1. From: Rational Interpolation of Car Motions
Date of download: 10/14/2017
Copyright © ASME. All rights reserved.
From: Rational Interpolation of Car Motions
J. Mechanisms Robotics. 2015;7(3): doi: /
Figure Legend:
Differential drive (left) and front-wheel steering cars (right)

2. From: Rational Interpolation of Car Motions
Date of download: 10/14/2017
Copyright © ASME. All rights reserved.
From: Rational Interpolation of Car Motions
J. Mechanisms Robotics. 2015;7(3): doi: /
Figure Legend:
Interpolated motion between two given poses. The black, gray, black dashed, and gray dashed curves have b1 = -1,1/3,1(2/3), and 3, respectively.

3. From: Rational Interpolation of Car Motions
Date of download: 10/14/2017
Copyright © ASME. All rights reserved.
From: Rational Interpolation of Car Motions
J. Mechanisms Robotics. 2015;7(3): doi: /
Figure Legend:
Interpolated motion for a translation in the y-direction

4. From: Rational Interpolation of Car Motions
Date of download: 10/14/2017
Copyright © ASME. All rights reserved.
From: Rational Interpolation of Car Motions
J. Mechanisms Robotics. 2015;7(3): doi: /
Figure Legend:
Interpolated motion between two poses with zero generalized velocity at either end. In (a) the black, gray, and dashed curves have b2 = 0, 2, and 4, respectively. In (b) the parameter values are b2 = −2, −4, and −6 for the black, gray and dashed curves, respectively.

5. From: Rational Interpolation of Car Motions
Date of download: 10/14/2017
Copyright © ASME. All rights reserved.
From: Rational Interpolation of Car Motions
J. Mechanisms Robotics. 2015;7(3): doi: /
Figure Legend:
Rest-to-rest motion in the y-direction. The two segments of each motion are shown solid and dashed, respectively. The values of γ used are, from left to right 3, 4, 5, and 7.5.

6. From: Rational Interpolation of Car Motions
Date of download: 10/14/2017
Copyright © ASME. All rights reserved.
From: Rational Interpolation of Car Motions
J. Mechanisms Robotics. 2015;7(3): doi: /
Figure Legend:
Minimal path-length. On the left is a contour plot for values of the integral J1 defined in the text. The right hand figure shows the motion given by the optimal values of the parameters a1 ≈ 5.665 and b1 ≈ 0.092.

7. From: Rational Interpolation of Car Motions
Date of download: 10/14/2017
Copyright © ASME. All rights reserved.
From: Rational Interpolation of Car Motions
J. Mechanisms Robotics. 2015;7(3): doi: /
Figure Legend:
Minimal control effort. The left hand graph shows the optimal path dashed and the rational approximation in black. On the right is a detail from the graph where the difference between the two can be seen more clearly. The value of the constant c is 1 in the appropriate units.