Abstract:In order to realize stable control of the underactuated biped robot on varying height steps with a known step height, a stable walking control strategy based on the adaptive feedforward control algorithm is proposed. Firstly, considering the ground deformation, pairs of spring-damper units are employed to model the ground, and a "robot-step" coupling dynamic model is established. Secondly, the "multiple-input-multiple-output" model of "robot-step" is simplified to the "single-input-single-output" model consisting of centroid displacement and velocity. Then varying height steps are equivalent to varying slopes, whose equivalent slope angle and the desired step length for each step can be calculated according to the each step height. An adaptive control coefficient is introduced into the control algorithm, and it is adjusted according to the equivalent slope angle to track the reference velocity of the CoM (center of mass). Finally, simulation experiments are conducted to validate the proposed controller in the environment where the varying height of the step is less than 0.032 m. The simulation results demonstrate that stable walking can be achieved on varying height steps with a known step height by implementing the proposed control strategy.
[1] 梶田秀司.仿人机器人[M].管贻生,译.北京:清华大学出版社,2007. Kajita S. Humanoid robot[M]. Guan Y S, trans. Beijing:Tsing-hua University Press, 2007.
[2] 汪柳青,尚伟伟.基于线性耦合振荡器模型的仿人机器人步态规划算法[J].中国科学技术大学学报,2014,44(10):795-803. Wang L Q, Shang W W. A gait pattern planning algorithm based on linear coupled oscillator model for humanoid robots[J]. Journal of University of Science and Technology of China, 2014, 44(10):795-803.
[3] 丁加涛,肖晓晖,王杨.双足步行机器人在线步态生成与偏航控制策略[J].中南大学学报:自然科学版,2016,47(4):1136-1143. Ding J T, Xiao X H, Wang Y. Strategy for biped gait robot online generation and yaw control[J]. Journal of Central South University:Science and Technology, 2016, 47(4):1136-1143.
[4] 毛勇,王家廞,贾培发,等.双足被动步行研究综述[J].机器人,2007,29(3):274-280. Mao Y, Wang J X, Jia P F, et al. Passive dynamic biped walking:A survey[J]. Robot, 2007, 29(3):274-280.
[5] Collins S, Ruina A, Tedrake R, et al. Efficient bipedal robots ba-sed on passive-dynamic walkers[J]. Science, 2005, 307(5712):1082-1085.
[6] Westervelt E R, Grizzle J W, Chevallereau C, et al. Feedback control of dynamic bipedal robot locomotion[M]. Boca Raton, USA:CRC Press, 2007.
[7] Grizzle J W, Abba G, Plestan F. Asymptotically stable walking for biped robots:Analysis via systems with impulse effects[J]. IEEE Transactions on Automatic Control, 2001, 46(1):51-64.
[8] Chevallereau C, Grizzle J W, Shih C L. Asymptotically stable walking of a five-link underactuated 3-D bipedal robot[J]. IEEE Transactions on Robotics, 2009, 25(1):37-50.
[9] 付成龙,黄元林,王健美,等.半被动双足机器人的准开环控制[J].机器人,2009,31(2):110-117,123. Fu C L, Huang Y L, Wang J M, et al. Quasi open-loop control for semi-passive biped robots[J]. Robot, 2009, 31(2):110-117, 123.
[10] Geng T, Porr B, Wörgötter F. Fast biped walking with a sensor-driven neuronal controller and real-time online learning[J]. International Journal of Robotics Research, 2006, 25(3):243-259.
[11] 田彦涛,孙中波,李宏扬,等.动态双足机器人的控制与优化研究进展[J].自动化学报,2016,42(8):1142-1157. Tian Y T, Sun Z B, Li H Y, et al. A review of optimal and control strategies for dynamic walking bipedal robots[J]. Acta Automatica Sinica, 2016, 42(8):1142-1157.
[12] Park H W, Ramezani A, Grizzle J W. A finite-state machine for accommodating unexpected large ground-height variations in bipedal robot walking[J]. IEEE Transactions on Robotics, 2013, 29(2):331-345.
[13] Dai H K, Tedrake R. L2-gain optimization for robust bipedal walking on unknown terrain[C]//IEEE International Conference on Robotics and Automation. Piscataway, USA:IEEE, 2013:3116-3123.
[14] Ames A D. Human-inspired control of bipedal robots via control Lyapunov functions and quadratic programs[C]//16th International Conference on Hybrid Systems:Computation and Control. New York, USA:ACM, 2013:31-32.
[15] Plestan F, Grizzle J W, Westervelt E R, et al. Stable walking of a 7-DOF biped robot[J]. IEEE Transactions on Robotics and Automation, 2003, 19(4):653-668.
[16] Miossec S, Aoustin Y. A simplified stability study for a biped walk with underactuated and overactuated phases[J]. International Journal of Robotics Research, 2005, 24(7):537-551.
[17] Chemori A, Le Floch S, Krut S, et al. A control architecture with stabilizer for 3D stable dynamic walking of SHERPA biped robot on compliant ground[C]//IEEE-RAS International Conference on Humanoid Robots. Piscataway, USA:IEEE, 2010:480-485.
[18] Bruneau O, Ouezdou F B. Distributed ground/walking robot interaction[J]. Robotica, 1999, 17(3):313-323.
[19] Wang Y, Ding J T, Xiao X H. An adaptive feedforward control method for under-actuated bipedal walking on the compliant ground[J]. International Journal of Robotics and Automation, 2017, 32(1):63-77.
[20] Pratt J E, Tedrake R. Velocity-based stability margins for fast bipedal walking[M]//Lecture Notes in Control and Information Sciences, vol.340. Berlin, Germany:Springer, 2006:299-324.
[21] 姚道金,王杨,姚渊,等.基于质心运动状态的双足机器人欠驱动步行稳定控制[J].机器人,2017,39(3):324-332. Yao D J, Wang Y, Yao Y, et al. Stable control of underactuated bipedal walking based on motion state of center-of-mass[J]. Robot, 2017, 39(3):324-332.