In this paper, we propose a new tractable ordinary differential equation formulation for dynamic simulation of fabric- reinforced inflatable soft robots. The method performs a lumped-parameter discretization of the continuum robot into discrete discs (inertia), spring elements, and threads (representing the inextensible fabric reinforcement). Using the repetition in the structure of the Lagrangian formulation of the dynamic equations of motion, a method is developed that outputs machine- readable analytical expressions for the equations of motion. The method does not require symbolic computation of derivatives. The recursive nature allows us to scale the model to an arbitrary number$N$discs, and can represent buckling, twisting, and pleating that is commonly seen in very soft robots. The expressions generated were validated against manually-derived equations of motion for the two-disc case using both Lagrangian and Newton-Euler means. A simulation environment which parses and evaluates the analytical expressions generated at run-time was used to numerically integrate and predict the response of a four-disc example robot. Trajectories observed varied smoothly and plausibly predicted the behavior envisioned in robots like these.

Soft robots can operate effectively inside confined spaces because their soft bodies can adapt to accommodate the geometry around them. When they interact with the environment, the presence of contact forces can dramatically change the dynamics of the robots. If a soft robot is in contact and the contact force is not known, the control action is still targeted for a free robot. Hence the robot may perform improper actions. Because a soft robot is deformable, it is quite challenging to determine the contact forces and the system states from sensor measurements. This paper proposes an observer design to estimate the states of a fabric-reinforced inflatable soft robot as well as the external contact forces. The soft robot is represented by the disc-thread model which results in a set of ordinary differential equations (ODEs). A linear parameter-varying (LPV) system including some subsystems is formed to represent the nonlinear robot. The observer is based on the sliding mode approach and includes a set of sub-observers corresponding to the subsystems in the LPV system. The observer is validated through simulations and an experiment. The simulation results show that the observer can estimate the angular positions and their rate of changes as well as assumed contact forces with no error in steady states. The experiment results display good tracking of the robot’s configurations compared to the ground truth data from the motion tracking system.

The human thumb's state contribution to grasping and dexterous manipulation of objects is a function of the kinematic multiplicity of joints and structure of the bones, joints, and ligaments. This paper looks at the design and evaluation of a human-like thumb for use in a robotic hand, where the thumb's state contribution to grasping and dexterous manipulation is a function of a simplified kinematic model based on that of the human thumb, but also on empirical trials of surgical techniques to retain functionality while reducing the number of joints in the thumb. Motion Capture Data of the End Effector is analyzed with the measured excursion of the tendons to determine the relationship between tendon velocities and task-space velocities. After validating the procedure experimentally, a simplified metric is proposed to represent this data, and shows that our prototype is predicted to have a relatively smooth mapping between tendon excursion velocity and end effector velocity.

In this paper we examine a novel method of core-located actuation that we believe can be used to vary gaits in a compass-gait walker, using critical analysis of a ball-in-tray mechanism to apply forces at the robot's "pelvis". The dynamic equations of motion of a tilting ball-tray system with several design parameters are developed and simulated for various tray designs. Results show that changes in tray design do indeed significantly affect the trajectory. When compared to a hardware ball-tray system, the results show good agreement with the simulation. The sagittal plane component of the ball's trajectory is applied to the motion of a corresponding mass at the "pelvis" of a compass-gait walker. Simulations of the compass-gait walker show that this trajectory generates a feasible gait.

Variable walking styles in bipedal robots may be used to communicate information about purpose and/or personality to human viewers- and may also help accommodate features of the environment. This paper presents variable gait in a simulation and results from a hardware prototype for gravity-driven rolling ball mechanism in a previously proposed bipedal design. First, optimal control inputs that produce a range of variable feasible gaits is generated on a simplified under-actuated planar model. Then, a tray-like mechanism that provides a curved path for a ball to roll on is presented. This mechanism is designed to replicate a notion of pelvic shift, described in Bartenieff Fundamentals, with movement of the ball (which is shaped by the tray) creating a shift of weight. Analysis of two gait styles and two tray designs shows comparable ranges of forces in the direction of travel between the simulated planar model and the hardware mechanism. This work is an important first step in generating feasible, stable- and variable- bipedal gaits using this hardware design.

Two leading qualities of skeletal muscle that produce good performance in uncertain environments are damage tolerance and the ability to modulate impedance. For this reason, robotics researchers are greatly interested in discovering the key characteristics of muscles that give them these properties and replicating them in actuators for robotic devices. This paper describes a method to harness the redundancy present in muscle-like actuation systems composed of multiple motor units and shows that they have these same two qualities. By carefully choosing which motor units are recruited, the impedance viewed from the environment can be modulated while maintaining the same overall activation level. The degree to which the impedance can be controlled varies with total activation level and actuator length. Discretizing the actuation effort into multiple parts that work together, inspired by the way muscle fibers work in the human body, produces damage-tolerant behavior. This paper shows that this not only produces reasonably good resolutions without inordinate numbers of units, but gives the control system the ability to set the impedance along with the drive effort to the load.

An approach to construct an elastic transmission mechanism for a compliant underactuated robotic hand from the interconnection of smaller compliant mechanisms is proposed, and a mathematical model for the interaction between multiple actuators and multiple digits is developed. It is proven that any interconnection of compliant objects results in an elastic transmission element that has a positive definite stiffness matrix, which indicates that small perturbations to tendon excursion will yield a stable grasp. The branch and cable circuit connections of two-port modeled digits in a simple grasping mechanism are analyzed mathematically.

Piezoelectric stack actuators have the advantages of zero backlash and no acoustic noise, but their stroke is too small to actuate robotic links directly. Because the force available is often more than the required, the stroke of the piezoelectric stack can be amplified by a compliant mechanism at the expense of force. It is not always clear what the geometry of this compliant mechanism should be. Compliant mechanisms have parallels in biology in that they describe two-way interactions between the actuator and the environment. In this paper, we employ the concept of a two-port network model from circuit theory to describe this two-way interaction and present a method to obtain each element of the two-port model as an analytical function of physical geometric parameters for a wide class of geometries. This method makes use of Castigliano's theorem and Euler-Bernoulli linearly elastic beam theory. To our knowledge, this is the first two-port representation of a compliant mechanism that is based on analytical expressions of geometric parameters. This analytical model agrees well with finite-element method calculations. We also examine a representative case experimentally and achieve accuracies better than 18%.

Using successive stages, or nesting compliant amplification mechanisms, soft actuators with performance suitable for robotic applications can be constructed with piezoelectric ceramic as the active material. This paper presents a mathematical framework that describes the interactions among the various amplification mechanisms in a hierarchical nested structure. A formal treatment of nested amplification mechanisms results in two theorems that describe the stiffness properties of the whole actuator in terms of the properties of each mechanism in the hierarchy. These theorems show that the stiffness properties of the actuator can be computed by considering only the outermost few layers in the nested configuration. By virtue of this hierarchical structure, the actuator also assumes a cellular structure; it functions by summing the effects of on-off inputs coupled by a flexible connective medium. This requires a paradigm shift when selecting control strategies. A multilayer strain amplification mechanism is designed to meet the required range of travel for a biologically inspired camera positioning mechanism, and a switching control method for the actuator's 16 on-off inputs is discussed.