Research On Dynamic Locomotion Control Of Legged Robot Based On Reduced SLIP Model

As the representation of marco biomimeitcs, legged robots target at imitating theconfiguration and locomotion characteristics of animal play an increasingly importantand irreplaceable role in seriels of extreme environment such as hilly transportation,battle field and nuclear site due to its unique structure, agile motion and outstandingterrain adapability. Since the quadruped robot BigDog, WildCat and biped robot Petman,Atlas of Boston Dynamics start to come out, an unprecedented boom for legged robotsdevelopment has been arised in worldwide.Dynamical locomotion control is one of the most challenge issues in legged robots.Due to the complexity of robot structure, high-dimensional nonlinearity of systemdynamics etc, there still exsits a considerable gap between the perfect motionperformance of animlas and the most advanced legged robot at present. On thetheoretical level of dynamical locomotion control, it is extremely difficult to satisfy therigorous requirement of locomotion stability via the traditional methods due to themotion coupling among the degree-of-freedoms (DoFs) and intrinsic nonlinearity of thehigh-dimension robot system. Meanwhile, although the reduced model in low-dimension could to some extent pressure of control system design caused by thedimension and nonlinearity of the system itself, the numerical method with intensivecomputation as an alternative due to lack of analytical approach isolate the inherentconnection between the structure/motion parameter and locomotion performance of themodel, through which the excellent control performance could not be attainedconsequently. Aiming at key fundamental theorectical isssues of legged robot, this paperchooses the classical model which describes dynamical locomotion of animal, namely,the Spring-Loaded Inverted Pendulum (SLIP) as the object in low-dimension motionspace and follows the clues of analyticity of system dynamics and dimension reductionof nonlinear system. The perturbation theory, dynamic inversion as well as apex returnmap has been introduced to completely resolve the motion control of the reduced SLIPmodel in low dimension, on the base of which the corresponding control methodologyhas been extended to legged robot system in high dimension. Therefore, the locomotioncontrol of monopedal, bipedal and quadrupedal robot could be settled concurrently. Inaddition, the theoretical mechanism of embedded SLIP model based locomotion controlof legged robots could be revealed correspondingly. This work could provide solutionsfor improving the overall performance of legged robot in dynamical motion and stability.This paper starts with the reduced SLIP model. On the base of developing an unified SLIP model, the dimensional analysis is introduced to eliminate the redundancyof the structure parameters. Aiming at issue of the second order non-integration causeby nonlinear terms in stance dynamics of complete passive SLIP model, the smallparameter based perturbation technique has been applied to obtain an analyticalapproximations in closed form with explicit mathematical expression. Compared to theexsiting approximations in relevant references, the perturbation solution exhibits higheraccuracy in the apex state prediction of SLIP model. The criterion of stability ofperiodic motion in SLIP model has been accordingly established via the apex returnmap and analysis of the fixed point.Sheding light upon the relationship between the structure/motion parameters andlocomotion performance of SLIP model, the performance specification of SLIP modelincluding the criterion of foot-ground interaction and locomotion stability. The criterionspecification of foot-grouand interaction is composed of the peak value of groundreaction force and ratio of ground reaction force to quantitively describe the conditionof foot-ground interaction. The criterion specification of locomotion stability iscomposed of the basin of attraction and Floquet multiplier of the fiexed point as well asthe maximum allowable disturbance which respectively features the sensitivity of initialcondition, convergence rate under initial condition derivations and disturbance rejectionof the motion state. The influence effects of the parameters of SLIP model on motionperformance, the structure parameter of which mainly contains the equavilent stiffnessof leg spring and motion parameter of which mainly contains the angle of attack, havebeen evaluated with the help of the approximate solution in stance phase. Furthermore,the parameter variation test of analysis data has been implemented to eliminate thedependence of the parameter selection of the model. The self-stability of SLIP modelhas been accordingly investigated. In order to overcome the limitations of the self-stability in locomotion, the apex Dead-beat control strategy of SLIP model based on theapproximations in stance phase has also been developed, through which the decouplingcontrol of the horizontal velocity and vertical height of apex is realized to improve thelocomotion performance of the system.The underactuated SLIP model with leg actuation is proposed based on thecomplete passive SLIP model. On the trajectory regulation, the trajectory planningbased on the virtual constraints (VC) of Center of Mass (CoM) in stance phase isdeveloped via Bézier polynomials to realize symmetrical/asymmetrical motion of SLIPmodel. On the locomotion control, the dynamic inversion based implicit trajectorytracking controller in stance phase has been developed in order to resolve the conflict oftrajectory planning and tracking of CoM caused by the expression diffference of the identical VC between rectangular and polar coordinates. Combined with local particalfeedback linearization, the locomotion control strategy of the underactuated SLIP modelhas been established to fulfill the stable locomotion of SLIP model in irregular terrain.The study of reduced SLIP model in low-dimension space provides sufficienttheorectical basis. On the purpose of dealing with the key issue of control patterntransformation between reduced model and robot system, the task space based controlpattern mapping has been developed to implement transformation from the desiredtrajectory generated by SLIP model to joint torque distribution of robot. Thecorresponding integrated SLIP-based hierachical locomotion architecture has beenestablished. On the regulation layer, the reduced SLIP model generates on-line desisedtrajectory of COM according to the feedback information of robot-environmentinteraction. On the operation layer, the specific joint control is fulfilled via the taskspace-based control patter mapping. In the application of the proposed algorithm, thetask space based hierachical locomotion controllers with single and multi-object havebeen developed to realize the stable locomotion of the hopping gait in monopod robot,running gait in biped robot and galloping gait in quadruped robot. Finally, theeffectiveness of the proposed algorithm has been validated via simulations.The involved work which contains the analytical study, parametrical analysis andapex Dead-beat motion control of the reduced SLIP model as well as the trajectorytracking controller of the underactuated SLIP model has provided abundant resource forcontroller design of legged robot. The corresponding hierachical controller provideseffective resolution to the dynamical locomotion control of legged robot, which is ofimportant theorectical guiding significance and practical values.