration constraints. This problem has a wide range of applications within motion planning. The advantage of the analytic solution compared to numerical optimization of the discretized problem is the unlimited resolution of the solution and the efficiency of the calculation, allowing sensor-based replanning and on-line trajectory generation

Trajectory Generation for Assembly Tasks Via Bilateral Teleoperation

Abstract in UndeterminedFor assembly tasks, the knowledge of both trajectory and forces are usually required. Consequently, we may use kinesthetics or teleoperation for recording human demonstrations. In order to have a more natural interaction, the operator has to be provided with a sense of touch. We propose a bilateral teleoperation system which is customized for this purpose. We introduce different coordinate frames to make the design of a 6-DOF teleoperation straightforward. Moreover, we suggest using tele-admittance, which simplifies instructing the robot. The compliance due to the slave controller allows the robot to react quickly and reduces the risk of damaging the workpiece

Master-Slave Coordination Using Virtual Constraints for a Redundant Dual-Arm Haptic Interface

Programming robots for tasks involving force interaction is difficult, since both the knowledge of the task and the dynamics of the robots are necessary. An immersive haptic interface for task demonstration is proposed, where theoperator can sense and act through the robot. This is achieved by coupling two robotic systems with virtual constraints such that they have the same coordinates in the operational space disregarding a fixed offset. Limitations caused by the singular configurations or the reach of the robots are naturally reflected to either side as haptic feedback

Hybrid Stiff/Compliant Workspace Control for Robotized Minimally Invasive Surgery

Abstract-This paper presents a novel control architecture for hybrid stiff and compliant control for minimally invasive surgery which satisfies the constraints of zero lateral velocity at the entry point for serial manipulators. For minimally invasive surgery it is required that there is no sideways motion at the point where the robots enter the abdomen. This is necessary to avoid any damage to the patient's body when the robot moves. We solve this at a kinematic level, i.e., we find a Jacobian matrix that maps the velocities in joint space to the end-effector velocities and at the same time guarantees that certain velocities at the entry point are zero. Because the new velocity variables are defined in the end-effector workspace we can use these for hybrid motion/force control. The approach is verified experimentally by implementing hybrid stiff and compliant control of the end effector and we show that the insertion point constraints are always satisfied

A Geografia dos Naturalistas-Geógrafos no Século das Luzes

Para nós, a geografia moderna nasceu de um sonho. Do sonho que habita o homem desde os primeiros tempos da modernidade – o de dominar o mundo e a natureza através da razão e da ciência. Do desejo que nutriu o Século das Luzes, de tudo compreender, de racionalizar o mundo, transformando-o num lugar visível, calculável e inteligível; de se utilizar a natureza e todas as suas criaturas para alcançar um progresso sem limites. Esse sonho que se encontrava então reforçado por uma série de elementos..

On Trajectory Generation for Robots

A fundamental problem in robotics is the generation of motion for a task. How to translate a task to a set of movements is a non-trivial problem. The complexity of the task, the capabilities of the robot, and the desired performance, affect all aspects of the trajectory; the sequence of movements, the path, and the course of motion as a function of time.This thesis is about trajectory generation and advances the state of the art in several directions. Special attention to trajectories in constrained situations when interaction forces are involved is paid. We bring a control perspective to trajectory generation and propose novel solutions for online trajectory generation with a rapid response to sensor inputs. We formulate and find optimal trajectories for various problems, closing the gap between path planning and trajectory generation. The inverse problem of finding the control signal corresponding to a desired trajectory is investigated and we extend the applicability of an existing algorithm to a broader class of problems.To collect human-generated trajectories involving force interactions, we propose a method to join two robotic manipulators to form a haptic interface for task demonstration. Furthermore, fast algorithms for fixed-time point-to-point trajectory generation are investigated. More importantly, two optimal closed-loop trajectory generation methods are proposed. We derive an optimal controller for the fixed-time trajectory-generation problem with a minimum-jerk cost functional. The other method is based on Model Predictive Control, which allows a more generic form of system dynamics and constraints. In addition, a ball-and-finger system is modeled for studying trajectory generation where interaction plays an important role. Efficient movements for rotating the ball are numerically computed and simulated.Iterative Learning Control (ILC) finds a proper control signal for obtaining a desired trajectory. We derive frequency-domain criteria for the convergence of linear ILC on finite-time intervals that are less restrictive than existing ones in the literature

Topics in Trajectory Generation for Robots

A fundamental problem in robotics is generating the motion for a task. How to translate a task to motion or a series of movements is a non-trivial problem. The complexity of the task, the structure of the robot, and the desired performance determine the sequence of movements, the path, and the course of motion as a function of time, namely the trajectory. As we discuss in this thesis, a trajectory can be acquired from a human demonstration or generated by carefully designing an objective function. In the first approach, we examine a number of robotic setups which are suitable for human demonstration. More notably, admittance control as a new dimension to the robot-assisted teleoperation is investigated. We also describe a free-floating behavior which makes robust lead-through programming possible. As a way to utilize these setups, we present some ideas for developing a high-level language for an event-based programming common to assembly tasks. Since immediate reaction to variations in the target state and/or robot state is desirable, we reformulate the trajectory generation problem as a controller design problem. Using the Hamilton-Jacobi-Bellman equation, we derive a closed-loop solution to the fixed-time trajectory-generation problem with a minimum-jerk cost functional. We show that the resulting trajectory coincides with a fifth-order polynomial function of time that instantaneously updates due to changes in the reference signal and/or the robot states. A short comparison is made between kinematic and dynamic models for generating optimal trajectories. The conclusion is that given conservative kinematic constraints, both models behave in a similar way. Having this in mind, we derive an analytic solution to the problem of fixed-time trajectory generation with a quadratic cost function under velocity and acceleration constraints. The advantage of the analytic solution compared to an on-line optimization approach lies in the efficiency of the computation. To extend the idea of closed-loop trajectory generation, we adapt the Model Predictive Control (MPC) framework. MPC is traditionally applied to tracking problems, i.e., when there is an explicit reference signal. Thus, it is a common practice to have a separate layer that generates the reference signal. We propose an integrated approach by introducing a final state constraint in the formulation. Additionally, we give the interpretation that the difference between tracking and point-to-point trajectory-planning problems is in the density of the specified desired reference signal. We utilize a strategy to reduce the discretization time successively. This way, we respect the real-time constraints for computation time while the accuracy of the solution is gradually improved as the deadline approaches. We have verified our proposed MPC approach to trajectory generation in a ball-catching experiment