This paper demonstrates the practical performance of a new theory of balance control that has been shown in simulation to out-perform earlier balance control theories in the sense of allowing the robot to make larger and faster movements while still maintaining its balance. The case studied here is that of a general planar double inverted pendulum, which resembles a legged robot's behaviour when the polygon of support shrinks to a line. The results show the speed and accuracy of the controller, as well as its robustness to external disturbances and slipping during fast movements.

This paper presents a simulation study of the problem of balancing a planar double pendulum in which the lower body (the leg) has been modified to include a spring-loaded passive prismatic joint. Robots of this kind can travel by hopping, and can also stand and balance on a single point. The purpose of this study is to investigate the degree to which a balance controller can cope with the large and rapidly changing forces from the spring. It is shown that good performance can be achieved using an existing balance controller if the spring-loaded joint is instrumented so that its position and velocity can be taken into account when calculating the state variables needed by the balance controller.

The ability of legged systems to traverse highly- constrained environments depends by and large on the performance of their motion and balance controllers. This paper presents a controller that excels in a scenario that most state- of-the-art balance controllers have not yet addressed: line walking, or walking on nearly null support regions. Our approach uses a low-dimensional virtual model (2-DoF) to generate balancing actions through a previously derived four- term balance controller and transforms them to the robot through a derived kinematic mapping. The capabilities of this controller are tested in simulation, where we show the 90kg quadruped robot HyQ crossing a bridge of only 6 cm width (compared to its 4 cm diameter spherical foot), by balancing on two feet at any time while moving along a line. Additional simulations are carried to test the performance of the controller and the effect of external disturbances. Lastly, we present our preliminary experimental results showing HyQ balancing on two legs while being disturbed.

This paper presents the first practical demonstration of a recently developed theory of balance control that aims to achieve high performance in the sense of allowing a robot to make large, fast movements while maintaining its balance on a narrow support. This theory includes a simple method of leaning in anticipation of future motion commands, which is largely responsible for the high performance. The experiments reported here use a robot acting as a reaction wheel pendulum, and they test only the 2-D version of the theory. The results show that the balance controller's performance in practice closely resembles its theoretical performance. This paper also presents a simple yet accurate balance offset observer that measures the difference between true and estimated balanced configurations.

This paper first presents a formula to predict the largest balance disturbance from which a legged robot can recover without taking a step. It then presents an actuator design criterion derived from this formula that maximizes the robot's ability to recover. In this study, it is assumed that the robot is using a single major joint (e.g, a hip joint) to perform its balance recovery movement, and that the actuator consists of an electric motor and reduction gear. It is also assumed that the robot's support polygon is sufficiently small that it can be approximated as a point, and that the balance recovery motion is essentially planar, so that a 2-D analysis remains valid in 3-D. Finally, it is assumed that, for the purpose of studying balance recovery motion, the robot can be approximated by a reaction wheel pendulum. The theory has been tested experimentally on a robot designed to be good at balancing, and was found to agree closely with experimental results.

We propose a reactive locomotion strategy, called height reflex, that is useful to address big elevation changes in the terrain (e.g. when a quadruped robot has to step down from a high platform). In these cases the swing leg can lose mobility creating issues in the subsequent steps. The height reflex is a foot trajectory replanning strategy that redistributes the swing motion (in a smart way) to the stance legs to “lower” the whole trunk and to aid the foothold searching motion. To spread the motion we exploit a massless link model of the robot with virtual dampers at the joints, which is used to replan the feet trajectories. The proposed approach is able to incorporate kinematic limits, it is easy-to-tune, computationally efficient and suitable for real-time implementations. The reflex is implemented and experimentally evaluated on the 80 kg hydraulic quadruped HyQ. With our approach we were able to address high steps, up to 24 cm which is 30% of HyQ leg length and 53% of its retractable leg range.

This paper presents an angular momentum based controller to control the balancing motion of a spatial underactuated robot with three degrees of under-actuation. The control algorithm is based on the idea of decoupling the robot's motion instantaneously into bending and swivelling motions. This property of the robot is obtained by using a constant velocity joint as the 2-DoF active joint of the robot. Simulation results show the performance of the controller during some interesting motions of the robot such as straightening, crouching and reorienting motions. The last two motions, which are the results of decoupling the robot's motion, are demonstrated here for the first time.

This paper presents a new nonlinear model of the normal force that arises during compliant contact between two spheres, or between a sphere and a flat plate. It differs from a well-known existing model by only a single term. The advantage of the new model is that it accurately predicts the measured values of the coefficient of restitution between spheres and plates of various materials, whereas other models do not.

In this paper, a new control algorithm is presented for implementing hopping and balancing motions on a planar hopping machine with a single actuated revolute joint. Starting with a simple control algorithm for balancing, it is extended to perform trajectory-tracking maneuvers, which enables it to perform the crouching, lift-off and flight phases of a single hop, as well as re-balancing after landing. Simulation results are presented showing that the control system works well, and that it is not significantly affected by small amounts of slipping between the foot and the ground.

This paper provides a reduced-order algorithm, the Extended-Force-Propagator Algorithm (EFPA), for the computation of operational-space inertia matrices in branched kinematic trees. The algorithm accommodates an operational space of multiple end-effectors, and is the lowest-order algorithm published to date for this computation. The key feature of this algorithm is the explicit calculation and use of matrices that propagate a force across a span of several links in a single operation. This approach allows the algorithm to achieve a computational complexity of O(N +md+m2) where N is the number of bodies, m is the number of end-effectors, and d is the depth of the system's connectivity tree. A detailed cost comparison is provided to the propagation algorithms of Rodriguez et al. (complexity O(N + dm2)) and to the sparse factorization methods of Featherstone (complexity O(nd2+ md2+ m2d)). For the majority of examples considered, our algorithm outperforms the previous best recursive algorithm, and demonstrates efficiency gains over sparse methods for some topologies.

This paper presents simulation and experimental results for closed-loop force control of single-wire Shape Memory Alloy (SMA) actuators. The simulation uses a model derived from the frequency response analysis of SMA. Although the large-scale response has hysteresis and nonlinearities, small-signal frequency response analysis is possible on SMA wires, with detectable force response at frequencies up to 100 Hz. The model has been demonstrated to accurately predict closed-loop behaviour. A high performance force control system using PID control is also demonstrated. Results show fast convergence, and excellent setpoint and tracking accuracy with practically no sign of limit cycles. Experimental results in this paper are the first to have demonstrated stable and accurate response with good rejection of large motion disturbances.

6-D vectors are routinely expressed in Plucker coordinates; yet there is almost no mention in the literature of the basis vectors that give rise to these coordinates. This paper identifies the Plucker basis vectors, and uses them to explain the following: the relationship between a 6-D vector and its Plucker coordinates, the relationship between a 6-D vector and the pair of 3-D vectors used to define it, and the correct way to differentiate a 6-D vector in a moving coordinate system

This paper examines the phenomenon of frictionless contact between rigid bodies that are already subject to kinematic constraints from some other source. Such contacts occur frequently when robots interact with their environments, in which case, the additional constraints come from the robot mechanisms. A proper analysis of these contacts must consider both sets of constraints. This paper presents a general model of constrained-body contact, expressed in invariant terms; a method of resolving equations of motion into decoupled subsystems with respect to the contact's motion and force freedoms; an equation of motion for possibly redundant robots experiencing constrained-body contact, which employs a novel decomposition of the robot's joint space into dynamically decoupled subspaces; and a dynamically decoupled hybrid motion/force-control system based on the same decomposition. It is shown that disturbances from an unknown dynamic environment are automatically confined to the force-control subsystem, and that a modification to the control law can factor these disturbances out of the controlled response.

This paper reviews some of the accomplishments in the field of robot dynamics research, from the development of the recursive Newton-Euler algorithm to the present day. Equations and algorithms are given for the most important dynamics computations, expressed in a common notation to facilitate their presentation and comparison.

Presents a general first-order kinematic model of frictionless rigid-body contact for use in hybrid force/motion control. It is formulated in an invariant manner by treating motion and force vectors as members of two separate but dual vector spaces. These more general kinematics allow us to model tasks that cannot be described using the Raibert-Craig model; a single Cartesian frame in which directions are either force- or motion-controlled is not sufficient. The model can be integrated with the object and manipulator dynamics in order to model both the kinematics and dynamics of contact. These equations of motion can be used to design force and motion controllers in the appropriate subspaces. To guarantee decoupling between the controllers, it is possible to apply projection matrices to the controller outputs that depend solely on the kinematic model of contact, not a dynamic one. Experimental results show a manipulation that involves controlling the force in two separate face-vertex contacts while performing motion. These multi-contact compliant motions often occur as part of an assembly and cannot be described using the Raibert-Craig model.

The constraint force algorithm, as originally described by Fijany et al. (1995), calculates the forward dynamics of a system comprising N rigid bodies connected together in an unbranched chain with joints from a restricted class of joint types. It was designed for parallel calculation of the dynamics, and achieves O(log N) time complexity on O(N) processors. This paper presents a new formulation of the constraint force algorithm that corrects a major limitation in the original, and sheds new light on the relationship between this algorithm and other dynamics algorithms. The new version is applicable to systems with any type of joint, floating bases, and short branches off the main chain. It is obtained using a new technique for analysing constrained rigid-body systems by means of a change of basis in a dual system of vector spaces. This new technique is also described.

A sphere hierarchy is a data structure that approximates the shape of a given object using a collection of spheres. They can be used for collision detection, motion planning and other related applications. This paper presents an algorithm for constructing an efficient sphere hierarchy from a geometric model of an object, as supplied by a CAD system or geometric modeller and it presents a branching factor analysis based on a general measure of the efficiency of a sphere hierarchy.

This paper presents and compares four simple numerical algorithms for transforming a parameterized curve (a path or trajectory) from task space to joint space. They are based on Newton's method, but offer substantially better accuracy for a given step size by making use of the continuity properties of the curve. They work for mechanisms with general geometry, and in both redundant and nonredundant situations; but they do not work at singularities or when the trajectory is out of reach. Some simulation results are presented.>