Gregory S. Chirikjian

Modular Self-Reconfigurable Robot Systems [Grand Challenges of Robotics]

The field of modular self-reconfigurable robotic systems addresses the design, fabrication, motion planning, and control of autonomous kinematic machines with variable morphology. Modular self-reconfigurable systems have the promise of making significant technological advances to the field of robotics in general. Their promise of high versatility, high value, and high robustness may lead to a radical change in automation. Currently, a number of researchers have been addressing many of the challenges. While some progress has been made, it is clear that many challenges still exist. By illustrating several of the outstanding issues as grand challenges that have been collaboratively written by a large number of researchers in this field, this article has shown several of the key directions for the future of this growing field

Nonholonomic Modeling of Needle Steering

As a flexible needle with a bevel tip is pushed through soft tissue, the asymmetry of the tip causes the needle to bend. We propose that, by using nonholonomic kinematics, control, and path planning, an appropriately designed needle can be steered through tissue to reach a specified 3D target. Such steering capability could enhance targeting accuracy and may improve outcomes for percutaneous therapies, facilitate research on therapy effectiveness, and eventually enable new minimally invasive techniques. In this paper, we consider a first step toward active needle steering: design and experimental validation of a nonholonomic model for steering flexible needles with bevel tips. The model generalizes the standard three degree-of-freedom (DOF) nonholonomic unicycle and bicycle models to 6 DOF using Lie group theory. Model parameters are fit using experimental data, acquired via a robotic device designed for the specific purpose of inserting and steering a flexible needle. The experiments quantitatively validate the bevel-tip needle steering model, enabling future research in flexible needle path planning, control, and simulation.

Useful metrics for modular robot motion planning

In this paper the problem of dynamic self-reconfiguration of a class of modular robotic systems referred to as metamorphic systems is examined. A metamorphic robotic system is a collection of mechatronic modules, each of which has the ability to connect, disconnect, and climb over adjacent modules. We examine the near-optimal reconfiguration of a metamorphic robot from an arbitrary initial configuration to a desired final configuration. Concepts of distance between metamorphic robot configurations are defined, and shown to satisfy the formal properties of a metric. These metrics, called configuration metrics, are then applied to the automatic self-reconfiguration of metamorphic systems in the case when one module is allowed to move at a time. There is no simple method for computing the optimal sequence of moves required to reconfigure. As a result, heuristics which can give a near optimal solution must be used. We use the technique of simulated annealing to drive the reconfiguration process with configuration metrics as cost functions. The relative performance of simulated annealing with different cost functions is compared and the usefulness of the metrics developed in this paper is demonstrated.

Kinematic design and commutation of a spherical stepper motor

This paper addresses the design and commutation of a novel kind of spherical stepper motor in which the poles of the stator are electromagnets and the poles of the rotor (rotating ball) are permanent magnets. Due to the fact that points on a sphere can only be arranged with equal spacing in a limited number of cases (corresponding to the Platonic solids), design of spherical stepper motors with fine rotational increments is fundamentally geometrical in nature. We address this problem and the related problem of how rotor and stator poles should be arranged in order to interact to cause motion. The resulting design has a much wider range of unhindered motion than other spherical stepper motor designs in the literature. We also address the problem of commutation, i.e., we determine the sequence of stator polarities in time that approximate a desired spherical motion.

Kinematics of a metamorphic robotic system

A metamorphic robotic system is a collection of mechatronic modules, each of which has the ability to connect, disconnect, and climb over adjacent modules. A change in the macroscopic morphology results from the locomotion of each module over its neighbors. That is, a metamorphic system can dynamically self-reconfigure. Metamorphic systems can therefore be viewed as a large swarm of physically connected robotic modules which collectively act as a single entity. What separates metamorphic systems from other reconfigurable robots is that they possess all of the following properties: (1) self-reconfigurability without outside help; (2) a large number of homogeneous modules; and (3) physical constraints ensure contact between modules. In this paper, the kinematic constraints governing a particular metamorphic robot are addressed.<<ETX>>

Efficient Generation of Feasible Pathways for Protein Conformational Transitions

We develop a computationally efficient method to simulate the transition of a protein between two conformations. Our method is based on a coarse-grained elastic network model in which distances between spatially proximal amino acids are interpolated between the values specified by the two end conformations. The computational speed of this method depends strongly on the choice of cutoff distance used to define interactions as measured by the density of entries of the constant linking/contact matrix. To circumvent this problem we introduce the concept of using a cutoff based on a maximum number of nearest neighbors. This generates linking matrices that are both sparse and uniform, hence allowing for efficient computations that are independent of the arbitrariness of cutoff distance choices. Simulation results demonstrate that the method developed here reliably generates feasible intermediate conformations, because our method observes steric constraints and produces monotonic changes in virtual bond and torsion angles. Applications are readily made to large proteins, and we demonstrate our method on lactate dehydrogenase, citrate synthase, and lactoferrin. We also illustrate how this framework can be used to complement experimental techniques that partially observe protein motions.

Evaluating efficiency of self‐reconfiguration in a class of modular robots

In this article we examine the problem of dynamic self-reconfiguration of a class of modular robotic systems referred to as metamorphic systems. A metamorphic robotic system is a collection of mechatronic modules, each of which has the ability to connect, disconnect, and climb over adjacent modules. A change in the macroscopic morphology results from the locomotion of each module over its neighbors. Metamorphic systems can therefore be viewed as a large swarm of physically connected robotic modules that collectively act as a single entity. What distinguishes metamorphic systems from other reconfigurable robots is that they possess all of the following properties: (1) a large number of homogeneous modules; (2) a geometry such that modules fit within a regular lattice; (3) self-reconfigurability without outside help; (4) physical constraints which ensure contact between modules. In this article, the kinematic constraints governing metamorphic robot self-reconfiguration are addressed, and lower and upper bounds are established for the minimal number of moves needed to change such systems from any initial to any final specified configuration. These bounds are functions of initial and final configuration geometry and can be computed very quickly, while it appears that solving for the precise number of minimal moves cannot be done in polynomial time. It is then shown how the bounds developed here are useful in evaluating the performance of heuristic motion planning/reconfiguration algorithms for metamorphic systems.

An obstacle avoidance algorithm for hyper-redundant manipulators

Novel kinematic algorithms for implementing planar hyperredundant manipulator obstacle avoidance is presented. Unlike artificial potential field methods, the method outlined is strictly geometric. Tunnels are defined in a workspace in which obstacles are presented. Methods of differential geometry are then used to formulate equations which guarantee that sections of the manipulator are confined to the tunnels and therefore avoid the obstacles. A general formulation is given with examples to illustrate this approach.<<ETX>>

Equilibrium Conformations of Concentric-tube Continuum Robots

Robots consisting of several concentric, preshaped, elastic tubes can work dexterously in narrow, constrained, and/or winding spaces, as are commonly found in minimally invasive surgery. Previous models of these “active cannulas” assume piecewise constant precurvature of component tubes and neglect torsion in curved sections of the device. In this paper we develop a new coordinate-free energy formulation that accounts for general preshaping of an arbitrary number of component tubes, and which explicitly includes both bending and torsion throughout the device. We show that previously reported models are special cases of our formulation, and then explore in detail the implications of torsional flexibility for the special case of two tubes. Experiments demonstrate that this framework is more descriptive of physical prototype behavior than previous models1 it reduces model prediction error by 82% over the calibrated bending-only model, and 17% over the calibrated transmissional torsion model in a set of experiments.

Elastic models of conformational transitions in macromolecules.

We develop a computationally efficient and physically realistic method to simulate the transition of a macromolecule between two conformations. Our method is based on a coarse-grained elastic network model in which contact interactions between spatially proximal parts of the macromolecule are modelled with Gaussian/harmonic potentials. To delimit the interactions in such models, we introduce a cutoff to the permitted number of nearest neighbors. This generates stiffness (Hessian) matrices that are both sparse and quite uniform, hence, allowing for efficient computations. Several toy models are tested using our method to mimic simple classes of macromolecular motions such as stretching, hinge bending, shear, compression, ligand binding and nucleic acid structural transitions. Simulation results demonstrate that the method developed here reliably generates sequences of feasible intermediate conformations of macromolecules, since our method observes steric constraints and produces monotonic changes to virtual bond angles and torsion angles. A final application is made to the opening process of the protein lactoferrin.