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Design of Continuous and Time-Invariant Controllers for Exponential Stabilization of Periodic Walking and Running Locomotion in Planar Bipedal Robots

Akbari Hamed, Kaveh | 2011

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  1. Type of Document: Ph.D. Dissertation
  2. Language: Farsi
  3. Document No: 41857 (05)
  4. University: Sharif University of Technology
  5. Department: Electrical Engineering
  6. Advisor(s): Sadati, Nasser
  7. Abstract:
  8. During the last decades there have been enormous advances in robot control of dynamic walking and running. The desire to study legged locomotion has been motivated by 1) the desire to replace humans in hazardous occupations, 2) the desire to assist disabled people to walk and 3) the desire to investigate the complicated motions of the mankind. The control of dynamic walking and running is complicated by (i) limb coordination, (ii) hybrid nature of running due to presence of impact and takeoff, (iii) underactuation and overactuation, (iv) inability to apply the Zero Moment Point (ZMP) criterion, (v) lack of algorithms to achieve feasible period-one orbits, and (vi) conservation of angular momentum about the robot’s center of mass (COM) during flight phases. The main objective of this dissertation is to present analytical approaches for design of continuous and time-invariant feedback laws to exponentially stabilize periodic orbits during walking, consisting of single and double support phases, and running, consisting of stance and flight phases, for planar bipedal robots or planar and spatial monopedal robots. Models describing the evolution of mechanical systems during walking and running are represented by hybrid systems consisting of continuous and discrete phases. The proposed control strategies are developed based on differential geometry, Poincaré return map and online nonholonomic motion planning algorithms. In particular, the control schemes are hybrid and employed at two levels. At the first level, within-stride controllers are employed which are continuous, time-invariant and parameterized feedback laws to create a family of finite-time attractive and forward invariant manifolds during the corresponding continuous phase. At the second level, parameters of the within-stride controllers are updated by event-based update laws (i.e., in a stride-to-stride manner) for hybrid invariance and stabilization. Hybrid invariance introduces a reduced-order hybrid model of walking or running for which stability behaviors of the periodic orbit can be analyzed and modified based on restricted Poincaré return maps. Moreover, the angular momentum about the COM is conserved during flight phases of running. To reduce the dimension of the hybrid model describing running, the configuration of the mechanical system should be transferred from a predetermined initial pose (immediately after takeoff) to a predetermined final pose (immediately before impact) during flight phases of running. However, the flight time and angular momentum about the COM may differ during consecutive steps of running. Consequently, the reconfiguration problem should be solved online. In particular, an online nonholonomic motion planning algorithm is proposed in this dissertation to solve the reconfiguration problem for different flight times and angular momentums. The algorithm is based on the reachability and optimal control formulations of a time-varying linear system with input and state constraints
  9. Keywords:
  10. Bipedal Robot ; Two Level Control ; Running ; Walking Robot ; Monopedal Robots ; Exponential Stability ; Poincare Return Map ; Online Nonholonomic Motion Planning Algorithm

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