Task 6: Dynamic, energy conserving, bipedal walking


The next exploratory stage in robotics is the humanoid robots, which has actualized the earlier cultivated walking research areas. Robots that walk in a human-like manner are a fascinating topic of the research. The potential benefits range from service robots, robots for entertainment, or via insights in the control of complex dynamical systems to knowledge for the restoration of damaged human locomotion. The walking algorithms are well researched and multiply demonstrated. The newly arisen actuality of the field is due to the recent questioning of the earlier approaches, by demonstrating the passive dynamic walking mechanisms. This naturally raised expectation for utilizing like ideas for the energy efficient walking. Actuated dynamic walking as opposite to the passive dynamic walking is meant to make the mechanism controllable while the mechanism itself is constructed so that the effects making the passive dynamic walking possible would as much as possible contribute to an energy efficient bipedal locomotion. From these the objectives of our research can be directly derived since practically no such device has been demonstrated yet though in theory it is very much doable. The reason for this is that with no previous employed approaches this task is possible. First of all, no satisfactory mechanisms have been built or proposed, secondly, the very much plausible control ideas have not yet been extended to such cases. The development processes of the bipedal mechanisms have been stuck, and basically are all alike. Anthropomorphism in the mechanism design have been raised but not yet solved.

In the Aalto University Department of Automation and Systems Technology, one of the main research topics is service robotics. Service robots are aimed to provide services to humans instead of manufacturing purposes. For instance, they shall autonomously carry out monotonous, dangerous or tedious tasks. Crucial prerequisites for performing services are mobility and autonomy. On flat surfaces, wheels are most efficient however for rough terrain or the anthroposphere (characterized by stairs etc.) the leg locomotion is more advantageous. The control of bipeds is usually more complicated, but they are more flexible in their motion and better adapted to the human environment. The hope of service robotics would be to put robots into new environments that have never before been explored, or into old ones which are hostile to humans. There are also obvious practical benefits to using walking robots for many natural environments that would increase the productivity of such application, for example: they are one of the smallest of all the locomotion robots, easy to carry around and requiring less energy, can access areas that other robots cannot like ladders or very narrow paths and they do not require change in the working environment since they use the same kind of locomotion humans use. Lately in service robotics the main attention has been redirected to the long time autonomy of the mobile robotics platforms. For that, much effort has been made to develop new more efficient electrical powered service robots, aiming to increase their productivity substantially. In that matter, the increase of energy efficiency also reduces environmental impacts that can help industries to fulfill new and stricter environmental regulation applied worldwide. To accomplish the previous tasks one of the main challenges is to obtain an efficient dynamic bipedal locomotion, which will render in a more useful walking robot in real life applications, as opposed to the static form of locomotion demonstrated by most of the current prototypes. A promising concept is the idea of passive dynamic walking where even completely unactuated and uncontrolled mechanisms can perform a stable gait when walking down a small slope. This concept could enable the construction of dynamically walking prototypes that are simpler yet more natural and efficient in their motions than the static bipeds.

Expected results

In the course of the project the following goals are aimed at:

1) a mechanical concept for the biped and its design
2) conventional algorithms to control the biped
3) advanced algorithms for improved energy efficiency
4) discussion in modeling issues, dynamical model presentation, flexibility in dynamical model

State of the art

Short summary of human walking research history

Although biped locomotion has been studied for a long time, it is only in the past twenty years, thanks to the fast development of computers, that real robots started to walk on two legs. Since then the problem has been tackled from different directions. First, there were robots that used static walking [5]. The control architecture had to make sure that the projection of the center of gravity on the ground was always inside the foot support area. This approach was abandoned because only slow walking speeds could be achieved, and only on flat surfaces. Then, dynamic walking robots appeared [13]. In this approach the centre of gravity can be outside of the support area, but the Zero Momentum Point (ZMP), which is the point where the total angular momentum is zero, cannot. Dynamic walkers can achieve faster walking speeds, running, stair climbing [14], [6], execution of successive flips [2], and even walking with no actuators [8].

The first dynamic walkers used the following architecture. First, the user supplies a command that represents the desired walking pattern. Then, a dynamic model of the biped, which is usually a simplified inverted pendulum model, determines the foot and center of gravity positions. The desired joint angles are obtained using the biped’s inverse kinematics model, and a linear feedback controller makes the robot joints follow the desired trajectories (Figure 1). The model used here is referred to as foot model because it uses foot positions as control action.

Later, another architecture that uses a Central Pattern Generator (CPG) appeared [1]. The biped model and the inverse kinematics model in the previous architecture are replaced by a CPG that generates periodic signals that represent the desired joint trajectories (Figure 2). The model used here is referred to as leg model because it focuses on leg movements.

These descriptions show only the general structure, while the actual implementations involve more complex control methods.

Another advances in biped locomotion was the introduction of neural networks and learning[9],[10],[11],[16]. With these methods, it is not necessary to know the robot’s exact dynamic model, the walker can find solutions that the user cannot think of in advance, and it can adapt to environment changes

Current status of the field

Over the past few years, two Japanese companies have unveiled walking robots that set new standards in competence, Honda and Sony. The Honda Humanoid-Type biped robots were the first free-roaming biped robots that the world had seen. The latest version of ASIMO includes actions like walking, turning, pushing a cart, climbing stairs and also running, all without any human intervention. They are fully self-contained, including on-board batteries; however they can only operate for about one hour in a typical indoor human environment, a time period that is of very little use for industrial or real life task applications.

However, so far almost all the solutions that have actually been implemented in hardware have one aspect in common. They all take a view of walking as a rigid and defined sequence of events meaning that it concentrates on placing the legs in the right place at the right time according to a predefined algorithm, this is the previously mention static walking.

As state before, probably the most obvious problem with static walking systems is that they are extremely slow moving. Asimo represents the state-of-the-art and yet it can only manage about 2,7km/h. There is another major problem with the static approach; namely that it consumes great amounts of energy in the basic walking motion, for instance Asimo consumes about 10 times as much power as a walking human. That way an alternative would be to make robots that walk more efficiently in terms of energy consumption.

These have lead to a new wave in dynamic walking solutions, one approach that was first pioneered by [13] and then widely expose in its passive version by McGeer [8],[7]. McGeer demonstrated that a four bar mechanism in the shape of the skeleton of the lower half of the human body could walk unaided down a slight incline. As long as the lengths and masses of the various components were correctly tuned, a simple pendulum motion is enough to produce very fluid and human-like walking. Curved feet complete the control by self-correcting for any mild perturbations. This approach is now known as McGeer's theory of passive dynamic bipedal locomotion, were the gait is simply a “natural repetitive motion of a dynamical system” [7],[8].

The advantage of this system is that it consumes minimal energy and requires no computer control for normal walking on flat surface; however the disadvantage of the plain skeleton is that it is good for nothing else. So what has been the focus of the attention lately is trying to find the means of reconciling both a passive and a dynamic aspect in the same system. For that reason, currently, one of the major challenges for research on human-like walking robots is to move gradually from static walking to dynamic walking.

Concept of both will be presented next, however the bigger insight will be given to dynamic waling since this appears to be the best performing method.

Samples of the existing biped robots and studies

This section presents a brief description of some biped locomotion realizations and studies made in this area.

In term of university in general one of the most highly praised by its work in this field is the Japanese Waseda University and a complete revision of his work history can be found in: Regarding individual works in this field there are several that are worth mentioning, for example Miller’s biped [11] uses a basic Central Pattern Generator (CPG) to generate desired joint positions according to user supplied commands. This CPG consists of a set of controllers. The CPG’s output is determined by a set of parameters that a Cerebellar Model Arithmetic Computer (CMAC [19]) neural network learns in order to achieve stable dynamic walking. By monitoring the differences between left and right, and front and back foot forces, the CMAC can determine whether the walking is stable or not. The CPG’s user supplied input commands represent the desired walking pattern: step length, step interval, and lift magnitude. Another CMAC learns kinematically consistent postures to ensure reasonable joint position commands. The biped can successfully walk on flat surfaces relying only on very simple dynamics and kinematics models.

The well known Asimo [17], use an approach that generate detailed joint trajectories offline using dynamic optimization algorithms that observe dynamic limitations. These trajectories are then tracked using simple high-impedance PD control laws. However, this approach is not very robust to disturbances, since it depends on close tracking of the reference trajectories. If a disturbance occurs, tracking error can easily become too large due to actuation limits related to imperfect ground contact and the system can lose its balance [18].

Bay and Hemami [1] use coupled Van Der Pol oscillators as a CPG. The parameters of these oscillators govern the magnitude, frequency, and offset of each oscillator. Additional parameters are used to couple the individual oscillators together to make them excite or inhibit each other, and work in a synchronized manner. By choosing the appropriate set of parameter values (mostly using trial and error), the oscillators generate signals that are used as desired joint trajectories for a biped walking robot. Different sets of parameter values can achieve different walking patterns. Zheng [16] uses a knowledge base where a few CPG trajectories are stored. The biped detects the floor’s slope using its foot sensors, and looks in the knowledge base for a corresponding pattern. If one exists it uses it, otherwise, it chooses the closest pattern and uses a neural network to modify it to suit the new terrain. Once the new pattern has been learned, it is stored in the knowledge base. With this method the robot learns to walk on flat and variably slopping surfaces. Zheng distinguishes between two types of behavior. When the walker finds a familiar terrain it uses an existing pattern, and does not need feedback. This is called voluntary motion. If the terrain, however, is not familiar the walker needs feedback in order to adjust its joint positions. This is called reflexive motion. Wagner et al. [15] use a slightly different approach. They find a set of optimal solutions through simulation and store them in a knowledge base. These solutions are invoked during walking and modified according to sensory inputs.

Stitt and Zheng [12] apply distal learning [3],[4] to control a biped. This method incorporates a forward model of the robot dynamics and uses it to convert stability information into information on how to adjust the robot’s joints so as to regain stability. In distal supervised learning the correct joint position is unknown. However, target values for the outcome of adjusted joint positions are known (i.e. foot forces). If the gait is adequate, the feet will provide a stable support. Thus a desired foot force trajectory is known. This is called a distal variable. When the robot walks using the wrong gait, the unbalanced condition will be sensed by foot force sensors. A neural network is trained to learn the relationship between the joint adjustments and the foot forces. Miller et al. [9],[10] use a similar approach to control a robot arm. A CMAC neural network learns the inverse model of the robot, and generates the appropriate command to track a desired trajectory.


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Planned publications

Mechanics; System description; Walking experiments with the robot


Doctoral Dissertation (Peralta)