Legged robots have superior advantages rather than wheeled robots for moving over uneven terrains in the presence of various obstacles. The design of an appropriate path for the main body and legs is an important issue for such robots especially on the uneven terrains. In this paper, the focus is to develop a stable gait for a quadruped robot to trot on uneven terrains. First, a stability condition is developed for a whole-body quadruped robot over uneven terrains based on avoiding the tumbling. By using a simple model, a point with zero moments is calculated in the three-dimensional space. Then, the reference path of this point is determined so that the tumbling moments become zero. The path of the main body will be calculated by using an optimal controller. The main feature of the proposed gait generation framework is that the height of robot can change continuously and stably on uneven terrains. To evaluate the robot stability, the tumbling moments around diagonal lines are calculated and some methods are proposed to reduce these moments to improve the robot stability. The tip of swing foot is also planned to avoid any collision with the environment. The proposed method will be demonstrated using an 18-Degrees of freedom (DOF) quadruped robot in simulation and experimental studies. The experimental setup is a small-size quadruped robot, which is composed of a rectangular plate as its main body with four legs that each one has three active joints with DC servo motors. Obtained results reveal that the robot can trot on uneven terrains stably. Besides, the comparison with the previous methods approves the merits of proposed algorithm on uneven terrains.
Raibert M. BigDog, the rough-terrain quadruped robot. In: Chung M (ed). Proceedings of the 17th IFAC World Congress. COEX, Korea, South, 2008.
2.
Semini C. HyQ—design and development of a hydraulically actuated quadruped robot. Italy: University of Genoa, 2010, p. 210.
3.
SpröwitzATuleuAVespignaniM. Towards dynamic trot gait locomotion: design, control, and experiments with Cheetah-cub, a compliant quadruped robot. Int J Robotics Res2013; 32: 932–950.
4.
HutterMGehringCHopflingerMA. Toward combining speed, efficiency, versatility, and robustness in an autonomous quadruped. Robotics IEEE Trans2014; 60: 1–14.
5.
HardarsonF. Stability analysis and synthesis of statically balanced walking for quadruped robots, PhD Thesis, Stockholm: Royal Institute of Technology, 2002.
6.
LiuFWuDChenK. The simplest creeping gait for a quadruped robot. Proc IMechE, Part C: J Mechanical Engineering Science2013; 227: 170–177.
7.
Zamani A, Khorram M and Moosavian SAA. Dynamics and stable gait planning of a quadruped robot. In: Proceeding of International Conference on Control, Automation and Systems (ICCAS), Gyeonggi-do, China, 26–29 October 2011, IEEE.
8.
Havoutis I, Semini C, Buchli J, et al. Quadrupedal trotting with active compliance. In: Proceeding of International Conference on Mechatronics, Vicenza, Italy, 27 Febuary–1 March 2013, IEEE.
9.
Gehring C, Coros S, Hutter M, et al. Control of dynamic gaits for a quadrupedal robot. In: Proceeding of nternational Conference on Robotics and Automation (ICRA), Karlsruhe, Germany, 6–10 May 2013, IEEE.
10.
MarhefkaDWOrinDESchmiedelerJP. Intelligent control of quadruped gallops. Mechatronics IEEE/ASME Trans2003; 8: 446–456.
11.
Poulakakis I, Smith JA and Buehler M. On the dynamics of bounding and extensions: Towards the half-bound and gallop gaits. In: Kimura H, Ishiguro A and Witte H (eds) Adaptive motion of animals and machines, Springer-Verlag, Tokyo, 2006, pp.79–88.
12.
VukobratovićMBorovacB. Zero-moment point—thirty five years of its life. Int J Hum Robot2004; 1: 157–173.
13.
KalakrishnanMBuchliJPastorP. Learning, planning, and control for quadruped locomotion over challenging terrain. Int J Robotics Res2011; 30: 236–258.
14.
HuangH-PYanJ-LChengT-H. State-incremental optimal control of 3D COG pattern generation for humanoid robots. Adv Robotics2013; 27: 175–188.
15.
Takao S, Yokokohji Y and Yoshikawa T. FSW (feasible solution of wrench) for multi-legged robots. In: Proceeding of International Conference on Robotics and Automation (ICRA), Taipei, Taiwan, September 2003, pp.14–19, IEEE.
16.
GarciaEEstremeraJde SantosPG. A comparative study of stability margins for walking machines. Robotica2002; 20: 595–606.
17.
Kajita S, Kanehiro F, Kaneko K, et al. The 3D Linear Inverted Pendulum Mode: A simple modeling for a biped walking pattern generation. In: Proceeding of IEEE/RSJ International Conference on Intelligent Robots and Systems, Maui, Hawaii, 29 October–3 November 2001, IEEE.
18.
Kajita S, Kanehiro F, Kaneko K, et al. Biped walking pattern generation by using preview control of zero-moment point, In: Proceeding of IEEE International Conference on Robotics and Automation, Taipei, Taiwan, 14–19 September 2003, IEEE.
19.
Takanishi A, Lim H-o, Tsuda M, et al. Realization of dynamic biped walking stabilized by trunk motion on a sagittally uneven surface. In: Proceeding of IEEE International Workshop on Intelligent Robots and Systems, Ibaraki, Japan, 3–6 July 1990, IEEE.
HaradaKKajitaSKanekoK. An analytical method for real-time gait planning for humanoid robots. Int J Humanoid Robotics2006; 3: 1–19.
22.
HongSOhYKimD. Real-time walking pattern generation method for humanoid robots by combining feedback and feedforward controller. Industr Electronics IEEE Trans2014; 61: 355–364.
23.
Wieber P-B. Trajectory free linear model predictive control for stable walking in the presence of strong perturbations. In: Proceeding of IEEE/RAS International Conference on Humanoid Robots, Genova, Italy, 4–6 December 2006, IEEE.
24.
AlbertAGerthW. Analytic path planning algorithms for bipedal robots without a trunk. J Intelligent Robotic Syst2003; 36: 109–127.
25.
KuindersmaSPermenterFTedrakeR. An efficiently solvable quadratic program for stabilizing dynamic locomotion. In: Proceeding of IEEE International Conference on Robotics and Automation (ICRA),Hong Kong, 31 May 2014–7 June 2014, IEEE.
26.
Kalakrishnan M, Buchli J, Pastor P, et al. Fast, robust quadruped locomotion over challenging terrain. In: Proceeding of IEEE International Conference on Robotics and Automation (ICRA), Anchorage, AK, 3–7 May 2010, IEEE.
27.
Sugihara T, Nakamura Y and Inoue H. Real-time humanoid motion generation through ZMP manipulation based on inverted pendulum control. In: Proceeding of IEEE International Conference on Robotics and Automation, Washington, DC, 11–15 May 2002, IEEE.
28.
SatoTSakainoSOhashiE. Walking trajectory planning on stairs using virtual slope for biped robots. Industr Electronics IEEE Trans2011; 58: 1385–1396.
29.
KolterJZNgAY. The Stanford LittleDog: a learning and rapid replanning approach to quadruped locomotion. Int J Robotics Res2011; 30: 150–174.
30.
Barasuol V, Buchli J, Semini C, et al. A reactive controller framework for quadrupedal locomotion on challenging terrain. In: Proceeding of IEEE International Conference on Robotics and Automation (ICRA), Karlsruhe, Germany, 6–10 May 2013, IEEE.
31.
Fukuoka Y, Kimura H, Hada Y, et al. Adaptive dynamic walking of a quadruped robot ‘Tekken’ on irregular terrain using a neural system model. In: Proceeding of IEEE International Conference on Robotics and Automation, Taipei, Taiwan 14–19 September 2003, IEEE.
32.
UgurluBHavoutisISeminiC. Pattern generation and compliant feedback control for quadrupedal dynamic trot-walking locomotion: experiments on RoboCat-1 and HyQ. Autonomous Robots2015; 38: 415–437.
33.
SantosCPMatosV. Gait transition and modulation in a quadruped robot: a brainstem-like modulation approach. Robotics Autonomous Syst2011; 59: 620–634.
34.
Ajallooeian M, Gay S, Tuleu A, et al. Modular control of limit cycle locomotion over unperceived rough terrain. In: Proceeding of IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), Tokyo, Japan, 3–7 November 2013, IEEE.
35.
RaibertMH. Trotting, pacing and bounding by a quadruped robot. J Biomechan1990; 23: 79–98.
36.
Kurazume R, Hirose S and Yoneda K. Feedforward and feedback dynamic trot gait control for a quadruped walking vehicle. In: Proceeding of IEEE International Conference on Robotics and Automation (ICRA), Seoul, Korea, 21–26 May 2001, IEEE.
37.
KurazumeRYonedaKHiroseS. Feedforward and feedback dynamic trot gait control for quadruped walking vehicle. Autonomous Robots2002; 12: 157–172.
38.
Ugurlu B, Havoutis I, Semini C, et al. Dynamic trot-walking with the hydraulic quadruped robot–HyQ: Analytical trajectory generation and active compliance control. In: Proceeding of IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), Tokyo, Japan, 3–7 November 2013, IEEE.
39.
ParkJHHanSKwonWH. LQ tracking controls with fixed terminal states and their application to receding horizon controls. Syst Contr Lett2008; 57: 772–777.
40.
Kolter JZ and Ng AY. Task-space trajectories via cubic spline optimization. In: Robotics and Automation, 2009 ICRA'09 IEEE International Conference on: IEEE, 2009, pp.1675–1682.
41.
TianLCollinsC. An effective robot trajectory planning method using a genetic algorithm. Mechatronics2004; 14: 455–470.
