A wide variety of strategies have been developed for assisting human locomotion using powered exoskeletons. Although these strategies differ in their aims as well as the control methods employed, they have the implicit property of causing a virtual modification of the dynamic response of the human limb. We use this property of the exoskeletons action to formulate a unified control design framework called Integral Admittance Shaping, which designs exoskeleton controllers capable of producing the desired dynamic response for the assisted limb. In this framework, a virtual increase in the admittance of the limb is produced by coupling it to an exoskeleton that exhibits active behavior. Specifically, our framework shapes the magnitude profile of the integral admittance (i.e. torque-to-angle relationship) of the coupled human-exoskeleton system, such that the desired assistance is achieved. This framework also ensures that the coupled stability and passivity are guaranteed. This paper presents a formulation of Integral Admittance Shaping for single degree-of-freedom (1-DOF) exoskeleton devices. We also present experimental results on a modified version of Honda's Stride Management Assist (SMA) device that successfully demonstrate motion amplification of the assisted hip joint during walking.

This paper addresses a new control strategy to reduce the damage to a humanoid robot during a fall. Instead of following the traditional approach of finding a favorable configuration with which to fall to the ground, this method attempts to stop the robot from falling all the way to the ground. This prevents the full transfer of the robot's potential energy to kinetic energy, and consequently results in a milder impact. The controlled motion of the falling robot involves a sequence of three deliberate contacts to the ground with the swing foot and two hands, in that order. In the final configuration the robot's center of mass (CoM) remains relatively high from the floor and the robot has a relatively stable three-point contact with the ground; hence the name tripod fall. The optimal location of the three contacts are learned through reinforcement learning algorithm. The controller is simulated on a full size humanoid, and experimentally tested on the NAO humanoid robot. In this work we apply our fall controller only to a forward fall.

Although the fall of a humanoid robot is rare in controlled environments, it cannot be avoided in the real world where the robot may physically interact with the environment. Our earlier work [1], [2] introduced the strategy of direction-changing fall, in which the robot attempts to reduce the chance of human injury by changing its default fall direction in real-time and falling in a safer direction. The current paper reports further theoretical developments culminating in a successful hardware implementation of this fall strategy conducted on the Aldebaran NAO robot[3]. This includes new algorithms for humanoid kinematics and Jacobians involving coupled joints and a complete estimation of the body frame attitude using an additional inertial measurement unit. Simulations and experiments are smoothly handled by our platform independent humanoid control software package called Locomote. We report experiment scenarios where we demonstrate the effectiveness of the proposed strategies in changing humanoid fall direction.

This paper presents a momentum-based reactive stepping controller for humanoid robot push recovery. By properly regulating combinations of linear and angular momenta, the controller can selectively encourage the robot to recover its balance with or without taking a step. A reference stepping location is computed by modeling the humanoid as a passive rimless wheel with two spokes such that stepping on the location leads to a complete stop of the wheel at the vertically upright position. In contrast to most reference points for stepping based on pendulum models such as the capture point, our reference point exists on both level and non-level grounds. Moreover, in contrast with continuously evolving step locations, our step location is stationary. The computation of the location of the reference point also generates the duration of step which can be used for designing a stepping trajectory. Momentum-based stepping for push recovery is implemented in simulations of a full size humanoid on 3D non-level ground.

Although falls are undesirable in humanoid robots, they are also inevitable, especially as robots get deployed in physically interactive human environments. We consider the problem of fall prediction, i.e., to predict if a robot's balance controller can prevent a fall from the current state. A trigger from the fall predictor is used to switch the robot from a balance maintenance mode to a fall control mode. Hence, it is desirable for the fall predictor to signal imminent falls with sufficient lead time before the actual fall, while minimizing false alarms. Analytical techniques and intuitive rules fail to satisfy these competing objectives on a large robot that is subjected to strong disturbances and therefore exhibits complex dynamics. Today effective supervised learning tools are available for finding patterns in high-dimensional data. Our paper contributes a novel approach to engineer fall data such that a supervised learning method can be exploited to achieve reliable prediction. Specifically, we introduce parameters to control the tradeoff between the false positive rate and lead time. Several parameter combinations yield solutions that improve both the false positive rate and the lead time of hand-coded solutions. Learned predictors are decision lists with typical depths of 5-10, in a 16-dimensional feature space. Experiments are carried out in simulation on an Asimo-like robot.

Humanoid robots are expected to share human environments in the future and it is important to ensure safety of their operation. A serious threat to safety is the fall of a humanoid robot, which can seriously damage both the robot and objects in its surrounding. This paper proposes a strategy for planning and control of fall. The controller's objective is to prevent the robot from hitting surrounding objects during a fall by modifying its default fall direction. We have earlier presented such a direction-changing fall controller in. However, the controller was applicable only when the robot's surrounding contained a single object. In this paper we introduce a generalized approach to humanoid fall-direction control among multiple objects. This new framework algorithmically establishes a desired fall direction through assigned scores, considers a number of control options, and selects and executes the best strategy. The fall planner is also able to select “No Action” as the best strategy, if appropriate. The controller is interactive and is applicable for fall occurring during upright standing or walking. The fall performance is continuously tracked and can be improved in real-time. The planning and control algorithms are demonstrated in simulation on an ASIMO-like humanoid robot.

We present a novel momentum-based method for maintaining balance of humanoid robots. By controlling the desired ground reaction force (GRF) and center of pressure (CoP) at each support foot, our method can naturally deal with non-level and non-stationary ground at each foot-ground contact, as well as different frictional properties. We do not make use of the net GRF and CoP which may be difficult or impossible to compute for non-level grounds. Our method minimizes the ankle torques during double support. We show the effectiveness of this new balance control method by simulating various experiments with a humanoid robot including maintaining balance when two feet are on separate moving supports with different inclinations and velocities.

The large number of degrees of freedom in legged robots give rise to complicated dynamics equations. Analyzing these equations or using them for control can therefore be a difficult and non-intuitive task. A simplification of the complex multi-body dynamics can be achieved by instantaneously reducing it to an equivalent single inertial entity called the locked inertia or the composite rigid body inertia.

Although fall is a rare event in the life of a humanoid robot, we must be prepared for it because its consequences are serious. In this paper we present a fall strategy which rapidly modifies the robot's fall direction in order to avoid hitting a person or an object in the vicinity. Our approach is based on the key observation that during “toppling” the rotational motion of a robot necessarily occurs at the leading edge or the leading corner of its support base polygon. To modify the fall direction the robot needs to change the position and orientation of this edge or corner vis-a-vis the prohibited direction. We achieve it through intelligent stepping as soon as a fall is detected. We compute the optimal stepping location which results in the safest fall. Additional improvement to the fall controller is achieved through inertia shaping techniques aimed at controlling the centroidal inertia of the robot. We demonstrate our results through the simulation of an Asimo-like humanoid robot. To our knowledge, this is the first implementation of a controller that attempts to change the fall direction of a humanoid robot.

Researchers at IHMC and Honda Research Institute are developing techniques for learning capture points for bipedal push recovery. A capture point is a point on the ground where a biped can step to in order to stop. Humans are very adept at stepping to capture points, while most bipedal robots cannot recover from significant pushes. To calculate approximate capture point locations, we use the linear inverted pendulum model introduced by Kajita and Tani. For a point mass biped walking at a constant height, this model exactly predicts the capture point. However, for a distributed mass biped, it is only an approximation. In order to better predict capture points, we learn a correction function to the linear inverted pendulum model. We used two learning methods, one online and one offline, to improve capture point prediction. In the offline learning method, the robot is pushed multiple times with a given force magnitude and direction. In the online learning technique, we use a radial basis function to represent the learned offsets from the capture point predicted by the linear inverted pendulum model.

The centroidal momentum of a humanoid robot is the sum of the individual link momenta, after projecting each to the robotpsilas Center of Mass (CoM). Centroidal momentum is a linear function of the robotpsilas generalized velocities and the centroidal momentum matrix is the matrix form of this function. This matrix has been called both a Jacobian matrix and an inertia matrix by others. We show that it is actually a product of a Jacobian and an inertia matrix.

A number of conceptually simple but behavior-rich "inverted pendulum" humanoid models have greatly enhanced the understanding and analytical insight of humanoid dynamics. However, these models do not incorporate the robot's angular momentum properties, a critical component of its dynamics. We introduce the reaction mass pendulum (RMP) model, a 3D generalization of the better-known reaction wheel pendulum. The RMP model augments the existing models by compactly capturing the robot's centroidal momenta through its composite rigid body (CRB) inertia. This model provides additional analytical insights into legged robot dynamics, especially for motions involving dominant rotation, and leads to a simpler class of control laws. In this paper we show how a humanoid robot of general geometry and dynamics can be mapped into its equivalent RMP model. A movement is subsequently mapped to the time evolution of the RMP. We also show how an "inertia shaping" control law can be designed based on the RMP.

We propose a novel control method for lowerlimb assist that produces a virtual modification of the mechanical impedance of the human limbs. This effect is accomplished through the use of an exoskeleton that displays active impedance. The proposed method is aimed at improving the dynamic response of the human limbs, while preserving the user’s control authority. Our goal is to use active-impedance exoskeleton control to improve the user’s agility of motion, for example by reducing the average time needed to complete a movement. Our control method has been implemented in a 1-DOF exoskeleton designed to assist human subjects performing knee flexions and extensions. In this paper we discuss an initial study on the effect of negative exoskeleton damping (a particular case of active-impedance control) on the subject’s time to complete a target-reaching motion. Experimental results show this effect to be statistically significant. On average, subjects were able to reduce the time to complete the motion by 16%.

Balance maintenance and upright posture recovery under unexpected environmental forces are key requirements for safe and successful co-existence of humanoid robots in normal human environments. In this paper we present a two-phase control strategy for robust balance maintenance under a force disturbance. The first phase, called the reflex phase, is designed to withstand the immediate effect of the force. The second phase is the recovery phase where the system is steered back to a statically stable “home” posture. The reflex control law employs angular momentum and is characterized by its counter-intuitive quality of “yielding” to the disturbance. The recovery control employs a general scheme of seeking to maximize the potential energy and is robust to local ground surface feature. Biomechanics literature indicates a similar strategy in play during human balance maintenance.

In order to engage in useful activities, upright legged creatures must be able to maintain balance. Despite recent advances, the understanding, prediction and control of biped balance in realistic dynamical situations remain an unsolved problem and the subject of much research in robotics and biomechanics. Here we study the fundamental mechanics of the rotational stability of multi-body systems with the goal of identifying a general stability criterion. Our research focuses on H/sub G/, the rate of change of centroidal angular momentum of a robot, as the physical quantity containing its stability information. We propose three control strategies using H/sub G/ that can be used for stability recapture of biped robots. For free walk on horizontal ground, a derived criterion refers to a point on the foot/ground surface of a robot where the total ground reaction force would have to act such that H/sub G/=0. This new criterion generalizes earlier concepts such as GCoM, CoP, ZMP, and FRI point, and extends their applicability.

We present a methodology for agent modeling that is scalable and efficient. It is based on the integration of nonlinear dynamical systems and kinetic data structures. The method consists of three-layers that model steering, flocking, and crowding agent behaviors among moving and static obstacles in 2 and 3D. The first layer, the local layer is based on the the use of nonlinear dynamical systems theory and models low level behaviors, it is fast and efficient, and does not depend on the total number of agents in the environment. The use of dynamical systems allows the use of continuous numerical parameters with which we can modify the interaction of each agent with the environment. This creates controllable distinctive behaviors. The second layer, a global environment layer consists of a specifically designed kinetic data structure to track efficiently the immediate environment of each agent and know which obstacles/agents are near or visible to the given agent. This layer reduces the complexity in the local layer. In the third layer, a global planning layer, the problem of target tracking is generalized in a way that allows navigation in maze-like terrains, avoidance of local minima and cooperation between agents. We implement this layer based on two approaches that are suitable for different applications. One is to track the closest single moving or static target. The second is to use a pre-specified vector field. This vector can be generated automatically (with harmonic functions, for example) or based on user input to achieve the desired output. We demonstrate the power of the approach through a series of experiments simulating single/multiple agents and crowds moving towards moving/static targets in complex environments.

In this paper we develop a set of inverse kinematics algorithms suitable for an anthropomorphic arm or leg. We use a combination of analytical and numerical methods to solve generalized inverse kinematics problems including position, orientation, and aiming constraints. Our combination of analytical and numerical methods results in faster and more reliable algorithms than conventional inverse Jacobian and optimization-based techniques. Additionally, unlike conventional numerical algorithms, our methods allow the user to interactively explore all possible solutions using an intuitive set of parameters that define the redundancy of the system.

The focus of the paper is the problem of foot rotation in biped robots during the single support phase. Foot rotation is an indication of postural instability and should be carefully treated in a dynamically stable walk and avoided altogether in a statically stable walk. We introduce the foot rotation indicator (FRI) point which is a point on the foot/ground contact surface where the net ground reaction force would have to act to keep the foot stationary. To ensure no foot rotation, the FRI point must remain within the convex hull of the foot support area. In contrast with the ground projection of the center of mass (GCoM), which is a static criterion, the FRI point incorporates the robot dynamics. As opposed to the center of pressure (CoP)-better known as the zero moment point (ZMP) in the robotics literature-which may not leave the support area, the FRI point may. Due to these important properties the FRI point helps not only to monitor the state of static stability of a biped robot during the entire gait cycle, but indicates the stability robustness or the severity of instability of the gait as well. In response to a recent need the paper also resolves the misconceptions surrounding the CoP/ZMP equivalence.

We address the problem of energy optimal gait generation for biped robots. Using a simplified robot dynamics that ignores the effects of centripetal forces, we obtain unconstrained optimal trajectories generated by piecewise constant inputs. The study a complete gait cycle comprising single support, double support and the transition phases. The energy optimal gaits for different step lengths and velocities are compared with natural human gait.

This paper proposes an analysis of the behavior of perhaps the simplest biped robot: the compass gait model. It has been shown previously that such a robot can walk down a slope indefinitely without any actuation. Passive motions of this nature are of particular interest since they may lead us to strategies for controlling active walking machines as well as to a better understanding of human locomotion. We show here that, depending on the parameters of the system, passive compass gait may exhibit 1-periodic, 2/sup n/-periodic and chaotic gaits proceeding from cascades of period-doubling bifurcations. Since compass equations are quite involved (they combine nonlinear differential and algebraic equations in a 4-dimensional space), our investigations rely, in part, on numerical simulations.

It is well-known that a suitably designed unpowered mechanical biped robot can "walk" down an inclined plane with a steady gait. The characteristics of the gait (e.g., velocity, time period, step length) depend on the geometry and the inertial properties of the robot and the slope of the plane. A passive motion has the distinction of being "natural" and is likely to enjoy energy optimality. Investigation of such motions may potentially lead us to strategies useful for controlling active walking machines. In this paper we demonstrate that the nonlinear dynamics of a simple passive "compass gait" biped robot can exhibit periodic and stable limit cycle. Kinematically the robot is identical to a double pendulum (or its variations such as the Acrobot and the Pendubot). Simulation results also reveal the existence of a stable gait with unequal step lengths. We also present an active control scheme which enlarges the basin of attraction of the passive limit cycle.

A passive wrist, of fixed design, can be programmed to execute a wide range of useful control laws. Considered in particular are wrists whose actuators are unpowered hydraulic cylinders, the ports of which are coupled to one another via variable-conductance constrictions. The wrist is programmed by selection of these conductances, much as an analog computer is programmed. The range of control laws such a device can compute is characterized mathematically.>