Name
Title | ||
|---|---|---|
Design of asymptotically stable walking for a 5-link planar biped walker via optimization |
Abstract | ||
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Closed-loop, asymptotically stable walking motions are designed for a 5-link, planar bipedal robot model with one degree of underactuation. Parameter optimization is applied to the hybrid zero dynamics, a 1-DOF invariant subdynamics of the full robot model, in order to create asymptotically stable orbits. Tuning the dynamics of this 1 DOF subsystem via optimization is interesting because asymptotically stable orbits of the zero dynamics correspond to asymptotically stabilizable orbits of the full hybrid model of the walker. The opti- mization process uses a sequential quadratic program- ming (SQP) algorithm and is able to satisfy kinematic and dynamic constraints while approximately minimiz- ing energy consumption and ensuring stability. This is in contrast with traditional approaches to the design of walking controllers where approximately optimal walk- ing (time-) trajectories are derived and then enforced on the robot using a trajectory tracking controller. ble the natural dynamics of the system. The heart of the method is the application of parameter optimiza- tion to a 1-DOF subsystem of the full hybrid model of the robot, recently developed in (3). In that work, it is shown that the zero dynamics of the swing phase (1) can be made invariant under the impact map, re- sulting in the deflnition of the hybrid zero dynamics, whose stability properties are directly relatable to the stabilizability of the orbits of the full hybrid system. The associated Poincare return map of the hybrid zero dynamics was explicitly computed and shown to be difieomorphic to a scalar, linear-time invariant system, thereby rendering transparent the existence and stabil- ity properties of periodic orbits of the hybrid zero dy- namics. By parameter optimization on the hybrid zero dynamics, kinematic and dynamic constraints can be met while approximately minimizing energy consump- tion. The overall concept is similar to (4), with the difierence that, in conjunction with the general feed- back approach developed in (1,2), an asymptotically stable orbit of the hybrid zero dynamics immediately yields a provably, asymptotically stable orbit in the full hybrid model. The use of optimization in the analysis and design of biped walking motions is not a new concept. Work |
Year | DOI | Venue |
|---|---|---|
2002 | 10.1109/ROBOT.2002.1013706 | Robotics and Automation, 2002. Proceedings. ICRA '02. IEEE International Conference |
Keywords | Field | DocType |
asymptotic stability,closed loop systems,legged locomotion,optimal control,quadratic programming,robot dynamics,robot kinematics,1-DOF invariant subdynamics,5-link planar biped walker,5-link planar bipedal robot model,SQP algorithm,approximate minimization,asymptotically stabilizable orbits,asymptotically stable orbits,asymptotically stable walking design,closed-loop asymptotically stable walking motions,dynamic constraints,dynamics tuning,energy consumption minimization,hybrid zero dynamics,kinematic constraints,parameter optimization,sequential quadratic programming algorithm | Optimal control,Control theory,Robot kinematics,Control engineering,Exponential stability,Quadratic programming,Underactuation,Sequential quadratic programming,Mathematics,Constrained optimization,Stability theory | Conference |
Volume | Issue | Citations |
3 | 1 | 10 |
PageRank | References | Authors |
1.31 | 8 | 2 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| E. R. Westervelt | 1 | 433 | 31.07 |
| J. w. Grizzle | 2 | 2188 | 215.15 |