Soumen Sen

Inverse kinematics of redundant serial manipulators using interval method in handling uncertainties

The paper presents an application of Interval method to solve the inverse kinematics of a serially connected redundant manipulator, aiming its use in design optimization of manipulators. The article attempts to solve inverse kinematics, when the lengths of the links of the manipulator are not precisely known. The sources of uncertainties include manufacturing tolerances, approximations for complex link geometries, inaccuracies in joint angle measurements etc. The inverse kinematics is intended to produce solutions for joint variables in interval of tolerances for specified end effector accuracy range. The redundancy resolution is cast as an optimization problem with arm isotropy as performance metric. In solving for the inverse kinematics, two stage interval optimization method is implemented, where, in the first stage, bisection technique is applied and in the second stage interval discrete random variable method is used. As exemplar problem solving, two cases, namely a planar3-degrees-of-freedom and a spatial 5-degrees-of-freedom serial link manipulators are considered.

Design and impedance estimation of a biologically inspired flexible mechanical transmission with exponential elastic characteristic

Nonlinear elasticity of transmission is indispensable in any passively variable stiffness mechanism. However, it remains obscure how to decide a desired nonlinear force-displacement function. On the other hand biological muscular actions are associated with stiffness/impedance variation in a wide range as demanded by everyday tasks. This paper addresses the issue of designing a nonlinear elastic transmission, where the elastic behaviour is obtained from the passive properties of biological muscle, which happens to be an exponential one, leading to existence of linearity between stiffness and force. In general, with passive damping, the transmission behaves as a mechanical impedance element, to be used in variable impedance actuation. Knowledge of the varying impedance is required to operate the transmission reliably. An off-line calibrated model can only be approximate and erroneous with noisy sensors and changing characteristics of the passive elements with time and environmental condition. This article implements an Extended Kalman Filter algorithm for on-line estimation of stiffness and impedance of such a damped series-elastic transmission. The underlined principle in stiffness-force affine relation is exploited favourably in stiffness estimation with reduced complexity. The effectiveness of the proposed estimator is examined through experiments on the mechanical transmission designed using the biological principle.

Estimation of Mechanical Impedance of a Flexible Transmission using Partial Knowledge of Elastic Characteristic and its Validation

Use of flexible joints in robotic system is the recent trend in applications involving physical human robot interaction. A compliant transmission introduces the flexibility for intrinsically safe robots, whereas the ability to vary Impedance recovers some of the lost performance due to presence of compliance. Stiffness/impedance variability needs presence of nonlinearity in the passive elastic and/or damping characteristic. In controlling robot joint impedance knowledge of stiffness/impedance of transmission becomes necessary. Obtaining a predetermined model of the transmission always introduces inaccuracies and uncertainties with varying characteristics of the transmission with time and ambiance. It proves almost indispensable to estimate the joint stiffness/ impedance during operation for reliable control of variable impedance. It also proves to be a difficult task to estimate impedance/stiffness online on the basis of sensory information of differential motion and differential force. In this article, in order to estimate stiffness of the transmission, a favourable characteristic of the transmission has been exploited. The flexible transmission is designed with a first principle obtained from property of biological muscle so that it maintains an affine relationship between the stiffness and the force being transmitted. This article implements an Extended Kalman Filter algorithm for on-the-fly estimation of stiffness (along with impedance) exploiting the linearity property for applicability of EKF and to reduce complexity of the procedure. The effectiveness of the proposed estimator is examined through experiments on the mechanical transmission designed from the above biological principle. The results are further validated by comparing with the results of estimation using full parameter identification of specified model of the transmission.

An investigation on the performance of an oscillating flat plate fin with compliant joint for underwater robotic actuation

Fishes are very good swimmers possessing impeccable maneuverability, efficiency, and stealth. Understanding the fish propulsion and mimicking the same is important in obtaining improved performance by non-conventional types of underwater robot/vehicle actuators. The role of the caudal fin in fish locomotion is predominant at higher swimming speeds producing most of the thrust force. Generally the fin motions are oscillatory in nature. In oscillatory trajectories, where reversal of motion is required, a normal actuator has to spend energy to accelerate as well as to decelerate(braking). During braking phase, a normal actuator, without any energy storage mechanism, dissipates energy. Ubiquitous presence of compliance in biological actuation system can store some energy which otherwise get dissipated. Fishes are evolved to tune their compliant joint stiffness according to the swimming conditions. The elastic joint(contributed by compliant muscle) can store energy in part of a cycle during fin oscillation and interaction with surrounding fluid in the form of potential energy and can release in next part of the cycle. This article investigates the role of compliance in the fin joint on propulsion performance through simulations. The analysis considers a rigid body model of trapezoidal flat fin with elastic joint and presents hydrodynamic force modeling for interacting fluid in Newton-Euler rigid body framework using blade element technique.

Caudal fin load characteristics with different motion patterns toward developing biorobotic fish-fin actuator

Traditionally underwater vehicles use thrusters as propulsion devices and achieve high speed. These thrusters come with their own limitations such as turbulence, cavitations etc. resulting into low efficiency and noise; the vehicles severely suffer from lack of efficiency in low speed operations. Maneuverability of vehicles using thrusters or jet propulsion devices is inherently limited. On the other hand, nature provides fins to fishes and aquatic animals for underwater locomotion with proven greater maneuverability, agility and efficiency in low speed motion, achieving a highly desirable quality of stealth. To adapt the biological mechanisms of thrust production to man-made underwater robotic vehicles, understanding of biomechanics and load characteristics of the natural fins is very important. In this paper, we consider the caudal fin of a fish, being the main propulsive actuator. This article aims to understand the load characteristics of different motion patterns of the fin in water through fluid-structure interaction (FSI) simulations and does not intend to access the performance of the fin propulsion as a whole. Numerical simulations have been carried out for determining the load characteristics of different motion patterns of the chosen caudal fin and the results are presented. The simulations are based on simple kinematic fin model and do not describe any working prototype. The simulations will eventually lead to the design and development of reduced order biorobotic replica of a caudal fin.

Biologically inspired elastic transmission for stiffness variability in actuation: Design and implementation

Muscular actions in the biological world are associated with stiffness/impedance variation in a wide range depending upon the need of the task. Again, in artificial world variable-stiffness-actuation finds applications in areas like legged machines, artificial prostheses, vibration control, automotive suspension, and compliant robots etc. Nonlinear elasticity of transmission is indispensable in any passively variable stiffness mechanisms. Many designs exist in the literature; however, majority of the designs attain nonlinearity for the sake of nonlinearity only; in most cases neither is there a preferred choice of the nonlinear force-displacement function, nor any design guideline exists. In this report a design is presented which is inspired by properties of muscles. A principle is derived from passive properties of muscle fibers and an elastic function is obtained from that. The elastic transmission is designed with an objective and a functional specification for some desired stiffness behaviour. Next, a generic method for realizing any continuous monotonic function is illustrated. Finally, as an exemplar implementation, an agonistic-antagonistic simple actuation arrangement similar to musculoskeletal system is described. Initial result of simultaneous control of motion and stiffness/internal-force on this one degree-of-freedom variable-stiffness-actuator is reported.

An Approach to Trajectory Planning for Underwater Redundant Manipulator Considering Hydrodynamic Effects

This article considers motion planning of a redundant serial link manipulator in fully submerged underwater scenario in the presence of obstacles, modelled as point objects. The proposed trajectory planning is based on minimizing the energy required in overcoming the hydrodynamic effects, and in the same time avoiding both obstacles and singularities. The presence of redundancy in joint space enables to choose optimal sequence of configurations and associated motion rates. The proposed approach is applied for motion planning of a three degrees-of-freedom planar manipulator avoiding a point obstacle and solved.

Effect of Whole-Body Flexibility of Caudal Fin on Propulsion Performance

Naturally evolved fish fins display superior qualities over conventional man-made thrusters by offering better maneuverability, less or no noise, and better efficiency. Caudal fin of a fish contributes most of the thrust force in fish swimming through body and fin undulations. Fish fins naturally happen to be flexible. The present work investigates the effect of whole-body flexibility of caudal fin on thrust production. A flexible trapezoidal fin is modeled as series of rigid segments connected with torsion springs and the governing equations of motion are obtained through multi-body dynamics approach. The hydrodynamic force acting on the fin segments is calculated as summation of drag and added mass force components. Simulations are carried out with different stiffness profiles for different motion parameters. The results show that flexible fins perform better than the rigid fin and different motion parameters require different stiffness profiles for higher thrust production and better efficiency.

Dynamic Analysis of Underwater Vehicle-Manipulator Systems

Dynamic model of an underwater robot is nonlinear in hydrodynamic parameters such as added mass, damping, etc. The hydrodynamic coefficients vary with time and configuration of the robot. This paper presents a modeling technique for the Underwater Vehicle-Manipulator System (UVMS) using the DeNOC matrices. Furthermore, as a starting point, some simple hydrodynamic experiments were performed which are used to validate the hydrodynamic simulation in MATLAB environment. For these simulations, the hydrodynamic coefficients were considered to be constant throughout the simulation of the manipulators. Two experiments were performed. In the first experiment, free fall of one-link arm was considered, and in the second, free fall of a two-link manipulator was considered. The simulation results obtained were found in good agreement with the experimental results, even with the constant hydrodynamic coefficients, because of the simple structure of the experiments.

Numerical analysis of Goldschmied geometry with boundary-layer suction

An effort is made to implement the phenomenon called the Aerodynamic Pressure Thrust (APT) for the purpose of effective propulsion of underwater vehicle. The two-dimensional Goldschmied body with boundary-layer ingestion near the stern section is considered for this purpose. This particular shape, which up to this point is being considered mainly for aerodynamic propulsion, can be preferred for autonomous underwater vehicles over conventional streamlined bodies for their large volume-to-length ratio. The wind-tunnel experiments of 1960s by Fabio R. Goldschmied paved a way for development of energy efficient propulsion through proper interaction of aerodynamic design and engine power. Decades later, this eventually led to the development of several futuristic crafts which exploit the Pressure Thrust technique. Similar idea is attempted here to obtain improved pressure recovery behind the aft of a blunt underwater vehicle to generate additional thrust. In the present study, a simplified version of the Goldschmied geometry is considered with a single slot for suction between the fore-body and the stern. The computations are carried out utilizing commercial CFD solver Ansys Fluent. The axi-symmetric shape of the Goldschmied body is employed to generate a fully-structured mesh throughout the entire domain. The simulations are carried out for a range of Reynolds number and the suction pressure. The distribution of pressure at different radial locations is examined and plotted, similar to the original work by Goldschmied, to illustrate the alternate zones of drag and thrust produced along the radius. A sizeable portion of the thrust region in the plot is required to overcome the drag force and to achieve self-propulsion solely by means of boundary layer suction. The results of the computational study indicate a trend in that direction.