Real-Time Planning with Primitives for Dynamic Walking over Uneven Terrain

We present an algorithm for receding-horizon motion planning using a finite family of motion primitives for underactuated dynamic walking over uneven terrain. The motion primitives are defined as virtual holonomic constraints, and the special structure of underactuated mechanical systems operating subject to virtual constraints is used to construct closed-form solutions and a special binary search tree that dramatically speed up motion planning. We propose a greedy depth-first search and discuss improvement using energy-based heuristics. The resulting algorithm can plan several footsteps ahead in a fraction of a second for both the compass-gait walker and a planar 7-Degree-of-freedom/five-link walker.Comment: Conference submissio

Bipedial Locomotion Up Sandy Slopes: Systematic Experiments Using Zero Moment Point Methods

Bipedal robotic locomotion in granular media presents a unique set of challenges at the intersection of granular physics and robotic locomotion. In this paper, we perform a systematic experimental study in which biped robotic gaits for traversing a sandy slope are empirically designed using Zero Moment Point (ZMP) methods. We are able to implement gaits that allow our 7 degree-of-freedom planar walking robot to ascend slopes with inclines up to 10°. Firstly, we identify a given set of kinematic parameters that meet the ZMP stability criterion for uphill walking at a given angle. We then find that further relating the step lengths and center of mass heights to specific slope angles through an interpolated fit allows for significantly improved success rates when ascending a sandy slope. Our results provide increased insight into the design, sensitivity and robustness of gaits on granular material, and the kinematic changes necessary for stable locomotion on complex media

Stability analysis and control for bipedal locomotion using energy methods

In this thesis, we investigate the stability of limit cycles of passive dynamic walking. The formation process of the limit cycles is approached from the view of energy interaction. We introduce for the first time the notion of the energy portrait analysis originated from the phase portrait. The energy plane is spanned by the total energy of the system and its derivative, and different energy trajectories represent the energy portrait in the plane. One of the advantages of this method is that the stability of the limit cycles can be easily shown in a 2D plane regardless of the dimension of the system. The energy portrait of passive dynamic walking reveals that the limit cycles are formed by the interaction between energy loss and energy gain during each cycle, and they are equal at equilibria in the energy plane. In addition, the energy portrait is exploited to examine the existence of semi-passive limit cycles generated using the energy supply only at the take-off phase. It is shown that the energy interaction at the ground contact compensates for the energy supply, which makes the total energy invariant yielding limit cycles. This result means that new limit cycles can be generated according to the energy supply without changing the ground slope, and level ground walking, whose energy gain at the contact phase is always zero, can be achieved without actuation during the swing phase. We design multiple switching controllers by virtue of this property to increase the basin of attraction. Multiple limit cycles are linearized using the Poincare map method, and the feedback gains are computed taking into account the robustness and actuator saturation. Once a trajectory diverges from a basin of attraction, we switch the current controller to one that includes the trajectory in its basin of attraction. Numerical simulations confirm that a set of limit cycles can be used to increase the basin of attraction further by switching the controllers one after another. To enhance our knowledge of the limit cycles, we performed sophisticated simulations and found all stable and unstable limit cycles from the various ground slopes not only for the symmetric legs but also for the unequal legs that cause gait asymmetries. As a result, we present a novel classification of the passive limit cycles showing six distinct groups that are consecutive and cyclical

Blind walking of a planar biped on sloped terrain

Thesis (M.S.)--Massachusetts Institute of Technology, Dept. of Mechanical Engineering, 1998.Includes bibliographical references (leaf 66).by Chee-Meng Chew.M.S

Generation and control of locomotion patterns for biped robots by using central pattern generators

This paper presents an efficient closed-loop locomotion control system for biped robots that operates in the joint space. The robot’s joints are directly driven through control signals generated by a central pattern generator (CPG) network. A genetic algorithm is applied in order to find out an optimal combination of internal parameters of the CPG given a desired walking speed in straight line. Feedback signals generated by the robot’s inertial and force sensors are directly fed into the CPG in order to automatically adjust the locomotion pattern over uneven terrain and to deal with external perturbations in real time. Omnidirectional motion is achieved by controlling the pelvis motion. The performance of the proposed control system has been assessed through simulation experiments on a NAO humanoid robot