Octopus arms, as well as elephant trunks, squid tentacles, and vertebrate tongues are termed muscular-hydrostats. In such structures, the volume of the organ remains constant during their motions, enabling diverse, complex, and highly controlled movements without the support of a skeleton. Such flexible structures show major advantages over articulated arms that have a rigid skeleton and joints. These advantages have been attracting roboticists aiming to apply these material properties to soft robot controls. In this paper, we show that the muscular-hydrostat system itself has the computational capacity to achieve a complex nonlinear computation. By using a 3D dynamic simulator of the system inspired by the octopus, we actually demonstrate that the system is capable of emulating complex nonlinear dynamical systems by exploiting its elastic body dynamics as a computational resource. In addition, we systematically analyze its computational power in terms of memory capacity, and show that the system has an intrinsic and characteristic short term memory profile. Finally, the implications for soft robot control and future application scenarios are discussed.

This paper presents an Octopus inspired walking robot with pneumatic muscle actuator (PMA) driven continuum arms. Each arm is made up of 4 longitudinally arranged PMAs, consistent with octopus arm anatomy. We first present the design and construction of a single continuum arm followed by its modeling and experimental validation. The design of the walking robot is then presented followed by details of extended dynamic model describing the full walking robot with four arms. Basic control architecture is introduced for the robot to achieve walking motion and experimental results analyzed. Initial results show good agreement between the experimental results and simulation results.

This paper presents the results of a multidisciplinary project where biologists, mechanical engineers and electronic engineers worked together to develop bio-inspired soft continuum arms, whose design captures and takes advantage of key features of the octopus anatomy and control. The cross-integration of such diverse expertise was channelled towards the design of soft continuum arms whose characteristics were inspired by nature, but with a focus on readily available engineering technologies and their effective integration from a system viewpoint. On one side the mechanical structure and the control was designed looking at the animal, in particular at the coupling between its anatomy and control system that allows the animal to survive in its ecosystem. On the other side engineering issues and constraints were carefully accounted for, namely material softness, intrinsic safety, energy efficiency, cost effectiveness and manufacturing aspects. The design evolution is presented through three different generations of prototypes where both bio-inspiration and engineering requirements are appropriately blended.

This paper presents the application of a hydraulic DC-DC converter, namely a step down Buck Converter to the actuation of a robot leg that is part of the quadruped robot HyQ. The use of a Hydraulic Buck Converter (HBC) offers significant advantages in terms of improved efficiency of hydraulic actuation systems analogously to an electric switching DC-DC converter as opposed to a rheostatic-type system. In this paper, a HBC consisting of two digital valves and two check valves is introduced to improve the efficiency performance of a singl leg of a hydraulic quadruped robot (HyQ). This type of hydraulic buck converter is able to support the locomotion in two directions. The HBC operates at a switching frequency of 100 Hz in pulse-width-modulation. The better energy performance compared to proportional control is achieved by the use of fast check valves. The performance of the system with a 3-way-4-position proportional valve is compared with the HBC drive. A test rig is set up to investigate the performance of HBC with two different controllers and a Hydraulic Proportional Drive (HPD) system, based on proportional valves which control flow, by throttling it, in a dissipative manner. The performance of position tracking and energy consumption is evaluated. The experimental results indicate that HBC systems can achieve similar position tracking with relatively less consumed energy.

Conventional rigid body robots typically use few degrees of freedom (DOF). This results in a manipulator that lacks flexibility and maneuverability when compared to continuum robots that utilize a much higher number of DOF. However, due to their continuous nature, the difficulty of measuring and controlling a large number of actuated DOF, and their high degree of nonlinearity, the development of control algorithms for continuum robot manipulators is an ongoing challenge. This paper presents an algorithm inspired by biological solutions from live octopus that utilizes division of functionality to achieve simple and robust control of continuum arm based systems. Simulated results for single and multiple dynamic continuum arms show the controller is capable of producing motions similar to that of octopus. The resulting controller is also computationally efficient enough for real-time implementation. In future this work will be implemented on a prototype robot with multiple continuum arms.

This paper presents an improved mode shape function-based 3D dynamic model for pneumatic muscle actuated continuum arms, and validates the model and simulation results through experimental testing. The model also facilitates the direct control of pneumatic muscle actuated continuum arms through the use of input pressure. This is achieved without additional intermediary transformations and does not have singularity problems present in previous models. The proposed arm model uses a new pneumatic muscle actuator (PMA) dynamic model with hysteresis that is capable of modelling both extending and contracting PMAs. The proposed hysteric model is simple, easily adaptable, and validated experimentally. The PMA model can be applied to dynamically model any PMA based system as well as PMA actuated continuum arms utilizing different actuator configurations.

This paper examines the design and control of a robotic arm inspired by the anatomy and neurophysiology of Octopus vulgaris in light of embodiment theory. Embodiment in an animal is defined as the dynamic coupling between sensorymotor control, anatomy, materials, and the environment that allows for the animal to achieve effective behaviour. Octopuses in particular are highly embodied and dexterous animals: their arms are fully flexible, can bend in any direction, grasp objects and modulate stiffness along their length. In this paper the biomechanics and neurophysiology of octopus have been analysed to extract relevant information for use in the design and control of an embodied soft robotic arm. The embodied design requirements are firstly defined, and how the biology of the octopus meets these requirements presented. Next, a prototype continuum arm and control architecture based on octopus biology, and meeting the design criteria, are presented. Finally, experimental results are presented to show how the developed prototype arm is able to reproduce motions performed by live octopus for contraction, elongation, bending, and grasping.

Continuum structures with a very high or infinite number of degrees of freedom (DOF) are very interesting structures in nature. Mimicking this kind of structures artificially is challenging due to the high number of required DOF. This paper presents a kinematic and dynamic model for an underwater robotic manipulator inspired by Octopus vulgaris. Then, a prototype arm inspired by live octopus is presented and the model validated experimentally. Initial comparisons of simulated and experimental results show good agreement.

Soft robots are difficult to control because of their compliant and elastic body dynamics compared with robots made of rigid bodies. In this paper, we present a control scheme inspired by the octopus called timing-based control for soft robotic arms. This control scheme is motivated to positively exploit the natural dynamics of the soft body. We demonstrate a scheme for controlling an object-reaching task by using an echo state network on a 3D physical soft robotic arm simulator and show that this network can successfully perform the task. Detailed analyses and evaluations of the generalization capacity of the network and the performances to the reaching task are presented.

This paper presents a control algorithm to achieve crawling locomotion for a multi-arm robotic system inspired by live octopuses. First the paper introduces a dynamic model of a continuum arm. The model accounts for the key features relevant to crawling locomotion, namely longitudinal muscles and suckers that provide force interaction with the surrounding environment. This single arm model is then validated against live octopus data and expanded to an 8-arm system. Appropriate coordination algorithms of the eight arms result in crawling locomotion. The results of this work can be used to study the motor control schemes for both multiple continuum arm robots and live octopuses.

This paper presents a new three dimensional kinematic and dynamic model for variable length continuum arm robotic structures using a novel shape function-based approach. The model incorporates geometrically constrained structure of the arm to derive its deformation shape function. It is able to simulate spatial bending, pure elongation, and incorporates a new stiffness control feature. The model is validated through numerical simulations, based on a prototype continuum arm, that yields physically accurate results.

Continuum robotic arms are based on non-rigid components that result in a nearly infinite number of degrees of freedom (DOF). Due to this reason it can be very complex to establish mathematical models for continuum robotic arms. This paper presents a 3D dynamic model of an arm based on octopus anatomy that utilizes 4 longitudinal and 4 radial muscles. The arm is composed of a multi-segment structure having distributed stiffness and damping to represent the muscles. The simulations are applied to a multi-segment arm, and results mimic several typical octopus arm motions.

This paper presents a new three dimensional (3D) kinematic model based on mode shape functions (MSF) for multisection continuum arms. It solves the singularity problems associated with previous models and introduces a novel approach for intuitively deriving exact, singularity-free MSFs, thus avoiding mode switching schemes and simplifying error models. The model is able to simulate spatial bending, pure elongation/contraction, and introduces inverse orientation kinematics for the first time to multisection continuum arms. Also, it carefully accounts for physical constraints in the joint space to provide enhanced insight into practical mechanics, and produces correct results for both forward and inverse kinematics. The model is validated through simulations, based on a prototype continuum robotic arm. Proposed approach is applicable to a broad spectrum of continuum robotic arm designs.

The octopus arm is a unique tool that combines strength and flexibility. It can shorten, elongate and bend at any point along its length. To model this behavior, a hyper-redundant manipulator composed of multiple segments is proposed. Each segment is a parallel robotic mechanism with redundant actuation. The kinematics and dynamics of this manipulator are analyzed and simulated utilizing a modular computational modeling method. Simulation results for some primitive movements are presented, and the effect of hydrodynamic forces is included.

This paper is focussed on the modelling and control of a hydraulically-driven biologically-inspired robotic leg. The study is part of a larger project aiming at the development of an autonomous quadruped robot (hyQ) for outdoor operations. The leg has two hydraulically-actuated degrees of freedom (DOF), the hip and knee joints. The actuation system is composed of proportional valves and asymmetric cylinders. After a brief description of the prototype leg, the paper shows the development of a comprehensive model of the leg where critical parameters have been experimentally identified. Subsequently the leg control design is presented. The core of this work is the experimental assessment of the pros and cons of single-input single-output (SISO) vs. multiple-input multiple-output (MIMO) and linear vs. nonlinear control algorithms in this application (the leg is a coupled multivariable system driven by nonlinear actuators). The control schemes developed are a conventional PID (linear SISO), a Linear Quadratic Regulator (LQR) controller (linear MIMO) and a Feedback Linearisation (FL) controller (nonlinear MIMO). LQR performs well at low frequency but its behaviour worsens at higher frequencies. FL produces the fastest response in simulation, but when implemented is sensitive to parameters uncertainty and needs to be properly modified to achieve equally good performance also in the practical implementation.

This paper deals with a comparative study on using water and air as actuation means for the control of a fluidic muscle (designed for air) and assesses the performance, particularly from a dynamic and energetic point of view. A medium with higher bulk modulus such as oil/water is believed to increase pressure and force bandwidths and reduce sensitivity to load variations, as is the case with conventional hydraulic stiff actuation systems. However in this application the inherent flexibility of the muscle plays a major role. Water has been chosen because of its non-flammability, environmental friendliness and the low solubility of air in it. The operating pressure range of the pneumatic muscle is 0-6 bar (typical range of a pneumatic system) that is well below typical operating pressures of hydraulic systems (typically over 100 bar). At such low pressures the dynamic behaviour of water is less predictable because of the higher likelihood of entrapped air in the water which physically occurs when operating at low pressures. This can majorly affect water bulk modulus and hence its dynamic performance. Therefore, the behaviour of the system in this unconventional pressure range for a liquid must be more thoroughly investigated. Theoretical and experimental analyses on a dedicated test rig have been carried out to assess these assumptions.

This paper is concerned with the application of switching technology to hydraulic actuation. Over the last 50 years with advances in power electronics, faster and faster static switches have been developed and applied to the control of motors. Hydraulic technology evolved in the opposite direction: switching control was not considered, and more and more accurate proportional flow/pressure control devices (servovalves etc) were developed. However despite the sophistication of such valves, from an energetic viewpoint proportional control is dissipative and inefficient. Indeed, by analogy it can be seen as the equivalent of resistive (rheostatic) motor control. In robotic applications where high power density, ruggedness and reliability are key requirements hydraulic actuation can be a sensible choice. However, the low efficiency of proportional control can be a limitation and it is necessary to go beyond the paradigm of proportional flow/pressure control. One response to this challenge is to revisit traditional on-off hydraulic technology and develop "power hydraulic" devices that behave in analogous manner to their power electronic counterparts. "Power hydraulics" is a challenging and little explored technology due to the markedly non-linear behaviour of hydraulic systems and the need of components with dynamic specifications that are not readily available off-the-shelf. After an analysis of the real on-off characteristics of a valve, a prototype hydraulic switching converter, inspired by the electric DC-DC Buck converter, is presented and its performance in pressure control mode, relative to a classical proportional valve-controlled system, are assessed. An energy saving of 75% is achieved. Merits and limitations of the current design are identified.

This paper focuses on the design of a robotic arm inspired to the anatomy and morphology of an octopus arm. The octopus is a boneless animal and its amazing dexterity is due to its muscular structure where longitudinal (axial), transverse (radial) and oblique muscles seamlessly interact while preserving hydrostaticity i.e. volume conservation (“muscular hydrostat”). Mimicking some features of the octopus is instrumental to design a dexterous and compliant system. After analysing the relevant anatomical and morphological characteristics of the octopus arm, the key biomechanical features of interest to the design of a robotic arm have been identified. A design methodology has been developed based on the analysis of the muscular hydrostat properties. A prototype arm has been built using bespoke contracting pneumatic muscles and expanding elements. In the current stage of development the system has 15 actuated degrees of motion (DOM) and 8 degrees of freedom (DOF), all independently controllable through valves and a dedicated electronics and software interface. Pros and cons of the current design as well as practical prototyping trade-offs are thoroughly described.

This paper focuses on the design and experimental evaluation of a hydraulically actuated robot leg. The evaluation of the leg prototype is an important milestone in the development of HyQ, a Hydraulically actuated Quadruped robot. The prototype features two rotary joints actuated by hydraulic cylinders and has a mass of 4.5kg. We performed several experiments with the leg prototype attached to a vertical slider to tests the robustness of the mechanical design and the hydraulic actuation system. Besides the experimental evaluation of the hydraulic components, we also extensively studied the sensor data of the leg during periodic hopping. The results show that hydraulic actuation is suitable for legged robots because of its high power-to-weight ratio, fast response and ability to cope with high impact force peaks. Furthermore, we compare the cylinder force data obtained by the load cell with the calculated value based on the cylinder pressures to analyze if it is possible to eliminate this sensory system redundancy in the future. Through these studies, weaknesses of the design were identified and suggestions on how to improve them are presented.

Hydraulic actuators are characterized by fast dynamics, high power density, high stiffness, large output force/torque, and in recent years are becoming increasingly attractive in the field of robotics. This paper presents the study of a 3-way proportional valve controlled, spring assisted electro-hydraulic rotary actuator, which consists of a 3-way proportional valve, a linear cylinder and a reciprocal spring. The operating principle is presented and a mathematical model is developed. Comparison analysis is made between the new actuator and a traditional one with an application to a hydraulically actuated legged robot.

The performance of highly dynamic robotic machines is directly associated with both the actuation means and the specific mechanical properties/configuration of the system. Hydraulic actuation demonstrates significant competitive advantages when minimum weight and volume, large forces and wide range of speeds are required and this makes it very suitable for systems such as legged robots. The geometry and design of leg mechanisms have great effect on the actuation system performance such as the required flow, which directly determines the size/weight and power density, in turn affecting the performance of the robot. This paper describes the mechanism and operation principle of two 2-DOF legs considered for HyQ, a hydraulically actuated quadruped robot. Numerical studies have been done to investigate the required flow, the pressure in the actuator chambers and the efficiency of the two leg mechanisms. The results show that the second leg design reduces the required flow significantly with less pressure-jump in the actuator and higher efficiency.