Foot trajectory approximation using the pendulum model of walking

Generating a natural foot trajectory is an important objective in robotic systems for rehabilitation of walking. Human walking has pendular properties, so the pendulum model of walking has been used in bipedal robots which produce rhythmic gait patterns. Whether natural foot trajectories can be produced by the pendulum model needs to be addressed as a first step towards applying the pendulum concept in gait orthosis design. This study investigated circle approximation of the foot trajectories, with focus on the geometry of the pendulum model of walking. Three able-bodied subjects walked overground at various speeds, and foot trajectories relative to the hip were analysed. Four circle approximation approaches were developed, and best-fit circle algorithms were derived to fit the trajectories of the ankle, heel and toe. The study confirmed that the ankle and heel trajectories during stance and the toe trajectory in both the stance and the swing phases during walking at various speeds could be well modelled by a rigid pendulum. All the pendulum models were centred around the hip with pendular lengths approximately equal to the segment distances from the hip. This observation provides a new approach for using the pendulum model of walking in gait orthosis design

Trajectory generation with natural ZMP references for the biped walking robot SURALP

Bipedal locomotion has good obstacle avoidance properties. A robot with human appearance has advantages in human-robot communication. However, walking control is difficult due to the complex robot dynamics involved. Stable reference generation is significant in walking control. The Linear Inverted Pendulum Model (LIPM) and the Zero Moment Point (ZMP) criterion are applied in a number of studies for stable walking reference generation of biped robots. This is the main route of reference generation in this paper too. We employ a natural and continuous ZMP reference trajectory for a stable and human-like walk. The ZMP reference trajectories move forward under the sole of the support foot when the robot body is supported by a single leg. Robot center of mass (CoM) trajectory is obtained from predefined ZMP reference trajectories by Fourier series approximation. We reported simulation results with this algorithm in our previous works. This paper presents the first experimental results. Also the use of a ground push phase before foot take-offs reported in our previous works is tested first time together with our ZMP based reference trajectory. The reference generation strategy is tested via walking experiments on the 29 degrees-of-freedom (DOF) human sized full body humanoid robot SURALP (Sabanci University Robotics Research Laboratory Platform). Experiments indicate that the proposed reference trajectory generation technique is successful

Pattern Generation for Walking on Slippery Terrains

In this paper, we extend state of the art Model Predictive Control (MPC) approaches to generate safe bipedal walking on slippery surfaces. In this setting, we formulate walking as a trade off between realizing a desired walking velocity and preserving robust foot-ground contact. Exploiting this formulation inside MPC, we show that safe walking on various flat terrains can be achieved by compromising three main attributes, i. e. walking velocity tracking, the Zero Moment Point (ZMP) modulation, and the Required Coefficient of Friction (RCoF) regulation. Simulation results show that increasing the walking velocity increases the possibility of slippage, while reducing the slippage possibility conflicts with reducing the tip-over possibility of the contact and vice versa.Comment: 6 pages, 7 figure

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

Orbit Characterization, Stabilization and Composition on 3D Underactuated Bipedal Walking via Hybrid Passive Linear Inverted Pendulum Model

A Hybrid passive Linear Inverted Pendulum (H-LIP) model is proposed for characterizing, stabilizing and composing periodic orbits for 3D underactuated bipedal walking. Specifically, Period-l (P1) and Period -2 (P2) orbits are geometrically characterized in the state space of the H-LIP. Stepping controllers are designed for global stabilization of the orbits. Valid ranges of the gains and their optimality are derived. The optimal stepping controller is used to create and stabilize the walking of bipedal robots. An actuated Spring-loaded Inverted Pendulum (aSLIP) model and the underactuated robot Cassie are used for illustration. Both the aSLIP walking with PI or P2 orbits and the Cassie walking with all 3D compositions of the PI and P2 orbits can be smoothly generated and stabilized from a stepping-in-place motion. This approach provides a perspective and a methodology towards continuous gait generation and stabilization for 3D underactuated walking robots