title: The effect of dimensional parameters on the dynamic performance of over-arch differential drive vehicles

authors: Tattersall, Andrew

subjects: Vehicle

abstract: This work contributes to the field of agricultural vehicle dynamics by assessing the dimensional sensitivity of over-arch differential drive vehicle performance. The findings from this work are important for vehicle optimisation with regards to drive forces, energy consumption, chassis loading, and vehicle stability. Dimensional optimisation of the vehicles has been ignored, which is a problem if efficient and environmentally friendly autonomous over-arch agricultural vehicles are to be built.

Worldwide, one in nine people do not have enough food to eat. The World Food Program has a goal to end hunger and improve the quality of available food by 2030. In New Zealand, the agricultural industry contributes $13.8 billion dollars to annual GDP and is growing, making agriculture’s contribution valuable to the New Zealand economy. However, there is a labour shortage in agriculture. This shortage of labour negatively effects food production. One potential solution to the labour shortage is automation.

Differential drive mobile robots (DDMRs) are often used in agricultural automation research because they are simple and cheap to build, and the drive system is ideal for an over-arch chassis design. Over-arch vehicles are often required in vineyards and apple orchards. Research into DDMRs is largely limited to optimisation of control and path tracking, but optimisation of the physical vehicle has been ignored. In order to optimise vehicle dimensions before manufacturing starts, the influence of dimensions on drive forces, energy consumption, chassis loading, and vehicle stability needs to be assessed.

In this study, a dynamic model of a large scale agricultural over-arch DDMR is constructed and the dimensional sensitivity of peak drive/braking force, energy consumption, chassis shear force and lateral chassis splay/compression force is assessed. The effects of caster trail and the lateral position of the center of mass on stability are also assessed. Results show that peak drive/braking force, energy consumption, stability and chassis loading are all sensitive to vehicle dimensions to different degrees. Energy consumption showed the least sensitivity, while forces were found to be significantly influenced. For a large scale DDMR traversing common agricultural trajectories, increasing caster trail by 0.2 m, decreasing longitudinal position of the center of mass by 0.2 m, and increasing track width by 0.2 m provides a decrease in peak drive force of 56.4 %, 13.9 % and 9.37 % respectively. These sample results illustrate the importance of understanding dimensional sensitivity, because they are not insignificant. The dimensional sensitivities were also found to be a good guide for vehicles of smaller scale. A case study was conducted on a Simulink model of a large scale over-arch DDMR designed for operating in vineyards. Dimensional optimisation was successfully performed such that the vehicle was able to operate adequately in the simulated vineyard environment. The case study illustrates that dimensional sensitivity is useful for the optimisation of a vehicle for its intended working environment.

This works shows that physical optimisation of these vehicles is extremely important. If optimised, savings could be found in energy consumption, cost, and materials. As automation becomes more important, accurate vehicle control is essential for performance and safety, and the work in this thesis helps to achieve this. The products of dimensional optimisation benefit the overall effort to fill the labour gap and supply enough food for the worlds growing population.

text: The effect of dimensional parameters on the dynamic performance of over-arch differential drive vehicles This work contributes to the field of agricultural vehicle dynamics by assessing the dimensional sensitivity of over-arch differential drive vehicle performance. The findings from this work are important for vehicle optimisation with regards to drive forces, energy consumption, chassis loading, and vehicle stability. Dimensional optimisation of the vehicles has been ignored, which is a problem if efficient and environmentally friendly autonomous over-arch agricultural vehicles are to be built.

Worldwide, one in nine people do not have enough food to eat. The World Food Program has a goal to end hunger and improve the quality of available food by 2030. In New Zealand, the agricultural industry contributes $13.8 billion dollars to annual GDP and is growing, making agriculture’s contribution valuable to the New Zealand economy. However, there is a labour shortage in agriculture. This shortage of labour negatively effects food production. One potential solution to the labour shortage is automation.

Differential drive mobile robots (DDMRs) are often used in agricultural automation research because they are simple and cheap to build, and the drive system is ideal for an over-arch chassis design. Over-arch vehicles are often required in vineyards and apple orchards. Research into DDMRs is largely limited to optimisation of control and path tracking, but optimisation of the physical vehicle has been ignored. In order to optimise vehicle dimensions before manufacturing starts, the influence of dimensions on drive forces, energy consumption, chassis loading, and vehicle stability needs to be assessed.

In this study, a dynamic model of a large scale agricultural over-arch DDMR is constructed and the dimensional sensitivity of peak drive/braking force, energy consumption, chassis shear force and lateral chassis splay/compression force is assessed. The effects of caster trail and the lateral position of the center of mass on stability are also assessed. Results show that peak drive/braking force, energy consumption, stability and chassis loading are all sensitive to vehicle dimensions to different degrees. Energy consumption showed the least sensitivity, while forces were found to be significantly influenced. For a large scale DDMR traversing common agricultural trajectories, increasing caster trail by 0.2 m, decreasing longitudinal position of the center of mass by 0.2 m, and increasing track width by 0.2 m provides a decrease in peak drive force of 56.4 %, 13.9 % and 9.37 % respectively. These sample results illustrate the importance of understanding dimensional sensitivity, because they are not insignificant. The dimensional sensitivities were also found to be a good guide for vehicles of smaller scale. A case study was conducted on a Simulink model of a large scale over-arch DDMR designed for operating in vineyards. Dimensional optimisation was successfully performed such that the vehicle was able to operate adequately in the simulated vineyard environment. The case study illustrates that dimensional sensitivity is useful for the optimisation of a vehicle for its intended working environment.

This works shows that physical optimisation of these vehicles is extremely important. If optimised, savings could be found in energy consumption, cost, and materials. As automation becomes more important, accurate vehicle control is essential for performance and safety, and the work in this thesis helps to achieve this. The products of dimensional optimisation benefit the overall effort to fill the labour gap and supply enough food for the worlds growing population.

year: 2022

title: Estimating the growth in Mordell-Weil ranks and Shafarevich-Tate groups over Lie extensions

authors: Delbourgo, Daniel

subjects: Science & Technology

abstract: Let E/Q be an elliptic curve, p > 3 a good ordinary prime for E, and K∞ a p-adic Lie extension of a number field k. Under some standard hypotheses, we study the asymptotic growth in both the Mordell–Weil rank and Shafarevich–Tate group for E over a tower of extensions K ₙ/ₖ inside K∞; we obtain lower bounds on the former, and upper bounds on the latter’s size.

text: Estimating the growth in Mordell-Weil ranks and Shafarevich-Tate groups over Lie extensions Let E/Q be an elliptic curve, p > 3 a good ordinary prime for E, and K∞ a p-adic Lie extension of a number field k. Under some standard hypotheses, we study the asymptotic growth in both the Mordell–Weil rank and Shafarevich–Tate group for E over a tower of extensions K ₙ/ₖ inside K∞; we obtain lower bounds on the former, and upper bounds on the latter’s size.

year: 2017

title: Maori land in Hauraki

authors: Hart, Philip

abstract: Imagining the Hauraki Peninsula to contain payable goldfields and knowing that land to the south of Thames had great agricultural potential, Pakeha were determined to acquire it, and were frustrated by what was considered to be ‘Maori intransigence’. For their part, Maori landowners were justifiably concerned about losing their land, and hindered and delayed opening it to settlement for as long as possible. A major difficulty for officials seeking to acquire land was how to determine boundaries between different blocks and how to identify the true owners when there were rival claims put forward by hapu and individuals. Land purchase agents used a variety of means to get blocks through the land court and then to individualize the title, notably the controversial ‘raihana’ policy, which benefited some landowners at the expense of others. The expensive legal process involved often forced those who had proved their ownership to sell land to pay for their success, a success which resulted in grantees treating the land as their personal property rather than tribal property. Some Pakeha as well as many Maori protested at the unfair process; even James Mackay, the most effective practitioner of raihana, came to lament his success and its consequences for the younger generation of Maori (he blamed the system, not himself). When far too late, it was urged that land should have been leased rather than sold and that proceeds from sales should not have been squandered.
Instead of having commissions of enquiry, as some suggested, the land court system meant that judges determined ownership on the evidence presented to them, even though some owners were not present nor had their interests represented. Sometimes the evidence was false, as was admitted by some witnesses when their perjury was exposed. And in the case of the Ohinemuri district, for which the records survive, when the land was sold to the Crown some Maori received too much money, some too little, and some missed out altogether. The struggles to open Ohinemuri to miners and settlers is examined in detail, revealing that some rangatira expected economic gain and that Te Hira’s party, who opposed the opening, were undermined by some of Te Hira’s followers: being ‘Hauhau’, they refused to take money from the Crown but instead took raihana, meaning goods which were charged against their land in a way they did not understand. Nor did anyone fully understand the system apart from Mackay, whose policy was eventually repudiated by the politicians who had encouraged it previously. Not all land was lost, but because the government did not assist landowners with advice and finance until well into the twentieth century what land that was retained could not be developed adequately.

text: Maori land in Hauraki Imagining the Hauraki Peninsula to contain payable goldfields and knowing that land to the south of Thames had great agricultural potential, Pakeha were determined to acquire it, and were frustrated by what was considered to be ‘Maori intransigence’. For their part, Maori landowners were justifiably concerned about losing their land, and hindered and delayed opening it to settlement for as long as possible. A major difficulty for officials seeking to acquire land was how to determine boundaries between different blocks and how to identify the true owners when there were rival claims put forward by hapu and individuals. Land purchase agents used a variety of means to get blocks through the land court and then to individualize the title, notably the controversial ‘raihana’ policy, which benefited some landowners at the expense of others. The expensive legal process involved often forced those who had proved their ownership to sell land to pay for their success, a success which resulted in grantees treating the land as their personal property rather than tribal property. Some Pakeha as well as many Maori protested at the unfair process; even James Mackay, the most effective practitioner of raihana, came to lament his success and its consequences for the younger generation of Maori (he blamed the system, not himself). When far too late, it was urged that land should have been leased rather than sold and that proceeds from sales should not have been squandered.
Instead of having commissions of enquiry, as some suggested, the land court system meant that judges determined ownership on the evidence presented to them, even though some owners were not present nor had their interests represented. Sometimes the evidence was false, as was admitted by some witnesses when their perjury was exposed. And in the case of the Ohinemuri district, for which the records survive, when the land was sold to the Crown some Maori received too much money, some too little, and some missed out altogether. The struggles to open Ohinemuri to miners and settlers is examined in detail, revealing that some rangatira expected economic gain and that Te Hira’s party, who opposed the opening, were undermined by some of Te Hira’s followers: being ‘Hauhau’, they refused to take money from the Crown but instead took raihana, meaning goods which were charged against their land in a way they did not understand. Nor did anyone fully understand the system apart from Mackay, whose policy was eventually repudiated by the politicians who had encouraged it previously. Not all land was lost, but because the government did not assist landowners with advice and finance until well into the twentieth century what land that was retained could not be developed adequately.

year: 2016