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

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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Objective method reveals minimum time required to quantify net cost of transport across slow to fast walking speeds

10.1101/2021.09.21.461248 ◽

2021 ◽

Author(s):

Bolatito Adeyeri ◽

Shernice A. Thomas ◽

Christopher J. Arellano

Keyword(s):

Time Window ◽

Minimum Time ◽

Objective Method ◽

Cost Of Transport ◽

Fast Walking ◽

Steady Rate ◽

Metabolic Data ◽

The One ◽

Time Required ◽

Walking Speeds

The U-shaped net cost of transport (COT) curve of walking has helped scientists understand the biomechanical basis that underlies energy minimization during walking. However, to produce an individual's net COT curve, data must be analyzed during periods of steady-rate metabolism. Traditionally, studies analyze the last few minutes of a 6-10 min trial, assuming that steady-rate metabolism has been achieved. Yet, it is possible that an individual achieves steady rates of metabolism much earlier. However, there is no consensus on how to objectively quantify steady-rate metabolism across a range of walking speeds. Therefore, we developed an objective method to determine the minimum time needed for humans to achieve steady rates of metabolism across slow to fast walking speeds. We hypothesized that a shorter time window could be used to produce a net COT curve that is comparable to the net COT curve created using traditional methods. We analyzed metabolic data from twenty-one subjects who completed several 7-min walking trials ranging from 0.50-2.00 m/s. We partitioned the metabolic data for each trial into moving 1-min, 2-min, and 3 min intervals and calculated their slopes. We statistically compared these slope values to values derived from the last 3-min of the 7-min trial, our 'gold' standard comparison. We found that a minimum of 2 min is required to achieve steady-rate metabolism and that data from 2-4 min yields a net COT curve that is not statistically different from the one derived from experimental protocols that are generally accepted in the field.

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Minimum-Time Optimal Trajectories for the Terminal Bunt Manoeuvre

AIAA Guidance, Navigation, and Control Conference and Exhibit ◽

10.2514/6.2005-5968 ◽

2005 ◽

Cited By ~ 2

Author(s):

Subchan Subchan ◽

Rafal Zbikowski

Keyword(s):

Minimum Time ◽

Optimal Trajectories ◽

Time Optimal

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Minimum-Time Optimal Control of Many Robots that Move in the Same Direction at Different Speeds

IEEE Transactions on Robotics ◽

10.1109/tro.2011.2173235 ◽

2012 ◽

Vol 28 (2) ◽

pp. 351-363 ◽

Cited By ~ 15

Author(s):

Timothy Bretl

Keyword(s):

Optimal Control ◽

Minimum Time ◽

Time Optimal Control ◽

Time Optimal

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Minimum time required to detect population trends: the need for long-term monitoring programs

10.7287/peerj.preprints.3168v2 ◽

2017 ◽

Author(s):

Easton R White

Keyword(s):

Time Series ◽

Statistical Power ◽

Time Series Data ◽

Conservation Status ◽

Monitoring Program ◽

Minimum Time ◽

Series Data ◽

Series Length ◽

Time Required

Long-term time series are necessary to better understand population dynamics, assess species' conservation status, and make management decisions. However, population data are often expensive, requiring a lot of time and resources. When is a population time series long enough to address a question of interest? We determine the minimum time series length required to detect significant increases or decreases in population abundance. To address this question, we use simulation methods and examine 878 populations of vertebrate species. Here we show that 15-20 years of continuous monitoring are required in order to achieve a high level of statistical power. For both simulations and the time series data, the minimum time required depends on trend strength, population variability, and temporal autocorrelation. These results point to the importance of sampling populations over long periods of time. We argue that statistical power needs to be considered in monitoring program design and evaluation. Time series less than 15-20 years are likely underpowered and potentially misleading.

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Instruments and Methods: The USA CRREL Drill for Thermal Coring in Ice

Journal of Glaciology ◽

10.3189/s0022143000031282 ◽

1969 ◽

Vol 8 (53) ◽

pp. 311-314 ◽

Cited By ~ 2

Author(s):

Herbert T. Ueda ◽

Donald E. Garfield

Keyword(s):

Minimum Time ◽

Vacuum System ◽

Polar Ice ◽

Electrical Cable ◽

Additional Equipment ◽

Melt Water ◽

The Usa ◽

Time Required ◽

Electrothermal Unit

The USA CRREL drill is an 80-kg, electrothermal unit designed for continuous coring in temperate or polar ice or snow. The drill melts a hole approximately 16.3 cm in diameter and retrieves a core approximately 12.2 cm in diameter at rates from 1.9 m h−1 in −28°C ice to 2.3 m h−1 in temperate ice. The melt water formed is removed by a vacuum system and stored in a tank. Additional equipment includes 450 m of armored electrical cable, a hoist, a 6.7-m tower and a gasoline generator. The minimum time required to drill a 450-m hole is 435 h. All of the equipment has been designed to be assembled and operated by two men and has a gross shipping weight of 1180 kg.

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