Locomotion speed is a key performance index of legged robots. However, methods to analyze and improve the locomotion speed capability are seldom developed, especially for six-legged robots. This paper develops a method to analyze and improve the omnidirectional walking speed and the turning speed of six-legged robots. The models of the inverse kinematics and the influence coefficients are built. Making use of the only-position-related property of the influence coefficients, a general optimization model of the locomotion trajectory is established. A two-step optimization method is introduced to solve the optimization problem. Based on the optimization, a comprehensive speed capability analysis is conducted on both omnidirectional walking and turning of the six-parallel-legged robot. The results clearly show the relationships among the speed capability, the walking direction and the duty cycle. The two-step optimization method improves the speed capability by 12.4%–13.2% for turning and 18.5%–20.5% for omnidirectional walking. Finally, the costs of the speed improvement are analyzed, including the stability, the energy consumption and the calculation time.
ErdenMSLeblebicioğluK.Free gait generation with reinforcement learning for a six-legged robot. Rob Auton Syst2008; 56: 199–212.
3.
PanYGaoFDuH.Fault tolerance criteria and walking capability analysis of a novel parallel-parallel hexapod break walking robot. Robotica2016; 34: 619–633.
4.
YoshikawaT.Manipulability of robotic mechanisms. Int J Rob Res1985; 4: 3–9.
5.
TianYGaoFLiuJ. Velocity/force capacities of a six-legged walking machine. In: ASME 2017 international design engineering technical conferences and computers and information in engineering conference. New York: American Society of Mechanical Engineers Digital Collection, 2017.
LiuX-JWangJPritschowG.Performance atlases and optimum design of planar 5R symmetrical parallel mechanisms. Mech Mach Theory2006; 41: 119–144.
8.
DubeyRLuhJY.Redundant robot control using task based performance measures. J Rob Syst1988; 5: 409–432.
9.
UchiyamaMShimizuKHakomoriK.Performance evaluation of manipulators using the Jacobian and its application to trajectory planning. Rob Res1985; 2: 447–454.
10.
AspragathosNAFoussiasS.Optimal location of a robot path when considering velocity performance. Robotica2002; 20: 139–147.
11.
ChamitoffGESaenz-OteroAKatzJG, et al. Admissible Subspace TRajectory Optimizer (ASTRO) for autonomous robot operations on the space station. In: AIAA guidance, navigation, and control conference. Reston, VA: AIAA, 2014, pp.1–17.
12.
GasparettoAZanottoV.Optimal trajectory planning for industrial robots. Adv Eng Softw2010; 41: 548–556.
13.
GasparettoALanzuttiAVidoniR, et al. Experimental validation and comparative analysis of optimal time-jerk algorithms for trajectory planning. Rob Comput-Integr Manuf2012; 28: 164–181.
14.
RubioFValeroFSunyerJ, et al. Optimal time trajectories for industrial robots with torque, power, jerk and energy consumed constraints. Ind Robot2012; 39: 92–100.
15.
LiuHLaiXWuW.Time-optimal and jerk-continuous trajectory planning for robot manipulators with kinematic constraints. Rob Comput-Integr Manuf2013; 29: 309–317.
16.
BiagiottiLMelchiorriC.Trajectory planning for automatic machines and robots. Berlin: Springer Science & Business Media, 2008.
17.
KrögerTWahlFM.Online trajectory generation: basic concepts for instantaneous reactions to unforeseen events. IEEE Trans Robot2010; 26: 94–111.
18.
ChettibiTLehtihetHEHaddadM, et al. Minimum cost trajectory planning for industrial robots. Eur J Mech – A/Solids2004; 23: 703–715.
19.
JanssensPVan LoockWPipeleersG, et al. Efficient computation of time-optimal point-to-point motion trajectories. IEEE Trans Contr Syst Technol2015; 23: 679–686.
20.
GhasemiMHKashiriNDardelM.Time-optimal trajectory planning of robot manipulators in point-to-point motion using an indirect method. Proc IMechE, Part C: J Mechanical Engineering Science2012; 226: 473–484.
21.
LeuMSinghS.Optimal trajectory generation for robotic manipulators using dynamic programming. J Dyn Syst Measure Control1987; 109: 88–96.
22.
VerscheureDDemeulenaereBSweversJ, et al. Time-optimal path tracking for robots: a convex optimization approach. IEEE Trans Automat Contr2009; 54: 2318–2327.
23.
DebrouwereFVan LoockWPipeleersG, et al. Time-optimal path following for robots with convex–concave constraints using sequential convex programming. IEEE Trans Robot2013; 29: 1485–1495.
24.
DebrouwereFVan LoockWPipeleersG, 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). Piscataway: IEEE, 2013, pp.1916–1921.
25.
ZhangQLiSGuoJ-X, et al. Time-optimal path tracking for robots under dynamics constraints based on convex optimization. Robotica2016; 34: 2116–2139.
26.
Reynoso-MoraPChenWTomizukaM. On the time-optimal trajectory planning and control of robotic manipulators along predefined paths. In: American control conference (ACC),2013. Piscataway: IEEE, 2013, pp.371–377.
27.
BobrowJEDubowskySGibsonJ.Time-optimal control of robotic manipulators along specified paths. Int J Rob Res1985; 4: 3–17.
SlotineJ-JEYangHS.Improving the efficiency of time-optimal path-following algorithms. IEEE Trans Robot Automat1989; 5: 118–124.
30.
PhamQ-C.A general, fast, and robust implementation of the time-optimal path parameterization algorithm. IEEE Trans Robot2014; 30: 1533–1540.
31.
AbdellatifHHeimannB. Adapted time-optimal trajectory planning for parallel manipulators with full dynamic modelling. In: ICRA 2005 Proceedings of the 2005 IEEE international conference on robotics and automation. IEEE, 2005, p. 411-6.
32.
BehzadipourSKhajepourA.Time-optimal trajectory planning in cable-based manipulators. Ieee Trans Robot2006; 22: 559–563.
33.
BrezakMPetrovicI. and Time-Optimal trajectory planning along predefined path for mobile robots with velocity and acceleration constraints. Advanced Intelligent Mechatronics (AIM), 2011. IEEE/ASME International Conference on. Piscataway: IEEE, 2011, pp.942–947.
34.
BoscariolPGasparettoA.Optimal trajectory planning for nonlinear systems: robust and constrained solution. Robotica2016; 34: 1243–1259.
35.
ConstantinescuDCroftEA.Smooth and time-optimal trajectory planning for industrial manipulators along specified paths. J Robotic Syst2000; 17: 233–249.
36.
ChoB-HYunJ-MLeeJ-M. Time optimal trajectory planning for a robot system under torque and impulse constraints. In: IEEE international symposium on industrial electronics. Piscataway: IEEE, 2004, pp.259–264.
37.
ZhaoM-YGaoX-SZhangQ.An efficient stochastic approach for robust time-optimal trajectory planning of robotic manipulators under limited actuation. Robotica2017; 35: 2400–2418.
38.
BobrowJE.Optimal robot path planning using the minimum-time criterion. IEEE J Robot Automat1988; 4: 443–450.
39.
PhamQ-CCaronSLertkultanonP, et al. Admissible velocity propagation: beyond quasi-static path planning for high-dimensional robots. Int J Rob Res2017; 36: 44–67.
40.
ChenZGaoF. Time-optimal trajectory planning method for six-legged robots under actuator constraints. Proc IMechE, Part C: J Mechanical Engineering Science2019; 233: 4990–5002.
41.
HuangZZhaoYSZhaoTS.Advanced spatial mechanism. Beijing: China Higher Education Press, 2006. (in Chinese)
42.
PanYGaoF. A new 6-parallel-legged walking robot for drilling holes on the fuselage. Proc IMechE, Part C: J Mechanical Engineering Science2013; 228: 753–764.
43.
PanYGaoF. Kinematic performance analysis for hexapod mobile robot using parallel mechanism. In: ASME 2014 international design engineering technical conferences and computers and information in engineering conference. New York: American Society of Mechanical Engineers, 2014, pp.V05AT8A089-V05AT08A.
44.
FaiglJČížekP.Adaptive locomotion control of hexapod walking robot for traversing rough terrains with position feedback only. Rob Auton Syst2019; 116: 136–147.
45.
NishiiJ.An analytical estimation of the energy cost for legged locomotion. J Theor Biol2006; 238: 636–645.
46.
ChenZGaoFSunQ, et al. Ball-on-plate motion planning for six-parallel-legged robots walking on irregular terrains using pure haptic information. Mech Mach Theory2019; 141: 136–150.
47.
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.
