What is a Control Moment Gyroscope (CMG)?
A basic type of reactionless actuator is an inertia wheel, where the angular momentum due to a spinning flywheel is exchanged from the spinning wheel to the body it is attached to. The inertia wheel and the attached body satisfy the conservation of angular momentum, thus the momentum exchange, or transfer of angular momentum, is done by slowing down the flywheel and accelerating the body. The overall angular momentum of the combined system (inertia wheel plus body) is constant, however the angular momentum is transferred between both bodies due to acceleration and deceleration of the flywheel.

In the case of an inertia wheel, the direction of the angular momentum remains in a fixed by the orientation of the flywheel, thus the torque due to change in angular momentum (by acceleration or deceleration of the flywheel) are also fixed in the same direction.

A CMG is basically an inertia wheel mounted on an actuated gimbal. The primary benefit of a CMG over an inertia wheel is that the output torque is proportional to both the flywheel angular velocity and the angular velocity of the gimbal, thus allowing for larger output torques than the torque required to spin the gimbal (this property is known as “torque amplification”). This provides a great advantage of being able to provide large output torques without the necessity of large actuators.

Figure above:
Left: The CMG device is worn as a backpack. Right: The scissored-pair CMG prototype hardware.

Principle of Tripod Fall:
The center of mass (CoM) of a humanoid robot is a uniquely important point in its dynamics. First of all, it is the effective location of the robot's total mass, and therefore, the point where its aggregate linear momentum is naturally defined. It is also the point through which the resultant gravity force acts. It should then come as no surprise that virtually all reduced humanoid models and control algorithms contain the CoM as an integral component.

Simulation:
A sequence of steps of a typical tripod fall shown as a set of snapshots from high-fidelity dynamic simulation.

Hardware Experiments:

Kinmatic models of single-axis and double-axis trailers:

Figure above:
Model parameters for vehicle–trailer systems consisting of a single-axle (left) and a double-axis (right) trailer. Both vehicles have front-steered wheels. The trailer of the single-axis system is unsteered but the trailer of the double-axis system has rear-steered wheels. The left and right steering angles of the vehicle are determined by Ackermann geometry. The vehicle and trailer are connected via a revolute hitch joint.

Simulation:
A number of ways in which jackknife is defined and characterized.

Why humanoids need fall control strategy?

Safety is a primary concern that must be addressed before humanoid robots can freely exist in interactive human surrounding. Although the loss of balance and fall are rare in typical controlled environments, it will be inevitable in physically interactive environments. Out of a number of possible situations where safety becomes an issue, one that involves a fall is particularly worrisome. Fall from an upright posture can cause damage to the robot itself, to delicate and expensive objects in the surrounding or can inflict injury to a human being. Regardless of the substantial progress in humanoid robot balance control strategies, the possibility of fall remains real, even unavoidable. Yet, only a few comprehensive studies of humanoid fall (encompassing fall avoidance, prediction, and control) have been undertaken in the literature.

A humanoid fall may be caused due to unexpected or excessive external forces, unusual or unknown slipperiness, slope or profile of the ground, causing the robot to slip, trip or topple. In these cases the disturbances that threaten balance are larger than what the balance controller can handle. Fall can also result from actuator, power or communication failure where the balance controller is partially or fully incapacitated. In this paper we consider only those situations in which the motor power is retained such that the robot can execute a prescribed control strategy.

One can ignore the possibility of a fall and wishfully hope that its effects will not be serious. However, failure studies, such as in car crash, have taught us against following this instinct. In fact, planning and simulation of failure situations can have enormous benefits, including system design improvements, and support for user safety and confidence. With this philosophy we closely focus our attention to the phenomenon of humanoid fall and attempt to develop practical control strategies to deal with this undesired and traumatic failure event.

A controller dealing with an accidental fall may have two primary and distinctly different goals: (a) self-damage minimization and (b) minimization of damage to others. When a fall occurs in an open space, a self-damage minimization strategy can reduce the harmful effects of the ground impact. If, however, the falling robot can damage nearby objects or injure persons, the primary objectivewould be to prevent this. The current paper reports a control strategy for changing the default fall direction of the robot so that it avoids contact with surrounding objects or people as a means of minimizing damage to others. Recently, Wilken et al. (2009) have reported a third possible goal of a fall controller, that of a deliberate fall of a humanoid soccer goalie. This is the case of a strategic fall.

Time is at a premium during the occurrence of a fall; a single rigid body model of a full-sized humanoid indicates that a fall from the vertical upright stationary configuration due to a mild push takes about 800–900 ms (Tan et al. 2006). In many situations the time to fall can be significantly shorter, and there is no opportunity for elaborate planning or timeconsuming control. Yet, through simulation and experiments we are able to demonstrate that meaningful modification to the default fall behavior can be achieved in a very short time and damage to the environment can be avoided.

Figure above:
The Aldebaran NAO robot is pushed from behind by a linear actuator. Its front semicircle is divided into four equal sectors of 45 degree each. Three dolls are placed in three arbitrary sectors while the fourth sector is empty. In four trials, we rearrange the dolls in order to change the location of the empty sector relative to the robot. Under an identical push the robot successfully changes the fall direction in real time and falls into the empty sector to avoid hitting the dolls.

Simulation video:
Click Here


Abstract:
This paper presents a novel whole-body torquecontrol concept for humanoid walking robots. The presented Whole-Body Motion Control (WBMC) system combines several unique concepts. First, a computationally efficient gravity compensation algorithm for floating-base systems is derived. Second, a novel balancing approach is proposed, which exploits a set of fundamental physical principles from rigid multi-body dynamics, such as the overall linear and angular momentum, and a minimum effort formulation. Third, a set of attractors is used to implement movement features such as to avoid joint limits or to create end-effector movements. Superposing several of these attractors allows to generate complex wholebody movements to perform different tasks simultaneously. The modular structure of the proposed control system easily allows extensions. The presented concepts have been validated both in simulations, and on the 29-dofs compliant torque-controlled humanoid robot COMAN. The WBMC has proven robust to the unavoidable model errors.

Features:

Figure above:
The behavior of the WBMC system is not always easy to predict. The torques generated by the MinEff (minimum effort) attractor in the case of a 2-link fixed-base robot, for instance, aim to bring the robot to a vertical position when gravity is the only external force acting on the robot, as shown in case (a) in the above figure. If another external force is applied as in case (b), instead, the MinEff locally searches for a configuration that minimizes all external disturbances. See the paper for other cases, c), d), and e), which are shown above.

Figure above:
We see snapshots from the video of the experimental validation of the WBMC with the COMAN robot (taken at 2Hz). In this case the robot configuration is perturbed by forcing the waist roll joint to change its angle. As the robot is released the MinEff (minimum effort) brings the robot back to a vertical, minimum effort configuration. The resulting motion is damped by the MomJ (joint moment) attractor, that prevents the velocity to grow uncontrolled.

Features:

Centroidal Dynamics:
The center of mass (CoM) of a humanoid robot is a uniquely important point in its dynamics. First of all, it is the effective location of the robot's total mass, and therefore, the point where its aggregate linear momentum is naturally defined. It is also the point through which the resultant gravity force acts. It should then come as no surprise that virtually all reduced humanoid models and control algorithms contain the CoM as an integral component.

In the well-known example of a freely flying multi-link chain, the average behavior of the chain can be adequately described in terms of its CoM. While the dynamics of individual member links can be quite complex, the motion of the CoM follows a point-mass projectile profile which can be easily described and communicated. Additionally, the rotational motion of the aggregate chain obeys the conservation of angular momentum about the CoM or, the centroidal angular momentum. For many applications, such reduced description is instrumental in the analysis and control of the system.

In a similar manner, surprisingly deep insight into the dynamics of a humanoid robot can be obtained simply by following the trajectory of its CoM, center of pressure (CoP), and the lean line connecting these two points. This has been known for a long time and has been utilized in the study of human motion. The study of humanoid dynamics has also inherited this trend and a number of progressively complex models, some of which are shown above, are currently used for analysis and control.

Figure above:
A number of progressively complex "inverted pendulum" models, which are currently used for the analysis and control of gait and balance of humanoid robots and humans.

Transformation Diagram:



Figure above:
Transformation diagram showing the relations among the velocities and momenta of a robot. These vector quantities can be expressed in joint space, system space, or the CoM space of the robot. The matrices representing the linear transformations between velocities and momenta in different spaces are also shown in this diagram. The dashed line at the lower left of the diagram represents a minimum kinetic energy transformation, which is not a general transformation.

Simulation:

Figure above:
We tested the momentum-based balance controller by simulating a humanoid robot model. In the simulation experiment the robot is subjected to a push from the lateral direction while standing on a narrow support, which is even slightly narrower than the width the robot's feet. In this environment, the robot must rotate its upper body in order to maintain balance, and our controller based on the centroidal momentum matrix (CMM) creates such a whole body motion in which the whole body segments including the trunk and arms are engaged to create the necessary admissible momentum rate change. We see a series of snapshots illustrating when the robot is subjected to an external push which is applied at the robot's CoM in the lateral direction from the robot's right side.

Simulation video:
Click Here


Abstract:
Safety and robustness will become critical issues when humanoid robots start sharing human environments in the future. In physically interactive human environments, a catastrophic fall is a major threat to safety and smooth operation of humanoid robots. It is therefore imperative that humanoid robots be equipped with a comprehensive fall management strategy. This paper deals with the problem of reducing the impact damage to a robot associated with a fall. A common approach is to employ damage-resistant design and apply impact-absorbing material to robot limbs, such as the backpack and knee, that are particularly prone to fall related impacts. In this paper, we select the backpack to be the most preferred body segment to experience an impact. We proceed to propose a control strategy that attempts to re-orient the robot during the fall such that it impacts the ground with its backpack. We show that the robot can fall on the backpack even when it starts falling sideways. This is achieved by generating and redistributing angular momentum among the robot limbs through dynamic coupling. The planning and control algorithms for fall are demonstrated in simulation.

Features:

Simulation:

Figure above (no controller):
An external force applied at the CoM of the robot to its left makes the robot fall. The robot locks all the joints without triggering the fall controller. It falls sideways, and can get badly damaged.

Figure above (with controller):
With our "fall on backpack" fall control strategy, the humanoid can successfully touch the ground with the backpack under the same push force as above. The assumption is that the design of the backpack is able to better survive an impact than other parts of the robot. The top, middle, and bottom rows show the side, top, and front views, respectively, of the simulation.

Simulation video:
Click Here

Abstract:
Recent research suggests the importance of controlling rotational dynamics of a humanoid robot in balance maintenance and gait. In this paper, we present a novel balance strategy that controls both linear and angular momentum of the robot. The controller's objective is defined in terms of the desired momenta, allowing intuitive control of the balancing behavior of the robot. By directly determining the ground reaction force (GRF) and the center of pressure (CoP) at each support foot to realize the desired momenta, this strategy can deal with non-level and non-stationary grounds, as well as different frictional properties at each foot-ground contact. When the robot cannot realize the desired values of linear and angular momenta simultaneously, the controller attributes higher priority to linear momentum at the cost of compromising angular momentum. This creates a large rotation of the upper body, reminiscent of the balancing behavior of humans. We develop a computationally efficient method to optimize GRFs and CoPs at individual foot by sequentially solving two small-scale constrained linear least-squares problems. The balance strategy is demonstrated on a simulated humanoid robot under experiments such as recovery from unknown external pushes and balancing on non-level and moving supports.

Features:

Overview of Momentum-Based Balance Controller.

Simulation:

Figure above:
Given a forward push, the balance controller controls both linear and angular momentum, and generates a motion comparable to human's balance control behavior. The robot is standing on stationary level platforms.

Figure above:
The single-supported robot on stationary level support successfully recovers from a leftward push.

Figure above:
The two supports translate forward and backward with the same speed. In order to maintain balance, the robot rotates its trunk in a periodic manner. The red arrows indicate the direction and magnitude of the linear momentum of the robot. Note that the two feet of the robot have different ankle angles to conform to the different slopes of the moving platforms.

Figure above:
The robot maintains balance on moving supports. The two foot support surfaces have different inclination angles and out of phase front-back velocities.

Abstract:
Backing-up of articulated vehicles poses a difficult challenge even for experienced drivers. While long wheelbase dual-axle trailers provide a benefit of increased capacity over their single-axle counterparts, backing-up of such systems is especially difficult. We propose a control strategy for such systems, introducing concepts of the hitch control space and no-slip curve derived from no-slip kinematics, allowing backing-up maneuvers to be intuitive to drivers without experience with trailers. Using hitch angle feedback, we show these concepts can be used to stabilize the trailer in back-up motion in the presence of arbitrary driver inputs. The controller is tested in simulation and on a scale model testbed, demonstrating that robust and stable backing-up of such systems can be achieved whilst allowing the driver to maintain full control of the vehicle.

The paper introduces 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.

Features:

Figure above:
Conceptual view of the state space of a hybrid dynamic system. Several N-step viable-capture basins are shown. The boundary between two N-step viable-capture basins is part of a step surface. The infinity-step viable-capture basin approximates the viability kernel. Several evolutions are shown: a) an evolution starting outside the viability kernel inevitably ends up in the set of failed states; b) the system starts in the 1-step viable-capture basin, takes a step, and comes to a rest at a fixed point inside the set of captured states (i.e. the 0-step viable-capture basin); c) an evolution that eventually converges to a limit cycle; d) an evolution that has the same initial state as c), but ends up in the set of failed states because the input u(.) was different; e) impossible evolution: by definition, it is impossible to enter the viability kernel if the initial state is outside the viability kernel.

Figure above:
a) A conceptual representation of the N- step capture regions for a human in a captured state (standing at rest). b) N-step capture regions for a running human. The capture regions have decreased in size and have shifted, as compared to a). c) N-step capture regions for the same state as b), but with sparse footholds (e.g. stepping stones in a pond). The set of failed states has changed, which is re ected in the capture regions.

Figure above:
Schematic representations of a 3D-LIPM (Linear Inverted Pendulum Model) with point foot, a 3D-LIPM with finite-sized foot and a 3D-LIPM with finite-sized foot and reaction mass with a non-zero mass moment of inertia tensor.