Active walking robot mimicking flat-footed passive dynamic walking

Many legged robots have been developed, and some of them have already achieved dynamically stable bipedal and quadruped locomotion. Common characteristics of these conventional legged robots are that their motions are precisely manipulated by their control (i.e., gait and balance). In the case of ASIMO (Hirose et al., 2001) and HRP2 (Kaneko et al., 2004), their dynamically stable bipedal locomotion is based primarily on the Zero Moment Point (ZMP) concept, which was originally developed by Vukobratovic (Vukobratovic, 1969): the ZMP is a fictitious point on the ground plane, where the torques around the (horizontal) x and y axes (generated by ground reaction forces, inertial forces, and torques) are equal to zero. These robots dynamically stabilize their balance by manipulating the ZMP to remain within the support polygon area defined by their square feet, and their gait control is applied on top of the balance control. As a result, these conventional legged robots require rapid information processing and high-power drives to achieve locomotion. Therefore, they are characterized as having more complex control systems and larger energy consumption than those of biological locomotion. On the other hand, these design requirements (i.e., fast information processing and highpower drives) are regarded as disadvantageous in biologically inspired robotics. In the field, the specific behaviors and/or structures of biological organisms are imitated (Vogel, 1998) (Alexander, 2002) with robotic technology. As a result, the robot systems have simple design requirements compared to conventional robot systems, and achieve complex tasks. Thus, the design effort tends to focus on control complexity and energy requirements. A representative instance is the Passive Dynamic Walker (PDW), which was originally developed by McGeer (McGeer, 1990). The PDW has no controller (i.e., no sensor and no motor), and the structure is based on the physical characteristics of human walking: passive hip joints, latch knee joints, and curved feet. The PDW walks down a slope, and its structure exploits gravity as the driving force. This design principle has been applied to the Cornell Biped (Collins & Ruina, 2005) and Denise at TU Delft (Wisse, 2003), and the powered passive dynamic walkers achieved passive dynamic walking on a flat plane. In a summary of these two approaches, conventional robots require expensive design components to achieve dynamically stable locomotion. On the other hand, biologically inspired robots require physical characteristics that exploit their own dynamics to achieve

Human biped locomotion is an ultimate style of biological movement that is a highly evolved function. Biped locomotion by robots is a dream to be attained by the most highly evolved or integrated technology, and research on this has a history of over 30 years. Many methods of generating gaits have been proposed. There has been a tendency to reduce the complicated dynamics of a walking robot to a simple inverted pendulum (Hemami et al., 1973), and to control its motion according to pre-designed time-dependent trajectories while guaranteeing zero moment point (ZMP) conditions (Vukobratovi & Stepanenko, 1972). Although such approaches have successfully been applied to practical applications and nowadays successful biped-himanoids are developed by them, problems on gait performances still remain. Several advanced approaches on the other hand have taken the robot's dynamics into account for generating gaits based on natural dynamics. Miura and Shimoyama studied dynamic bipedal walking without ankle-joint actuation (Miura & Shimoyama, 1984) and they developed robots on stilts whose foot contact occurred at a point. Sano and Furusho accomplished natural dynamic biped walking based on angular momentum using ankle-joint actuation (Sano & Furusho, 1990). Kajita proposed a method of control based on a linear inverted pendulum model with a potential-energy-conserving orbit (Kajita et al., 1992). These approaches utilized the robot’s own dynamics effectively but did not investigate the energy-efficiency by introducing performance indices. It was unclear whether or not efficient gaits were generated. McGeer's passive dynamic walking (PDW) (McGeer, 1990) has provided clues to solve these problems. Passive-dynamic walkers can walk without any actuation on a gentle slope, and they provide an optimal solution to the problem of generating a natural and energy-efficient gait. The objective most expected to be met by PDW is to attain natural, high-speed energyefficient dynamic bipedal walking on level ground like humans do. However, we need to supply power-input to the robot by driving its joint-actuators to continue stable walking on level ground, and certain methods of supplying power must be introduced. Ankle-joint torque is mathematically very important for effectively propelling the robot's center of mass (CoM) in the walking direction, and it is thus required relatively more often than other joint torques. However, to exert ankle-joint torque on a passive-dynamic walker, we need to add feet and this creates the ZMP constraint problem. We clarified that there is a trade-off between optimal gait and ZMP conditions through parametric studies, and O pe n A cc es s D at ab as e w w w .ite ch on lin e. co m

In this paper, we analysis gaits of 3D quasi-passive walker with flat feet driven by an antagonistic pneumatic artificial muscle. Many bipedal robots have been proposed to realize the high energy efficiency walking. The passive dynamic walking does not require control input. Generally, a foot shape of passive dynamic walking robot is an arc foot. It is intended to establish a control method and walking mechanism to achieve energy efficient and stable gait. Therefore, we developed 3D quasi-passive walker with flat feet. An antagonistic mechanism is constituted by a pair of McKibben muscle. And an antagonistic pneumatic system is used as joint actuators of linkage mechanisms which control the torque, joint stiffness and position simultaneously. This paper shows that the 3D quasi-passive walking in the level ground can realize by the simple swinging (sine) input of the frontal direction, and the stride of the robot is proportional to lateral-plane input. Finally, we examine the structure of an ankle, the control method of an antagonistic pneumatic system and these gaits analysis using COP (Center Of Pressure) and ROS (Roll-Over Shapes).

The aim of this research is to manage the precise and rhythmic movements of a bipedal robot with a compass configuration as it undergoes a passive dynamic walk. To approximate the walking pattern of a biped robot, we implement an impulsive hybrid nonlinear system. To start with, we showcase the fact that a passive walk by a bipedal compass robot can exhibit unexpected behaviors like bifurcations and chaos with the aid of bifurcation diagrams. In order to suppress such complex nonlinear tendencies, we resort to two methods for regulating the bipedal compass-type robot and achieving a one-periodic gait. The control approach used in this study is based on the passive dynamic walking of the biped robot, and the objective is to follow the trajectory of the period-1 passive movement during the swing phase.

The compass-gait biped robot is a two-DoF legged mechanical system that has been known by its passive dynamic walking. This kind of passive biped robot is modeled by an impulsive hybrid nonlinear system that exhibits complex behaviors. This paper is concerned with the stabilization of the passive dynamic walking of the compass-gait biped robot by designing an analytical expression of the controlled Poincare map. The suggested analytical method starts with the time-piecewise linearization of the impulsive system augmented with the controller, around a desired one-periodic passive hybrid limit cycle. By virtue of the first-order Taylor series, we design an explicit expression of the controlled Poincare map. We present also a simplified expression of the controlled Poincare map having a reduced dimension. In order to accomplish our goal concerned with the stabilization of the passive walking dynamics of the compass-gait biped robot, we develop first the linearized Poincare map around the period-1 fixed point of the Poincare map and we adopt a state-feedback control law to stabilize it. Furthermore, in order to enhance the effectiveness and robustness of the stabilization process, we adopt an LMI-based optimization approach by considering the controlled Poincare map to design the feedback gain. In the end of this work, we provide some numerical and graphical simulation results, to show the validity of the designed control law by means of the controlled Poincare map in the stabilization of the passive dynamic walking of the compass-gait biped robot.

This research compares walking over ground, on a split-belt treadmill, on a tied-belt treadmill, and on the Gait Enhancing Mobile Shoe (GEMS) in both humans and simulated on a passive dynamic model. Passive Dynamic Walkers (PDW) have been researched for decades, yet only recently has the model been used significantly in gait rehabilitation. We aim to identify how well the two-dimensional PDW can be used as a kinematic approximation tool for gait analysis. In this work, the PDW was scaled according to an anthropomorphic human model. For comparison, measurements were taken of humans walking in the same four environments. For normal walking, the PDW was found to be a good approximation for symmetric and rhythmic hip position, foot position, and velocity profiles. Tied-belt and split-belt treadmill model estimations revealed that the PDW's lack of dorsiflexion, joint stiffness, and joint damping limited the comparison, however trends between the human and the model agreed. The kinematics of the GEMS showed good agreement in interlimb interactions indicating that the PDW can be used as a good kinematic predictor for the GEMS.

Passive dynamic walking is a manner of walking developed, partially or in whole, by the energy provided by gravity. Studying passive dynamic walking provides insight into human walking and is an invaluable tool for designing energy efficient biped robots. The objective of this research was to develop a continuous mathematical model of passive dynamic walking, in which the Hunt-Crossley contact model and the LuGre friction model were used to represent the normal and tangential ground reactions. A physical passive walker was built to validate the proposed mathematical model. A traditional impact-based passive walking model was also used as a reference to demonstrate the advancement of the proposed passive dynamic walking model. The simulated gait of the proposed model matched the gait of the physical passive walker exceptionally well, both in trend and magnitude.

Animals, including human beings, can travel in a variety of environments adaptively. Legged locomotion makes this possible. However, legged locomotion is temporarily unstable and finding out the principle of walking is an important matter for optimum locomotion strategy or engineering applications. As one of the challenges, passive dynamic walking has been studied on this. Passive dynamic walking is a walking phenomenon in which a biped walking robot with no actuator walks down a gentle slope. The gait is very smooth (like a human) and much research has been conducted on this. Passive dynamic walking is mainly about bipedalism. Considering that there are more quadruped animals than bipeds and a four-legged robot is easier to control than a two-legged robot, quadrupedal passive dynamic walking must exist. Based on the above, we studied saggital plane quadrupedal passive dynamic walking simulation. However, it was not enough to attribute the result to the existence of quadrupedal passive dynamic walking. In this research, quadrupedal passive dynamic walking is experimentally demonstrated by the four-legged walking robot 'Quartet 4'. Furthermore, changing the type of body joint, slope angle, leg length and variety of gaits (characteristics in four-legged animals) was observed passively. Experimental data could not have enough walking time and could not change parameters continuously. Then, each gait was analyzed quantitatively by the experiment and three-dimensional simulation.

Reinforcement learning for quasi-passive dynamic walking of an unstable biped robot

Passive dynamic walking refers to the dynamical behavior of mechanical devices that are able to naturally walk down a shallow slope in a stable manner, without using actuation or sensing of any kind. Such devices can attain motions that are remarkably human-like by purely exploiting their natural dynamics. This suggests that passive dynamic walking machines can be used to model and study human locomotion; however, there are two major limitations: they can be difficult to design, and they cannot walk on level ground or uphill without some kind of actuation. This thesis presents a mechanism design optimization framework that allows the designer to find the best design parameters based on the chosen performance metric(s). The optimization is formulated as a convex problem, where its solutions are globally optimal and can be obtained efficiently. To enable locomotion on level ground and uphill, this thesis studies a robot based on a passive walker: the rimless wheel with an actuated torso. We design and validate two control policies for the robot through the use of scalable methodology based on tools from mathematical analysis, optimization theory, linear algebra, differential equations, and control theory.

The objective of this project was to geometrically model and create a miniature robot that can walk on two feet and to test the feasibility of using the Holy Numbers in future bipedal robots. The purpose was to imitate human motion and to take advantage of the benefits of bipedalism, such as flexibility in terms of accessible terrain, the ability to add on arm-like limbs and prosthetics to neuromuscularly tmpaired humans. The structure of the small-scale bipedal robot was based off Theo Jansen's 11 Holy Numbers, a set of ratios between the lengths of parts and connectors used in creating an artificial leg that could replicate the movement of a human teg [1]. Though they are named the “11 Holy Numbers,” there are actually 13 relevant numbers. The two extra numbers deal with the central axis and offset axis that make up the crankshaft, not the actual teg. The Holy Numbers were modified to fit the design of a teg found in a bipedal toy created by Gakken Otonano Kagaku Mook [2]. Since bipedal robots cannot rely on the multi-legged nature of the Strandbeests to ensure balance, the Holy Numbers ratio must be modified to produce the optimal footpath for a bipedal robot. The Holy Numbers have never been applied to bipedal robots, and by doing this, construction of bipedal robots can be made cheaper and more efficient while still being able to harness the existing benefits of bipedalism as stated above. Ultimately, the mechanics of Jansen's Strandbeest can be adapted to utilize the benefits of bipedalism to be applied to foture bipedal robots.

The presented work is motivated to implement the principles of passive dynamic walking (PDW) on the powered bipeds. The Virtual Slope Walking (VSW), as one PWD control approach, is chosen to be mathematically analyzed and realized to achieve fast dynamic walking. Our method of formulating the fixed point of the limit cycle gait is presented, and the walking pattern generation is designed in the polar coordinate for the better consistency with the model. The algorithms are implemented on a planar robot Stepper-2D, which achieved the walking speed from 0.69m/s upto 1.03m/s. The self-stabilized walking has the best robustness at the speed of 0.81m/s, where the robot was able to walk on the level ground, step over random obstacles smaller than 4% of the leg length, and step over a big obstacle of 7.2% of the leg length.

A passive dynamic walking robot that has a deterministic nonlinear gait

This paper presents the gait generation and mechanical design of a humanoid robot based on a limit cycle walking method-Virtual Slope Control. This method is inspired by Passive Dynamic Walking. By shortening the swing leg, the robot walking on level ground can be considered as on a virtual slope. Parallel double crank mechanisms and elastic feet are introduced to the 5 DoF robot leg, to make the heelstrike of the swing leg equivalent to the point-foot collision used in Virtual Slope Control. In practical walking, the gait is generated by connecting the two key frames in the sagittal and lateral plane with sinusoids. With the addition of leg rotational movement, the robot achieves a fast forward walking of 2.0leg/s and accomplishes omnidirectional walking favorably.

SUMMARYThis paper presents a bipedal locomotion model for passive dynamic walking with flat feet and compliant ankles. The two-dimensional seven-link model extends the simplest walking model with the addition of hip actuation, knee joints, flat feet and torsional springs based compliance on ankle joints, concerning heel-strike and toe-strike transitions, to achieve adaptive bipedal locomotion on level ground with controllable walking speed. We investigate the effects of foot geometric parameters and ankles stiffness on bipedal walking. The model achieves satisfactory walking results not only on even ground but also on uneven terrain with no active control and on different walking velocities. In addition, from the view of stability, there is an optimal foot-ankle ratio of the passivity-based walker. The results can be used to explore further understanding of bipedal walking, and help the design of future intelligent ankle-foot prosthesis and passivity-based robot prototypes towards more practical uses.