Coordinate transformation as a help for controller design in walking robots

For walking robots, the robot’s absolute position must be re- flected in the state. Usually one chooses to include the pose and velocity of the torso in the state (i.e., the torso is taken as the reference body). However, sometimes it is useful to choose a different reference body; in particular the stance foot is a good choice

Control of walking robots using virtual springs

At the Control Engineering group of the University of Twente, we are conducting research on control of bipedal robots. In our search for robust and energy efficient control, we are making extensive use of simulation. In order to facil- itate the development of algorithms, we want to design con- trollers that work in a space of “meaningful variables”; i.e. we don’t control joint angles directly but we control things as “position and velocity of center of mass”, “shape of the robot’s locked inertia ellipsoid” [1] and “foot position”

Realisation of an energy efficient walking robot

In this video the walking robot ‘Dribbel’ is presented, which has been built at the Control Engineering group of the University of Twente, the Netherlands. This robot has been designed with a focus on minimal energy consumption, using a passive dynamic approach. It is a so-called four-legged 2D walker; the use of four legs prevents it from falling sideways. During the design phase extensive use has been made of 20-sim. This power port based modeling package was used to simulate the dynamic behaviour of the robot in order to estimate the design parameters for the prototype. The parameters obtained by the simulation were then used as a basis for the real robot. The real robot is made of aluminum and weighs 9.5 kg. Each of the nine joints (one hip, four knees, four feet) has a dedicated electronic driver board for interfacing the joint sensors. For walking a simple control loop is used: when the front feet touch the ground, the rear legs are swung forward. The control parameters can be adjusted online using a serial link. Using this simple control loop, the robot walks at a speed of 1.2 km/h and a step frequency of 1.1 Hz. The hip actuator consumes 6.7 W. The walking behaviour of the robot is very similar to the simulation, regarding both walking motion and power consumption. With the serial link real time data acquisition in the simulation package (running on the PC) is possible. This allows for advanced verification and fine tuning of the control algorithm. The simulation package can also be used directly within the control loop. Future research is planned on energy based control of the walking motion, using impedance control for the hip actuator and design of more advanced (and actuated) foot shapes

An Energy Efficient Knee Locking Mechanism for a Dynamically Walking Robot

In this work, we present the design and the implementation of an innovative knee locking mechanism for a dynamically walking robot. The mechanism consists of a four-bar linkage that realizes a mechanical singularity for locking the knee when the leg is in the extended position. Once extended, the knee remains locked without energy consumption, while unlocking it only costs a small amount of energy. Tests showed that the robot walks robustly and that the energy consumption of the new system is low

Dynamic walking stability of the TUlip robot by means of the extrapolated center of mass

The TUlip robot was created to participate in the teensize league of Robocup. The TUlip robot is a bipedal robot intended for dynamic walking. It has six degrees of freedom for each leg: three for the hip, one for the knee and two for the ankle. This paper elaborates on the algorithm for the sideways control during gait. The algorithm uses the extrapolated center of mass (XcoM) to achieve limit cycle stability. The algorithm is tested in simulation using a linear inverted pendulum and, then, experimentally applied to the TUlip robot. The result is an adaptive behavior of the TUlip robot, promising for future application to legged robot stability

Compact analysis of 3D bipedal gait using geometric dynamics of simplified models

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 re- ducing it to an equivalent single inertial entity called the locked inertia or the composite rigid body inertia. In this paper, we adopt the methods of geometric dynamics to analyze the gait using the locked inertia of the robot. The analysis includes the rolling of a biped on a 3D rigid foot and 3D impacts. An example of numerical optimization of foot shape parameters is shown. Our long-term objective is to develop the theoretical frame- work and to provide the necessary tools for systematic analysis, design, and control of efficient biped robots

Analysis, Control and Design of Walking Robots

In this thesis five research questions are discussed that are related to the development of two-legged (bipedal) walking robots. The research questions are categorized in three main topics: analysis, control and actuation and design. The research questions are: - How can we analyze the behavior of a 2D passive dynamic walker that is walking on rough terrain? -- An extension to the Poincare̿ mapping is proposed that allows the use of this method on non-flat terrain. - By looking at the robot from a different 'perspective', can we gain more insight in its dynamics? -- The use of coordinate transformations is discussed, a coordinate-free interpretation of the Zero-Moment Point is given and an analysis of a simplified model of the robot (the 'locked inertia model') is given. - How can we control a walking robot in order to stabilize it in the lateral (sideways) direction? -- A linear controller which takes advantage of some specific properties of the robot model is introduced, and experimental results of the 'extrapolated center of mass' are discussed. - How can we improve the actuators in order to get minimum energy consumption? -- A concept is introduced for a new type of actuator which can store negative work mechanically and re-use it later. - How can we improve the knee and ankle joints of a walking robot? -- New mechanical designs for the knees of the 2D walking robot Dribbel and the ankles of the 3D walking robot TUlip are proposed. Each chapter of this thesis is based on an article which was published at or submitted to a conference

Is the impact of public investment neutral across the regional income distribution?: evidence from Mexico

This paper investigates the contribution of public investment to the reduction of regional inqualities, with a specific application to Mexico. We use quantile regressions to examine the impact of public investment on regional disparities according to the position of each region in the conditional distribution of regional income. Results confirm the hypothesis that regional inequalities can indeed be atrributed to the regional distribution of public investment, where the observed pattern shows that public investment mainly helped to reduce regional inequalities between the richest regions- Aquest article examina la contribució de la inversió pública en la reducció de les desigualats regionals, amb una aplicació específica Mèxic. Utilitzem la regressió quantílica per examinar l'impacte de la inversió pública en reduir les disparitats regional dependent de la posició de cada regió en la distribució condicional de la renda regional. Els resultants confirmen la hipòtesi pel la qual les desigualtats regional poden atribuir-se a la distribució de la inversió pública de manera que ha contribuït a reduir les desigualtats entre les regions més riques

Using time-reversal symmetry for stabilizing a simple 3D walker model

A new method is presented for controlling the lateral foot placement of a simple 3D compass biped model. The method is based on the fact that, in the limit cycle, the gait is time-reversal symmetric and that, after a disturbance, the degree of asymmetry is indicated by a single variable. This variable is used for feedback with a proportional controller. Simulation results show that the controller works very well for a large range of gaits, without any adaptation of the parameter values