A Simple Algorithm for Generating Stable Biped Walking Patterns
Wen-Hong Zhu2014, International Journal of Computer Applications
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Abstract
This paper proposes a thorough algorithm that can tune the walking parameters (hip height, distance traveled by the hip, and times of single support phase SSP and double support phase DSP) to satisfy the kinematic and dynamic constraints: singularity condition at the knee joint, zero-moment point (ZMP) constraint, and unilateral contact constraints. Two walking patterns of biped locomotion have been investigated using the proposed algorithm. The distinction of these walking patterns is that the stance foot will stay fixed during the first sub-phase of the DSP for pattern 1, while it will rotate simultaneously at beginning of the DSP for pattern 2. A seven-link biped robot is simulated with the proposed algorithm. The results show that the proposed algorithm can compensate for the deviation of the ZMP trajectory due to approximate model of the pendulum model; thus balanced motion could be generated. In addition, it is shown that keeping the stance foot fixed during the first sub-phase of the DSP is necessary to evade deviation of ZMP from its desired trajectory resulting in unbalanced motion; thus, walking pattern 1 is preferred practically.
Key takeaways
- Static stability restricts the biped center of gravity (COG) to be inside the support polygon represented by the stance foot during single support phase (SSP) and the bounded area between the support feet during double support phase (DSP) [3].
- The parameter can govern the continuity of the biped motion through the following equation (6) Every value of has corresponding value of (time of DSP) which cannot be determined arbitrary.
- In effect, interpolation of the foot trajectory during the constrained DSP, can result in discontinuity in velocity/acceleration at the transition instances.
- Since the biped robot does not have a unique solution during the DSP, we assume a linear transition function for the ground reaction forces of the front foot (right foot) as follows [7] (18) where , denote the absolute time of the SSP and DSP respectively, is the mass of the center of gravity and represents the acceleration of the biped COG.
- We selected initial parameters for our biped model ( ; here and represent local time of the SSP and the DSP respectively.
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