Prasun Choudhury

A general strategy based on the Newton–Euler approach for the dynamic formulation of parallel manipulators

Abstract This paper presents a general strategy based on the Newton–Euler approach to the dynamic formulation of parallel manipulators. It is shown that, for parallel manipulators, through appropriate selection and ordering of the equilibrium equations, the Newton–Euler method can be used with advantage not only for inverse dynamics computations, but also for the derivation of dynamic equations in closed form. The proposed strategy has been illustrated through its application to several planar and spatial manipulators. Cases of parallel manipulators requiring particular considerations are also discussed with recommendations of special measures to be taken in different classified cases.

Bixels: picture samples with sharp embedded boundaries

Pixels store a digital image as a grid of point samples that can reconstruct a limited-bandwidth continuous 2-D source image. Although convenient for anti-aliased display, these bandwidth limits irreversibly discard important visual boundary information that is difficult or impossible to accurately recover from pixels alone. We propose bixels instead: they also store a digital image as a grid of point samples, but each sample keeps 8 extra bits to set embedded geometric boundaries that are infinitely sharp, more accurately placed, and directly machine-readable. Bixels represent images as piecewise-continuous, with discontinuous intensities and gradients at boundaries that form planar graphs. They reversibly combine vector and raster image features, decouple boundary sharpness from the number of samples used to store them, and do not mix unrelated but adjacent image contents, e.g blue sky and green leaf. Bixels are meant to be compatible with pixels. A bixel is a image sample point with an 8 bit code for local boundaries. We describe a boundary-switched bilinear filter kernel for bixel reconstruction and pre-filtering to find bixel samples, a bixels-to-pixels conversion method for display, and an iterative method to combine pixels and given boundaries to make bixels. We discuss applications in texture synthesis, matting and compositing. We demonstrate sharpness-preserving enlargement, warping and bixels-to-pixels conversion with example images.

Singularity and controllability analysis of parallel manipulators and closed-loop mechanisms

This paper presents a study of kinematic and force singularities in parallel manipulators and closed-loop mechanisms and their relationship to accessibility and controllability of such manipulators and closed-loop mechanisms, Parallel manipulators and closed-loop mechanisms are classified according to their degrees of freedom, number of output Cartesian variables used to describe their motion and the number of actuated joint inputs. The singularities in the workspace are obtained by considering the force transformation matrix which maps the forces and torques in joint space to output forces and torques ill Cartesian space. The regions in the workspace which violate the small time local controllability (STLC) and small time local accessibility (STLA) condition are obtained by deriving the equations of motion in terms of Cartesian variables and by using techniques from Lie algebra.We show that for fully actuated manipulators when the number ofactuated joint inputs is equal to the number of output Cartesian variables, and the force transformation matrix loses rank, the parallel manipulator does not meet the STLC requirement. For the case where the number of joint inputs is less than the number of output Cartesian variables, if the constraint forces and torques (represented by the Lagrange multipliers) become infinite, the force transformation matrix loses rank. Finally, we show that the singular and non-STLC regions in the workspace of a parallel manipulator and closed-loop mechanism can be reduced by adding redundant joint actuators and links. The results are illustrated with the help of numerical examples where we plot the singular and non-STLC/non-STLA regions of parallel manipulators and closed-loop mechanisms belonging to the above mentioned classes

Rolling Manipulation with a Single Control

Underactuated manipulation is the process of controlling several object degrees-of-freedom with fewer robot actuators. Underactuated manipulation allows us to build dexterous robots with only a few actuators. In this paper we explore the possibility of useful dynamic manipulation with only a single actuator. Our case study is a ball rolling in an asymmetrical bowl which can be accelerated along one linear degree-of-freedom. We show that the state of the ball relative to the bowl is controllable by this single controlled acceleration. In particular, it is possible to control the equilibrium orientation of the ball on the three-dimensional manifold SO(3) using this single input. We have built an experimental demonstration of this system and we have constructed a motion planner to find a sequence of motions of the bowl to accomplish a desired reorientation.

Trajectory Planning for Kinematically Controllable Underactuated Mechanical Systems

We develop trajectory planners for a class of second-order underactuated mechanical systems called kinematically controllable systems. For kinematically controllable systems, the problem of planning fast collision-free trajectories can be decoupled into the computationally simpler problems of path planning for a kinematic system followed by time-optimal time scaling. This paper describes efficient path planners using randomized algorithms and dynamic programming to solve the path planning problem for the kinematic system. The resulting kinematic paths are time scaled to produce fast trajectories.

Inverse kinematics-based motion planning for underactuated systems

We study the problem of generating motion plans for kinematically controllable underactuated systems in environments cluttered with obstacles. We develop a computationally efficient motion planning algorithm that finds fast trajectories by exploiting closed-form inverse kinematics of the robot. The completeness property of the motion planning algorithm can be proven using appropriate metrics defined in the configuration space of the kinematically controllable systems. The snakeboard is used as an example of a kinematically controllable underactuated system to test the motion planning algorithm, and motion plans have been implemented on an experimental snakeboard.

Controllability of single input rolling manipulation

This paper investigates the controllability of underactuated rolling systems consisting of a smooth object rolling on a moving smooth surface. Our system consists of a spherical ball which rolls on the inside of an ellipsoidal bowl. The bowl has a single translational degree of freedom not aligned with any of its principal axes. The single control input is the bowls acceleration in this direction. The object and contact motions are governed by a nonlinear system of equations derived from the kinematics and dynamics of rolling. Using existing results on small time local accessibility and weakly positive Poisson stable vector fields, and assuming that the ball stays in the bowl, we show that the ball is globally controllable on its five-dimensional space of configurations relative to the bowl. Our next step is on motion planning algorithms with our experimental setup to control the equilibrium configuration of the ball.

Rolling manipulation with a single control

Underactuated manipulation is the process of controlling several object degrees-of-freedom with fewer robot actuators. Underactuated manipulation allows us to build dextrous robots with only a few actuators. In this paper we explore the possibility of useful dynamic manipulation with only a single actuator. Our case study is a ball rolling in an asymmetrical bowl which can be accelerated along one linear degree-of-freedom. For a real physical system we show that it is possible to control the equilibrium orientation of the ball on the three-dimensional manifold SO(3) using the single input. We built an experimental demonstration of this system and constructed a motion planner to find a sequence of motions of the bowl to accomplish a desired reorientation.