A Simple Analytical Tool for Legged Robot Design

Although legged locomotion is better at tackling complicated terrains compared with wheeled locomotion, legged robots are rare, in part, because of the lack of simple design tools. The dynamics governing legged locomotion are generally nonlinear and hybrid (piecewise-continuous) and so require numerical simulation for analysis and are not easily applied to robot designs. During the past decade, a few approximated analytical solutions of Spring-Loaded Inverted Pendulum (SLIP), a canonical model in legged locomotion, have been developed. However, SLIP is energy conserving and cannot predict the dynamical stability of real-world legged locomotion. To develop new analytical tools for legged robot designs, we first analytically solved SLIP in a new way. Then based on SLIP solution, we developed an analytical solution of a hip-actuated Spring-Loaded Inverted Pendulum (hip-actuated-SLIP) model, which is more biologically relevant and stable than the canonical energy conserving SLIP model. The analytical approximations offered here for SLIP and the hip actuated-SLIP solutions compare well with the numerical simulations of each. The analytical solutions presented here are simpler in form than those resulting from existing analytical approximations. The analytical solutions of SLIP and the hip actuated-SLIP can be used as tools for robot design or for generating biological hypotheses.

Stiffness Modeling of Robotic-Manipulators Under Auxiliary Loadings

The paper focuses on the extension of the virtual-joint-based stiffness modeling technique for the case of different types of loadings applied both to the robot end-effector and to manipulator intermediate points (auxiliary loading). It is assumed that the manipulator can be presented as a set of compliant links separated by passive or active joints. It proposes a computationally efficient procedure that is able to obtain a non-linear force-deflection relation taking into account the internal and external loadings. It also produces the Cartesian stiffness matrix. This allows to extend the classical stiffness mapping equation for the case of manipulators with auxiliary loading. The results are illustrated by numerical examples.

Jacobian Analysis of a Fully Decoupled Parallel Manipulator for Minimally Invasive Surgery

This paper presents the Jacobian analysis of a parallel manipulator that has a fully decoupled 4-DOF remote center-of-motion for application in minimally invasive surgery. Owing to the special structure of the manipulator, the Jacobian matrix of the manipulator is expressed as a combination of three special Jacobian matrices, namely the Jacobian of motion space, Jacobian of constraints, and Jacobian of actuations. Based on these Jacobian matrices, the singular configurations of the manipulator are then identified. It shows that the configuration singularity only exists at the central point and the boundary of the reachable workspace of the manipulator.

Combined Graph Layout Algorithms for Automated Sketching of Kinematic Chains

The graph layout problem arises frequently in the conceptual stage of mechanism design, specially in the enumeration process where a large number of topological solutions must be analyzed. Two main objectives of graph layout are the avoidance or minimization of edge crossings and the aesthetics. Edge crossings cannot be always avoided by force-directed algorithms since they reach a minimum of the energy in dependence with the initial position of the vertices, often randomly generated. Combinatorial algorithms based on the properties of the graph representation of the kinematic chain can be used to find an adequate initial position of the vertices with minimal edge crossings. To select an initial layout, the minimal independent loops of the graph can be drawn as circles followed by arcs, in all forms. The computational cost of this algorithm grows as factorial with the number of independent loops. This paper presents a combination of two algorithms: a combinatorial algorithm followed by a force-directed algorithm based on spring repulsion and electrical attraction, including a new concept of vertex-to-edge repulsion to improve aesthetics and minimize crossings. Atlases of graphs of complex kinematic chains are used to validate the results. The layouts obtained have good quality in terms of minimization of edge crossings and maximization of aesthetic characteristics.

Simple Leg Placement Strategy for a One Legged Running Model

The Spring Loaded Inverted Pendulum (SLIP) model was developed to describe center of mass movement patterns observed in animals, using only a springy leg and a point mass. However, SLIP is energy conserving and does not accurately represent any biological or robotic system. Still, this model is often used as a foundation for the investigation of improved legged locomotion models. One such model called Torque Damped SLIP (TD-SLIP) utilizes two additional parameters, a time dependent torque and dampening to drastically increase the stability. Forced Damped SLIP (FD-SLIP), a predecessor of TD-SLIP, has shown that this model can be further simplified by using a constant torque, instead of a time varying torque, while still maintaining stability. Using FD-SLIP as a base, this paper explores a leg placement strategy using a simple PI controller. The controller takes advantage of the fact that the energy state of FD-SLIP is symmetric entering and leaving the stance phase during steady state conditions. During the flight phase, the touch down leg angle is adjusted so that the energy dissipation due to dampening, during the stance phase, compensates for any imbalance of energy. This controller approximately doubles the region of stability when subjected to velocity perturbations at touchdown, enables the model to operate at considerably lower torque values, and drastically reduces the time required to recover from a perturbation, while using less energy. Finally, the leg placement strategy used effectively imitates the natural human response to velocity perturbations while running.

Reconfiguration and Unified Kinematics Analysis of a Metamorphic Parallel Mechanism With Bifurcated Motion

This paper introduced a new metamorphic parallel mechanism consisting of four reconfigurable rTPS limbs. Based on the reconfigurability of the reconfigurable Hooke (rT) joint, the rTPS limb has two phases while in one phase the limb has no constraint to the platform, in the other it constrains the spherical joint center to lie on a plane. This results in the mechanism to have ability of reconfiguration between different topologies with variable mobility. Geometric constraint equations of the platform rotation matrix and translation vector are set up based on the point-plane constraint, which reveals the bifurcated motion property in the topology with mobility 2 and the geometric condition with mobility change in altering to other mechanism topologies. Following this, a unified kinematics limb modeling is proposed considering the difference between the two phases of the reconfigurable rTPS limb. This is further applied for the mechanism modeling and both the inverse and forward kinematics is analytically solved by combining phases of the four limbs covering all the mechanism topologies.

Kinematic Synthesis of Planar, Shape-Changing Compliant Mechanisms Using Pseudo-Rigid-Body Models

This paper presents a procedure using Pseudo-Rigid-Body Models (PRBMs) to synthesize partially compliant mechanisms capable of approximating a shape change defined by a set of morphing curves in different positions. To generate a single-piece compliant mechanism, flexural pivots and flexible beams are both utilized in the mechanism. New topologies defined by compliant mechanism matrices are enumerated by modifying the components that make up a single degree-of-freedom (DOF) rigid-body mechanism. Because of the introduction of the PRBM for flexural pivots and the simplified PRBM for flexible beams, torsional springs are attached at the characteristic pivots of the 1-DOF rigid-body mechanism in order to generate a corresponding pseudo-rigid-body mechanism. A multi-objective genetic algorithm is employed to find a group of viable compliant mechanisms in the form of candidate pseudo-rigid-body mechanisms that tradeoff minimizing shape matching error with minimizing actuator energy. Since the simplified beam model is not accurate, an optimization loop is established to find the position and shape of the flexible beam using a finite link beam model. The optimal flexible beams together with the pseudo-rigid-body mechanism define the solution mechanism. The procedure is demonstrated with an example in which a partially compliant mechanism approximating two closed-curve profiles is synthesized.

Robot Task Planning and Trajectory Learning for Flexible Automation

A task planning method is presented to model and reproduce robot trajectories based on those captured from human demonstrations. In the framework of the Programming by Demonstration (PbD) approach, task planning algorithm is developed to determine the general type of trajectory pattern, its parameters, and its kinematic profile. The pattern is described independently of the shape of the surface on which it is demonstrated. Key pattern points are identified based on changes in direction and velocity, and are then reduced based on their proximity. The results of the analysis are provided are used inside a task planning algorithm, to produce robot trajectories based on the workpiece geometries. The trajectory is output in the form of robot native language code so that it can be readily downloaded on the robot.

Controllable, High Force Amplification Using Elastic Cable Capstans

This paper presents the design and experimental characterization of a continuously variable linear force amplifier based on the theory of capstans. In contrast to traditional capstan amplifiers, the design presented here uses an elastic cable, enabling a control actuator to not only continuously clutch output to a rotating drum but also passively declutch by releasing tension. Our experimental results demonstrate successful declutching at all force amplification ratios up to the limit of our experimental apparatus, 21 — significantly higher than previously published values. A system of distributed capstan amplifiers driven by a central torque source with cable engagement switched by lightweight, low torque actuators has potential to reduce the mass of distal actuators and enable more dynamic performance in robotic applications.

Design of an Orthosis for the Weight Balance of Human Lower Limbs

Most existing lower limb orthosis use actuators and active controller to guide the motion of human lower limbs. Actuators with relatively large power are usually required to compensate the gravity effect of the human lower limbs, even for a normal walking. Hence, design of an orthosis for the weight balance of human lower limbs is desired. For the motion compatibility, the human hip joint is treated as a planar pair and the knee joint as a revolute pair. As a consequence, while the lower limb is in motion, the exact positions of the mass centers of the human lower limbs cannot be obtained. Hence, in this work, topological synthesis of the orthosis mechanisms, which can trace the mass centers of the human thigh and shank, respectively, is implemented. The weight balance of the human lower limbs is achieved by fitting a minimum number of zero-free-length springs. Based on the anthropometric parameters, dimensions of the lower limb orthosis is determined and the proposed design is justified by the simulation executed by the software of ProEngineer. Finally, a first generation prototype is built.