Intelligent Approaches in Locomotion - A Review <s> Trajectories for non-bipeds <s> A new control strategy is used to stabilize numerical simulations of a horse model in the trotting quadrupedal gait. Several well-established experimental findings are predicted by the model, including how stride frequency and stride length change with forward running speed. Mass is distributed throughout the model's legs, trunk, and head in a realistic manner. Leg and trunk flexion is modeled using four flexible legs, a back joint, and a neck joint. In the control model, pitch stabilization is achieved without directly controlling body pitch, but rather by controlling both the aerial time and the foot speed of each stance leg. The legs behave as ideal springs while in contact with the ground, enabling the model to rebound from the ground with each trotting step. Numerical experiments are conducted to test the model's capacity to overcome a change in ground impedance. Model stability is maximized and the metabolic cost of trotting is minimized within a narrow range of leg stiffness where trotting horses o... <s> BIB001 </s> Intelligent Approaches in Locomotion - A Review <s> Trajectories for non-bipeds <s> Abstract This paper presents methods and experiments of a reactive control architecture for a four-legged walking machine. Starting with a description of the existing control architecture we introduce the concepts of reflexes and behaviours as well as their integration into the system. The used reactive network and the development process is described in detail. The paper concludes with a description of various experiments. <s> BIB002 </s> Intelligent Approaches in Locomotion - A Review <s> Trajectories for non-bipeds <s> We present a new stability analysis for hybrid legged locomotion systems based on the “symmetric” factorization of return maps. We apply this analysis to two-degrees-of-freedom (2DoF) and three-degrees-of-freedom (3DoF) models of the spring loaded inverted pendulum (SLIP) with different leg recirculation strategies. Despite the non-integrability of the SLIP dynamics, we obtain a necessary condition for asymptotic stability (and a sufficient condition for instability) at a fixed point, formulated as an exact algebraic expression in the physical parameters. We use this expression to characterize analytically the sensory cost and stabilizing benefit of various feedback schemes previously proposed for the 2DoF SLIP model, posited as a low-dimensional representation of running. We apply the result as well to a 3DoF SLIP model that will be treated at greater length in a companion paper as a descriptive model for the robot RHex. <s> BIB003 </s> Intelligent Approaches in Locomotion - A Review <s> Trajectories for non-bipeds <s> In this paper we compare models and experiments involving Scout II, an untethered four-legged running robot with only one actuator per compliant leg. Scout II achieves dynamically stable running of up to 1.3 m s-1 on flat ground via a bounding gait. Energetics analysis reveals a highly efficient system with a specific resistance of only 1.4. The running controller requires no task-level or body-state feedback, and relies on the passive dynamics of the mechanical system. These results contribute to the increasing evidence that apparently complex dynamically dexterous tasks may be controlled via simple control laws. We discuss general modeling issues for dynamically stable legged robots. Two simulation models are compared with experimental data to test the validity of common simplifying assumptions. The need for including motor saturation and non-rigid torque transmission characteristics in simulation models is demonstrated. Similar issues are likely to be important in other dynamically stable legged robots as well. An extensive suite of experimental results documents the robot's performance and the validity of the proposed models. <s> BIB004 </s> Intelligent Approaches in Locomotion - A Review <s> Trajectories for non-bipeds <s> We analyze a simple model for running: a three-dimensional spring-loaded inverted pendulum carrying a point mass (3D-SLIP). Our formulation reduces to the sagittal plane SLIP and horizontal plane lateral leg spring (LLS) models in the appropriate limits. Using the intrinsic geometry and symmetries and appealing to the case of stiff springs, in which gravity may be neglected during stance, we derive an explicit approximate mapping describing stride-to-stride behavior. We thereby show that all left-right symmetric periodic gaits are unstable, deriving a particularly simple mapping for sagittal plane dynamics. Continuation to fixed points for the "exact" mapping confirms instability of these gaits, and we describe a simple feedback stabilization scheme for leg placement at touchdown. <s> BIB005 </s> Intelligent Approaches in Locomotion - A Review <s> Trajectories for non-bipeds <s> It is a widespread idea that animal-legged locomotion is better than wheeled locomotion on natural rough terrain. However, the use of legs as a locomotion system for vehicles and robots still has a long way to go before it can compete with wheels and trucks, even on natural ground. This paper aims to solve two main disadvantages plaguing walking robots: their inability to react to external disturbances (which is also a drawback of wheeled robots); and their extreme slowness. Both problems are reduced here by combining: 1) a gait-parameter-adaptation method that maximizes a dynamic energy stability margin and 2) an active-compliance controller with a new term that compensates for stability variations, thus helping the robot react stably in the face of disturbances. As a result, the combined gait-adaptation approach helps the robot achieve faster, more stable compliant motions than conventional controllers. Experiments performed with the SILO4 quadruped robot show a relevant improvement in the walking gait <s> BIB006 </s> Intelligent Approaches in Locomotion - A Review <s> Trajectories for non-bipeds <s> An antagonistic muscle mechanism that regulates joint compliance contributes enormously to human dynamic locomotion. Antagonism is considered to be the key for realizing more than one locomotion mode. In this paper, we demonstrate how antagonistic pneumatic actuators can be utilized to achieve three dynamic locomotion modes (walking, jumping, and running) in a biped robot. Firstly, we discuss the contribution of joint compliance to dynamic locomotion, which highlights the importance of tunable compliance. Secondly, we introduce the design of a biped robot powered by antagonistic pneumatic actuators. Lastly, we apply simple feedforward controllers for realizing walking, jumping, and running and confirm the contribution of joint compliance to such multimodal dynamic locomotion. Based on the results, we can conclude that the antagonistic pneumatic actuators are superior candidates for constructing a human-like dynamic locomotor. <s> BIB007 </s> Intelligent Approaches in Locomotion - A Review <s> Trajectories for non-bipeds <s> This paper presents an approach for the closed-loop control of a fully actuated biped robot that leverages its natural dynamics when walking. Rather than prescribing kinematic trajectories, the approach proposes a set of state-dependent torques, each of which can be constructed from a combination of low-gain spring-damper couples. Accordingly, the limb motion is determined by interaction of the passive control elements and the natural dynamics of the biped, rather than being dictated by a reference trajectory. In order to implement the proposed approach, the authors develop a model-based transformation from the control torques that are defined in a mixed reference frame to the actuator joint torques. The proposed approach is implemented in simulation on an anthropomorphic biped. The simulated biped is shown to converge to a stable, natural-looking walk from a variety of initial configurations. Based on these simulations, the mechanical cost of transport is computed and shown to be significantly lower than that of trajectory-tracking approaches to biped control, thus validating the ability of the proposed idea to provide efficient dynamic walking. Simulations further demonstrate walking at varying speeds and on varying ground slopes. Finally, controller robustness is demonstrated with respect to forward and backward push-type disturbances and with respect to uncertainty in model parameters. <s> BIB008 </s> Intelligent Approaches in Locomotion - A Review <s> Trajectories for non-bipeds <s> This paper considers the effect of natural material compliance on the stiffness and stability of frictional multi-contact grasps and fixtures. The contact preload profile is a key parameter in the nonlinear compliance laws governing such contacts. The paper introduces the Hertz-Walton contact compliance model which is valid for linear contact loading profiles. The model is specified in a lumped parameter form suitable for on-line grasping applications, and is entirely determined by the contact friction and by the material and geometric properties of the contacting bodies. The model predicts an asymmetric stiffening of the tangential reaction force as the normal load at the contact increases. As a result, the composite stiffness matrix of multi-contact grasps governed by natural compliance effects is asymmetric, indicating that these contact arrangements are not governed by any potential energy function. Based on the compliant grasp dynamics, the paper derives rules indicating which contact point locations and what preload profiles guarantee grasp and fixture stability. The paper also describes preliminary experiments supporting the contact model predictions. <s> BIB009
Bipedal movement is of significant interest because it allows control of human like systems, as well as posing challenging stability problems. In conducting this review, more papers were found examining biped gaits than any other. However, in this section we show that several different systems have also been examined. Most of the other systems examined are legged, but research can be found for specific control problems such as hand grasping BIB009 . With extra legs, stability becomes less of a problem, and the focus then shifts to developing gait algorithms -methods of moving the feet in order to move the system in a particular direction. Different types of gaits have been developed, to be used at different speeds, such as ambling, trotting, bounding and galloping BIB001 - BIB004 . In order to improve manoeuvrability, forward and crab (perpendicular) gaits for flat and sloped terrain were developed in  . Other research has looked at fine tuning the gaits, including comparing different modelling assumptions on final real-world accuracy BIB004 , and increasing efficiency by utilising the natural dynamics of the system BIB008 . Some stability conditions have been considered in quadrupeds. For example, a set of reactive behaviours were developed in BIB002 in order to improve stability. In BIB003 , an analysis of a spring loaded variation of the inverted pendulum model (also see BIB005 ) was used to compare sensory feedback strategies for stabilising hexapod motion (as well as providing an analytical framework that could be applied to other systems). In order to be able to function in an uneven natural environment, and to support high speeds, a gait parameter and active-compliance parameter algorithms were developed in BIB006 . Gait adaptation was used to adjust to changes in the environment and provide a maximum stability margin, and compliance was used to deal with impulsive perturbations. The greater stability itself enabled faster movement across the uneven terrain. In BIB007 , the authors added two legs to a bipedal robot, in such a way that they were rigidly connected to the first to. This provided stability while only requiring a two-legged control algorithm. As well as creating a stable robot, the authors increased mechanical efficiency by introducing passive joint compliance. Altering compliance was done using pneumatic joints and, through exhaustive search, optimal compliance was found for walking, running and jumping gaits. Control algorithms have been developed for unipeds. For example, in  a pogo stick style (a body plus one springy leg) robot was controlled with an established algorithm, but with the addition of variable correction term to minimize velocity error. The research in  examined the possibility of using uniped algorithms to control multi-legged systems (thus raising the possibility of utilising previous research in one domain across several). Firstly, they developed single legged gaits, which are gaits for multi-legged systems where only one foot is in contact with the ground at any one time. Following this they developed the concept of a virtual single leg that modelled the situation when two legs were in contact with the ground, this way expanding the number of possible gaits.