Current studies on time-optimal trajectory planning centers on cases with fixed base and only one end-effector. However, the free-floating body and the multiple legs of the legged robot make the current methods inapplicable. This paper proposes a time-optimal trajectory planning method for six-legged robots. The model of the optimization problem for six-legged robots is built by considering the base and the end-effectors separately. Both the actuator constraints and the gait cycle constraints are taken into account. A novel two-step optimization method is proposed to solve the optimization problem. The first step solves the time-optimal trajectory of the body and the second step solves the time-optimal trajectory of the swinging legs. Finally, the method is applied to a six-parallel-legged robot and validated by experiments on the prototype. The results show that the velocity of the optimized gait is improved by 17.8% in contrast to the non-optimized one.
RaibertMH. Legged robots that balance, Cambridge, MA: MIT Press, 1986.
2.
Feng S, Xinjilefu X, Atkeson CG, et al. Optimization based controller design and implementation for the Atlas robot in the DARPA Robotics Challenge Finals. In: 2015 IEEE-RAS 15th international conference on humanoid robots (humanoids) IEEE 2015, Seoul, South Korea, pp.1028–1035.
3.
Zhang Y, Luo J, Hauser K, et al. Motion planning and control of ladder climbing on DRC-Hubo for DARPA robotics challenge. In: 2014 IEEE international conference on robotics and automation (ICRA), IEEE 2014, Hong Kong, China, p.2086.
4.
Yang H, Baradat C, Krut S, et al. An agile manufacturing system for large workspace applications. The International Journal of Advanced Manufacturing Technology 2016; 85(1-4): 25–35.
5.
Pan Y and Gao F. A new 6-parallel-legged walking robot for drilling holes on the fuselage. Proc IMechE, Part C: J Mechanical Engineering Science 2013; 228(4): 753–764.
6.
PratiharDKDebKGhoshA. Optimal path and gait generations simultaneously of a six-legged robot using a GA-fuzzy approach. Robot Auton Syst2002; 41: 1–20.
7.
TianYGaoF. Efficient motion generation for a six-legged robot walking on irregular terrain via integrated foothold selection and optimization-based whole-body planning. Robotica2018; 36: 333–352.
8.
ChenZ-JGaoFPanY. Novel door-opening method for six-legged robots based on only force sensing. Chin J Mech Eng2017; 30: 1227–1238.
9.
ChaiXGaoFQiCet al.Obstacle avoidance for a hexapod robot in unknown environment. Sci China Technol Sci2017; 60: 818–831.
10.
DingXX. Kun Gait analysis of a radial symmetrical hexapod robot based on parallel mechanisms. Chin J Mech Eng2014; 27: 867–879.
11.
ChenX-BGaoF. Energy expenditure of trotting gait under different gait parameters. Chin J Mech Eng2017; 30: 943–950.
12.
BiagiottiLMelchiorriC. Trajectory planning for automatic machines and robots, Berlin, Heidelberg: Springer Science & Business Media, 2008.
13.
LeuMSinghS. Optimal trajectory generation for robotic manipulators using dynamic programming. J Dyn Syst Meas Control1987; 109: 88–96.
14.
PfeifferFJohanniR. A concept for manipulator trajectory planning. IEEE J Robot Automat1987; 3: 115–123.
15.
VerscheureDDemeulenaereBSweversJet al.Time-optimal path tracking for robots: a convex optimization approach. IEEE Trans Automat Control2009; 54: 2318–2327.
16.
DebrouwereFVan LoockWPipeleersGet al.Time-optimal path following for robots with convex–concave constraints using sequential convex programming. IEEE Trans Robot2013; 29: 1485–1495.
17.
Debrouwere F, Van Loock W, Pipeleers G, et al. Time-optimal path following for robots with trajectory jerk constraints using sequential convex programming. In: 2013 IEEE international conference on robotics and automation (ICRA), IEEE 2013, Karlsruhe, Germany, pp.1916–1921.
18.
Reynoso-Mora P, Chen W and Tomizuka M. On the time-optimal trajectory planning and control of robotic manipulators along predefined paths. In: 2013 American control conference (ACC), IEEE 2013, Portland, OR, USA, pp.371–377.
19.
ZhangQLiSGuoJ-XGaoX-S. Time-optimal path tracking for robots under dynamics constraints based on convex optimization. Robotica2016; 34: 2116–2139.
20.
SlotineJ-JEYangHS. Improving the efficiency of time-optimal path-following algorithms. IEEE Trans Robot Automat1989; 5: 118–124.
21.
Abdellatif H and Heimann B. Adapted time-optimal trajectory planning for parallel manipulators with full dynamic modelling. In: 2005 ICRA 2005 proceedings of the 2005 IEEE international conference on robotics and automation, IEEE 2005, Barcelona, Spain, pp.411–416.
22.
BehzadipourSKhajepourA. Time-optimal trajectory planning in cable-based manipulators. IEEE Trans Robot2006; 22: 559–563.
23.
BoscariolPGasparettoA. Optimal trajectory planning for nonlinear systems: robust and constrained solution. Robotica2016; 34: 1243–1259.
24.
Brezak M and Petrovic I. Time-optimal trajectory planning along predefined path for mobile robots with velocity and acceleration constraints. In: 2011 IEEE/ASME international conference on advanced intelligent mechatronics (AIM), IEEE 2011, Besançon, France, pp.942–947.
25.
CostantinescuDCroftE. Smooth and time-optimal trajectory planning for industrial manipulators along specified paths. J Robot Syst2000; 17: 233–249.
26.
Cho B-H, Yun J-M and Lee J-M. Time optimal trajectory planning for a robot system under torque and impulse constraints. In: 2004 IEEE international symposium on industrial electronics, IEEE 2004, Cairns, Australia, pp.259–264.
27.
ZhaoM-YGaoX-SZhangQ. An efficient stochastic approach for robust time-optimal trajectory planning of robotic manipulators under limited actuation. Robotica2017; 35(12): 2400–2417.
28.
Hauser K. Fast dynamic optimization of robot paths under actuator limits and frictional contact. In: 2014 IEEE international conference on robotics and automation (ICRA), IEEE 2014, pp.2990–2996.
29.
PhamQ-CStasseO. Time-optimal path parameterization for redundantly actuated robots: a numerical integration approach. IEEE/ASME Trans Mechatron2015; 20: 3257–3263.
30.
DiebelJ. Representing attitude: Euler angles, unit quaternions, and rotation vectors. Matrix2006; 58: 1–35.
