Jerry E. Pratt

Virtual Model Control: An Intuitive Approach for Bipedal Locomotion

Virtual model control is a motion control framework that uses virtual components to create virtual forces generated when the virtual components interact with a robot system. An algorithm derived based on the virtual model control framework is applied to a physical planar bipedal robot. It uses a simple set of virtual components that allows the robot to walk successfully over level terrain. This paper also describes how the algorithm can be augmented for rough terrain walking based on geometric consideration. The resulting algorithm is very simple and does not require the biped to have an extensive sensory system. The robot does not know the slope gradients and transition locations in advance. The ground is detected using foot contact switches. Using the algorithm, we have successfully compelled a simulated seven-link planar biped to walk blindly up and down slopes and over rolling terrain.

Series elastic actuator development for a biomimetic walking robot

Series elastic actuators have linear springs intentionally placed in series between the motor and actuator output. The spring strain is measured to get an accurate estimate of force. A second order linear actuator model is broken into two fundamental cases: fixed load-high force (forward transfer function), and free load-zero force (impedance). This model is presented with dimensional analysis and extends previous linear models to include friction. Using the model and dimensionless groups, we examine nonlinear effects of motor saturation as it relates to large force bandwidth and nonlinear friction effects such as stiction. The model also helps to clarify how the springs help and hinder the operation of the actuator. The information gained from the model helps to create a design procedure for series elastic actuators. Particular emphasis is placed on choosing the spring constant for the elastic element.

Virtual model control of a bipedal walking robot

The transformation from high level task specification to low level motion control is a fundamental issue in sensorimotor control in animals and robots. This paper describes a control scheme called virtual model control that addresses this issue. Virtual model control is a motion control language that uses simulations of imagined mechanical components to create forces, which are applied through real joint torques, thereby creating the illusion that the virtual components are connected to the robot. Due to the intuitive nature of this technique, designing a virtual model controller requires the same skills as designing the mechanism itself. A high level control system can be cascaded with the low level virtual model controller to modulate the parameters of the virtual mechanisms. Discrete commands from the high level controller would then result in fluid motion. Virtual model control has been applied to a physical bipedal walking robot. A simple algorithm utilizing a simple set of virtual components has successfully compelled the robot to walk continuously over level terrain.

Capturability-based analysis and control of legged locomotion, Part 1: Theory and application to three simple gait models

This two-part paper discusses the analysis and control of legged locomotion in terms of N-step capturability: the ability of a legged system to come to a stop without falling by taking N or fewer steps. We consider this ability to be crucial to legged locomotion and a useful, yet not overly restrictive criterion for stability. In this part (Part 1), we introduce a theoretical framework for assessing N-step capturability. This framework is used to analyze three simple models of legged locomotion. All three models are based on the 3D Linear Inverted Pendulum Model. The first model relies solely on a point foot step location to maintain balance, the second model adds a finite-sized foot, and the third model enables the use of centroidal angular momentum by adding a reaction mass. We analyze how these mechanisms influence N-step capturability, for any N > 0. Part 2 will show that these results can be used to control a humanoid robot.

Intuitive control of a planar bipedal walking robot

Bipedal robots are difficult to analyze mathematically. However, successful control strategies can be discovered using simple physical intuition and can be described in simple terms. Five things have to happen for a planar bipedal robot to walk. Height has to be stabilized. Pitch has to be stabilized. Speed has to be stabilized. The swing leg has to move so that the feet are in locations which allow for the stability of height, pitch, and speed. Finally, transitions from support leg to support leg must occur at appropriate times. If these five objectives are achieved, the robot will walk. A number of different intuitive control strategies can be used to achieve each of these five objectives. Further, each strategy can be implemented in a variety of ways. We present several strategies for each objective which we have implemented on a bipedal walking robot. Using these simple intuitive strategies, we have compelled a seven link planar bipedal robot, called Spring Flamingo, to walk. The robot walks both slowly and quickly, walks over moderate obstacles, starts, and stops.

Capturability-based analysis and control of legged locomotion, Part 2: Application to M2V2, a lower-body humanoid

This two-part paper discusses the analysis and control of legged locomotion in terms of N-step capturability: the ability of a legged system to come to a stop without falling by taking N or fewer steps. We consider this ability to be crucial to legged locomotion and a useful, yet not overly restrictive criterion for stability. Part 1 introduced the N-step capturability framework and showed how to obtain capture regions and control sequences for simplified gait models. In Part 2, we describe an algorithm that uses these results as approximations to control a humanoid robot. The main contributions of this part are (1) step location adjustment using the 1-step capture region, (2) novel instantaneous capture point control strategies, and 3) an experimental evaluation of the 1-step capturability margin. The presented algorithm was tested using M2V2, a 3D force-controlled bipedal robot with 12 actuated degrees of freedom in the legs, both in simulation and in physical experiments. The physical robot was able to recover from forward and sideways pushes of up to 21 Ns while balancing on one leg and stepping to regain balance. The simulated robot was able to recover from sideways pushes of up to 15 Ns while walking, and walked across randomly placed stepping stones.

Stiffness Isn't Everything

Most robot designers make the mechanical interface between an actuator and its load as stiff as possible[9][10]. This makes sense in traditional position-controlled systems, because high interface stiffness maximizes bandwidth and, for non-collocated control, reduces instability. However, lower interface stiffness has advantages as well, including greater shock tolerance, lower reflected inertia, more accurate and stable force control, less damage during inadvertent contact, and the potential for energy storage. The ability of series elasticity (usually in the form of a compliant coating on an end-effector) to stabilize force control during intermittent contact with hard surfaces is well known. This paper proposes that for natural tasks where small-motion bandwidth is not of paramount concern, actuator to load interfaces should be significantly less stiff than in most present designs. Furthermore, by purposefully placing the majority of interface elasticity inside of an actuator package, a new type of actuator is created with performance characteristics more suited to the natural world. Despite common intuition, such a series-elastic actuator is not difficult to control.

Virtual actuator control

Robots typically have an individual actuator at each joint which can result in a nonintuitive and difficult control problem. In this paper we present a control method in which the real joint actuators are used to mimic virtual actuators which can be more intuitive and hence make the control problem more straightforward. Our virtual actuator control method requires a solution to the force distribution problem when applied to parallel mechanisms. An extension of Gardners partitioned actuator set control method (1991) is presented. This extended method allows for dealing with constrained degrees of freedom in which the torque cannot be specified but can be measured. A simulated hexapod robot was developed to test the proposed control method. The virtual actuators allowed textbook control solutions to be used in controlling this highly nonlinear, parallel mechanism. Using a simple linear control law, the robot walked while simultaneously balancing a pendulum and tracking an object.

Series Elastic Actuators for legged robots

Series Elastic Actuators provide many benefits in force control of robots in unconstrained environments. These benefits include high force fidelity, extremely low impedance, low friction, and good force control bandwidth. Series Elastic Actuators employ a novel mechanical design architecture which goes against the common machine design principal of stiffer is better. A compliant element is placed between the gear train and driven load to intentionally reduce the stiffness of the actuator. A position sensor measures the deflection, and the force output is accurately calculated using Hooke’s Law (F=Kx). A control loop then servos the actuator to the desired output force. The resulting actuator has inherent shock tolerance, high force fidelity and extremely low impedance. These characteristics are desirable in many applications including legged robots, exoskeletons for human performance amplification, robotic arms, haptic interfaces, and adaptive suspensions. We describe several variations of Series Elastic Actuators that have been developed using both electric and hydraulic components.

Stable adaptive control of a bipedal walking; robot with CMAC neural networks

We present a stable adaptive control approach for a bipedal walking robot. This approach utilizes a self-organizing CMAC neural network mechanism which has a fast training rate, high approximation accuracy and significant reduction in space complexity. In order to apply this control approach to a bipedal walking robot, a Cartesian virtual dynamics space is introduced based on the virtual model control concept. The adaptive CMAC neural network control approach identifies the unmodelled dynamics of the bipedal robot and ensures asymptotic system stability in a Lyapunov sense. It can also better accommodate unexpected external disturbances, enhancing the control robustness of the bipedal robot. The CMAC neural network structure, its training algorithm, and bipedal locomotion control are described. The simulation results for a walking robot are presented.