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Research Papers

Minimum Time Kinematic Motions of a Cartesian Mobile Manipulator for a Fruit Harvesting Robot

[+] Author and Article Information
Moshe P. Mann

Faculty of Civil and Environmental Engineering,
Technion-Israel Institute of Technology,
Haifa 32000, Israel
e-mail: mpm@tx.technion.ac.il

Boaz Zion

Institute of Agricultural Engineering,
Agricultural Research Organization,
The Volcani Center,
Bet Dagan 50250, Israel
e-mail: boazz@volcani.agri.gov.il

Dror Rubinstein

Faculty of Civil and Environmental Engineering,
Technion-Israel Institute of Technology,
Haifa 32000, Israel
e-mail: agdror@tx.technion.ac.il

Raphael Linker

Associate Professor
Faculty of Civil and Environmental Engineering,
Technion-Israel Institute of Technology,
Haifa 32000, Israel
e-mail: linkerr@tx.technion.ac.il

Itzhak Shmulevich

Professor
Faculty of Civil and Environmental Engineering,
Technion-Israel Institute of Technology,
Haifa 32000, Israel
e-mail: agshmilo@tx.technion.ac.il

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL. Manuscript received June 13, 2013; final manuscript received March 2, 2014; published online June 12, 2014. Assoc. Editor: Jwu-Sheng Hu.

J. Dyn. Sys., Meas., Control 136(5), 051009 (Jun 12, 2014) (9 pages) Paper No: DS-13-1247; doi: 10.1115/1.4027088 History: Received June 13, 2013; Revised March 02, 2014

This paper describes an analytical procedure to calculate the time-optimal trajectory for a mobile Cartesian manipulator to traverse between any two fruits it picks up it. The goal is to minimize the time required from the retrieval of one fruit to that of the next while adhering to velocity, acceleration, location, and endpoint constraints. This is accomplished using a six stage procedure, based on Bellman's Principle of Optimality and nonsmooth optimization that is completely analytical and requires no numerical computations. The procedure sequentially calculates all relevant parameters, from which side of the mobile platform to place the fruit on to the velocity profile and drop-off point, that yield a minimum time trajectory. In addition, it provides a time window under which the mobile manipulator can traverse from any fruit to any other, which can be used for a globally optimal retrieving sequence algorithm.

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References

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Figures

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Fig. 1

Schematic of robotic fruit harvester

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Fig. 2

Time lapse sequence of melon harvesting. The manipulator picks a melon and places on the conveyor belt and then reaches for the next melon.

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Fig. 3

Time of location unconstrained trajectory as function of distance traversed

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Fig. 4

The displacement profile (top) and velocity profile (bottom) for unconstrained location (red) and constrained location (blue). The manipulator must at all times remain behind the front edge (orange line) and in front of the back edge (yellow line).

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Fig. 5

Velocity profile for Type III (top) and Type II (bottom) at l = lmin. While the Type II takes longer, the distance traversed is equal.

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Fig. 6

Dimensions and distances of manipulator relative to melon and platform for reach phase

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Fig. 7

Minimum time required to reach point lx, ly as a function of lx given ly. The minima of the time, Ty, occurs for displacements with Tx(l) ≤ Ty. The interval of arguments of these minima is bounded by points lms and lmf as shown.

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Fig. 8

The minimum regions Mp and Mr and their endpoints. As shown, one of the endpoints is the minimum argument of T(x).

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Fig. 9

Arc time windows TWij and the time span Tij denoted by the dashed arrows for forward traversal (left, xm1 = 2, xm2 = 5) and backward traversal (right, xm1 = 4, xm2 = 3) from melon i to melon j in a platform 3 m long. The trajectory must remain at all times behind the front edge (blue slanted line) and in front of the back edge (red slanted line).

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Fig. 10

Top view of melon harvesting robot

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Fig. 11

Velocities and accelerations of the x- and y-coordinates of the manipulator

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Fig. 12

Trajectory of robotic melon harvester including drop-off points

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Fig. 13

The x-coordinate of the mobile manipulator satisfies the location constraints

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Fig. 14

Traversal between melon i (left of line segments) and melon j (right of line segments) must begin within the respective time window (x-coordinates) and consumes a certain amount of time (y-coordinate). A close up shot of some of the time window segments is shown.

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