4.3 Introduction of Envelope Two and Three
4.3.2 The Result of Simulation of Envelope Two and Three
From Fig. 4.16 (a) and (b), 4.17 (a) and (b), we can find out the variation of angular displacement and the location of ankle with both legs. We can classify the biped locomotion into several type situations, CoM moving, leg swing and landing. Notice that the CoM moving motion is for the purpose to maintain the balance either in double support condition or in single support condition. During the period of support area was changed, the support area which associate with the stability is extremely reducing to a small area, therefore, the constraint of location of CoM moving is much important. Arbitrary leg swing causes the location of ankle is changed, and the position of both leg will be exchanged to opposite one, then the original front leg exchange to back leg, and the back exchange to front leg.
From Fig. 4.18 (a) to (l) we can see the practical simulation of KHR-1 robot, the upper body of KHR-1 robot is always keep straight up, therefore the end-effector of link three of kinematical model of KHR-1 robot in X-direction will be the same as location of hip, point H.
In this sense, we can simplify the kinematical model of KHR-1 robot to a two link serial type manipulator, and make the development of biped gait is easier.
Fig. 4.13 Consequently locomotion of all envelopes.
(1) (2) (3) (4) (5) (6)
(7) (8) (9) (10) (11)
Fig. 4.14 Consequently locomotion of all envelopes.
(12) (13) (14) (15) (16)
Detail Process of Biped Gait Generation in Envelope Two
Range of Unity Circle of end-effector
Table 4.3 Detail process of biped gait generation in envelope two.
Z
Detail Process of Biped Gait Generation in Envelope Two
Range of Unity Circle of end-effector
Inverse kinematics for back leg
Table 4.4 Detail process of biped gait generation in envelope two.
X
Detail Process of Biped Gait Generation
Range of Unity Circle of end-effector
Table 4.5 Detail process of biped gait generation in envelope three.
Z
Detail Process of Biped Gait Generation
Range of Unity Circle of end-effector
Table 4.6 Detail process of biped gait generation in envelope three.
X
Detail Process of Biped Gait Generation
Range of Unity Circle of end-effector
Inverse kinematics for back leg
Table 4.7 Detail process of biped gait generation in envelope three.
Z
Detail Process of Biped Gait Generation
Range of Unity Circle of end-effector
Table 4.8 Detail process of biped gait generation in envelope three.
X
Detail Process of Biped Gait Generation
Range of Unity Circle of end-effector
Table 4.9 Detail process of biped gait generation in envelope three.
Z
(1) Define the initial condition of arbitrary node in arbitrary interval of time i,
13 17 19 23 2 1 2
1 ,θ ,θ ,θ ,θ ,θ ,θ ,θ θ F F B B
(2) Calculate Jacobian matrix
(3) Determine the θ& or 1F θ& 1B
F
θ& or2 θ& depend on which leg 2B is as master of manipulator through velocity ellipsoid.
(7) Determine location Q′X of Q′ in X-Z plane
(4) Determine the θ& ,23 θ& ,17 θ&19θ& through velocity 13 ellipsoid in Z-Y plane.
(6) Determine the θ23,θ19,θ17,θ13 in interval of time i+1.
(5) Determine the
F
θ ,1 θ ,2F θ ,1B θ in interval of 2B time i+1.
(8) Determine location Q′Z of Q′ in X-Z plane
(9) Check if the
(
QX′ ,Qz′)
is within the ZMP areaYes
Modify the θ& ,23 θ& ,17 θ&19θ& 13 No
Fig 4.15 Process Flows of Envelope Two and Three.
(a)
(b)
Angular displacement of back leg in envelope two and three
-20 0 20 40 60 80 100 120
1 15 29 43 57 71 85 99 113 127 141 155 169 183 197 211 225 239 253 267 step
Angular displacement(rad/s)
theta 1 Back theta 2 Back
Angular displacement of front leg in envelope two and three
-50 0 50 100 150
1 15 29 43 57 71 85 99 113 127 141 155 169 183 197 211 225 239 253 267
step
angular displacement(rad/s)
theta 1 Front theta 2 Front
Fig 4.16 (a) Angular displacement of front leg.
(b) Angular displacement of back leg.
(a)
(b)
Location of back ankle
0.00 0.01 0.02 0.03
0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10 0.11 0.12 0.13 0.14 0.15 x(meter)
y(meter)
Location of front ankle
0 0.01 0.02 0.03
0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1 0.11 0.12 0.13 0.14 x(meter)
y(meter)
Fig 4.17 (a) Location of front ankle.
(b) Location of back ankle.
(a)
(b)
(c)
Fig. 4.18 (1) Practical simulation of envelope two and three.
(d)
(e)
(f)
Fig. 4.18(2) Practical simulation of envelope two and three.
(g)
(h)
(i)
Fig. 4.18 (3) Practical simulation of envelope two and three.
(j)
(k)
(l)
Fig. 4.18 (4) Practical simulation of envelope two and three.
CHAPTER 5
Conclusions and Future Work
The trajectory planning of biped robot is a significant study in biped robot research and implementation. In this thesis we proposed a gait generation method based on a manipulability ellipsoid algorithm to design a series of gait envelops, such as squat to stand, humanoid walking motion for KHR-1 biped robot. The object of the study are mainly simplifying the procedure of biped robot motion design, reducing the cycle-time of trajectory planning, and providing a stable and successfully trajectory data. Any point on the unity end-effector velocity circle in the proposed manipulability ellipsoid method represents the linear velocity of end-effector of a robot manipulator. And it can be mapped to a corresponding point which represents the angular velocity of each joint on the velocity ellipsoid.
5.1 Conclusions
Several significant results of the current research are summarized and listed as follows.
(1) A new biped robot gait generation methodology is proposed, which can shorten and simplify the cycle time of gait planning of the locomotion of biped robot. Based on the manipulability ellipsoid algorithm, the proposed method can assist to generate the high stability motion gait. Zero-Moment point (ZMP) algorithm has also been introduced into the planning system as the stability criteria of joint trajectory generation for the KHR-1 biped robot instead of using try and error processes which is time consuming.
(2) Based on the manipulability ellipsoid algorithm, the output of joint torque will further be planed to reduce energy consumption in specific biped robot gait.
and input with prescribed gait data. The verification of the microchip controlled biped walking robot via some typical gait envelopes has demonstrated its advantage and usefulness on the gait planning using the proposed methodology.