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Robotic Attribute Enhancement


My Solutions:

First I will introduce effective robotic attributes. Humanoid robots will all have effective mental attributes (based on programming, computing power, and memory) and most of the normal physical attributes. The one attribute that doesn't seem to apply is PE: robots are designed to function "tirelessly" until their fuel runs out. This attribute is reflected well in the power system configuration and capacity, avoiding the need for an effective physical attribute. PP and PB, however, seem to be wholely appropriate as reflections of the same features non-robotic humanoid bodies display. Beauty may be in the eye of the beholder, but some robots do look more intimidating, more streamlined, more humanoid, or just plain cooler than others. Whatever the basis for beauty may be, robots seem to have an effective representation of the humanoid attribute.


My Basic Approach to Robotic Attribute Enhancement

The system I have devised (after a few trials and errors) determines the cost of an attribute upgrade using a seemingly complex algebraic formula. This formula is based on the approximation that as attributes increase it becomes tangentially more difficult to further increase that attribute. Integrating over that tangential cost increase yields the following basic form:

I = ( - B * C ) { ln ( cos [ f(attribute bonus) ] ) }

Increase in Cost of System =
( -1 * Base Cost * Cost Coefficient) * { natural logarithm of ( cosine of [ some function describing the attribute increase ] ) }

For the different types of upgrades I will alter the function describing the attribute increase, but it always has the form of a fraction ranging from zero to 90 degrees. If you follow the equations below and have your calculator set to degree mode (as opposed to radian mode) everything will work itself out.

The value of the Cost Coefficient, C, sets the scale of the price increases compared to the base price of the unaltered system. I believe that a fair price is achieved when the character receives half of the possible attribute increase and spends twice the base price on the total upgraded system. The value of C that gives this result is:

C = ( -1 ) / [ ln ( cos ( 45 ) ] = 2.8854

If you disagree with my assessment of fair pricing you can adjust this value as you see fit. Raising it by 10% will increase your upgrade prices by 10% compared to the base price, lowering it by 30% will lower your upgrade prices by 30%.... This can also be a simple way to adjust for available prices that characters have to pay in a game setting (black market, high / low quality, or used items, etc...). Each merchant effectively has his own value of C based on his place in the robotics market.

If the formulae for calculating price increases are properly employed we will see that the total cost of a robotic system resembles the following:

Total System Cost

In the specific sections below I have determined available ranges of possible attribute bonuses for each robotic subsystem. Further, as technology advances we will see higher possible attribute bonuses than are currently available. If you disagree with my assessment of a robotic system for motivations from game balance, setting, or anything else this system easily adjusts to your limits of robotic attributes. I simply provide the limits that I feel are appropriate based on my understanding of math, mechanics, and physics. The most important change I've made is the introduction of the integrated-tangent pricing system.

Buying New Systems for Old Robots

Many characters will earn money during their adventures, and will wish to upgrade their attributes. To balance the cost and incompatibilities involved, installation will retain the base system, but scrap out and replace the previous upgrades. Therefore, when upgrading a robot one has to purchase a new upgrade, calculated as the "Increase in Cost" over the base price above. This price may or may not be available, given market fluctuations, and it may not include removal and installation costs (robotic engineers aren't cheap!). If they can find a buyer, the used upgrades could be sold for some fraction of their original cost, determined by the "mileage" and availability in the market. Of course, new systems built by the original manufacturer are probably easier to install than those built by different companies, and costs could reflect this.


Upgrading Robotic Leg and Locomotion Systems

To simplify the construction process, increases in the Speed attribute will correspond to increases in the cost of the Robotic Legs and Locomotion systems purchased for your character. The table below contains initial values and maximum possible attribute increases for each type of available system, as well as the base prices for each unaltered system. The upgrade costs are purchased once for each Leg or Locomotion system. Much of this information is unchanged from the standard rules of HU2, but most of the maximum speed increases have been reduced.

System Type
Human sized Legs (x2):
Giant Sized Legs (x2):
Animal Legs (x4): Small
Animal Legs (x4): Medium
Animal Legs (x4): Large
Giant Animal Legs (x4):
Insect Legs (x4):
Insect Legs (x6):
Insect Legs (x8):
Fuel Injected Engine:
Turbo Engine:
Turbo-Jet Engine:
Concealed VTOL Helicopter:
Hover Jet (Standard, see HU2 pg 203):

Speed Base: Max Bonus
10 : +290
10 : +190
10 : +90
15 : +135
20 : +230
20 : +280
20 : +130
25 : +225
30 : +300
176 : +174
290 : +590
150 : +1150
220 : +200
150 : +200

Base System Cost
$500,000
$1,200,000
$350,000
$500,000
$1,000,000
$2,000,000
$500,000
$750,000
$1,200,000
$25,000
$50,000
$250,000
$340,000
$500,000

Calculating the cost of an increase in the Speed attribute of a particular system uses the following formula:

I = ( - B * C ) [ ln ( cos [ ( 90 ) * iSpd / ( iSpdmax + 1 ) ] ) ]

Increase in Cost of System =
( Base Cost * Cost Coefficient) * [ natural logarithm of ( cosine of [ ( 90 ) * desired Spd bonus / ( max possible Spd bonus + 1 ) ] ) ]

For example, if I were to design a robot with normal human sized legs and an enhanced Speed attribute I would use the formula above. I want to purchase an upgrade of 140 attribute points, giving my robot a total Speed attribute of 150. The cost of the system upgrade would be:

I = ( - $500,000 * 2.8854 ) [ ln ( cos [ ( 90 ) 140 / 291 ] ) ] = $458,417

making the total cost of my robot's legs:

Total Cost = B + I = $500,000 + $458,417 = $958,417

If I were instead trying to upgrade my robot's Speed attribute to 300, the maximum possible, the legs would cost $8,033,412. This may seem too expensive at first glance, but consider that this speed attribute represents the pinnacle of robotic engineering.  The cost for a system with a Speed attribute of 290 is considerably less, $4,574,809. Just like in the real world, getting a slight increase in performance from a very high end piece of technology is very expensive.


Upgrading Robotic Arm Systems

To simplify the construction process, increases in PS and PP will correspond to increases in the cost of the Robotic Arms purchased for your character. Each system has a base PS and PP, and upgrading one attribute means that it will be more difficult to upgrade the other. On the table below are the base PS and PP attributes for each type of Arm system, the maximum possible number of attribute points available for purchase with an upgrade, and the base cost of the unaltered system. The costs here will purchase one arm/hand unit for each type of system with the exception of exoskeletal systems, where one upgrade effects the entire robot.

Type of Robotic Arms
Human-like, normal size, lightweight
Human-like, normal size
Human-like, 2x normal size
Human-like, 3x normal size
Human-like, 4x normal size
Human-like, 5x normal size
Utility Arm
Tentacle, 2 cm diameter
Tentacle, 5 cm diameter
Tentacle, 10 cm diameter
Tentacle, 20 cm diameter

PS Base: Max Bonus
10 : +10
10 : +35
15 : +45
20 : +60
25 : +75
30 : +100
4 : +12
2 : +4
4 : +8
8 : +12
10 : +20

PP Base: Max Bonus
6 : +10
10 : +18
10 : +16
9 : +13
8 : +11
7 : +10
12 : +10
4 : +4
8 : +10
10 : +12
8 : +10

Base System Cost
$120,000
$150,000
$200,000
$300,000
$500,000
$800,000
$100,000
$40,000 + $15,000 / meter
$60,000 + $10,000 / meter
$70,000 + $10,000 / meter
$80,000 + $15,000 / meter

To compute the cost of upgrading a system from the base attributes one can use the formula:

I = ( - B * C ) { ln ( cos [ ( 45 ) * [ iPS / ( iPSmax +1 ) + ( iPP / iPPmax) ] ] ) }

Increase in Cost of System =
( Base Cost * Cost Coefficient) * { natural logarithm of ( cosine of [ ( 45 ) * [ ( desired PS bonus / max possible PS bonus ) + ( desired PP bonus / max possible PP bonus ) ] ] ) }

For example, if I purchased a robot with two normal size human-like arms, and wish to upgrade the PS attribute to the maximum possible without improving on the PP attribute, I calculate the upgrade cost to be:

I = ( - $300,000 * 2.8854 ) { ln ( cos [ ( 45 ) * [ ( 35 / 36 ) + ( 0 / 18 ) ] ] ) } = $281,522

resulting in a total cost for both arms of $581,522, a little less than twice the cost of the unaugmented system. This isn't too exorbitant, but if we now increase the PP attribute to 20, an increase of 10 points, the cost is $1,178489. If we increase the PP even further to 28 (making the attributes as high as possible) the cost of the total system is $3,611,138. Only top-of-the-line models will have these incredibly expensive enhancements, but for a reasonable and realistic price a robot designer can either focus on one attribute or purchase a smaller upgrade of both attributes.


Upgrading Exoskeleton Attributes

The robotic attributes of Type 3 robots are more closely interlinked than are those of other types due to space considerations and technical issues. The three appropriate physical attributes are linked; upgrading one attribute will increase the expense of upgrading another. In terms of the formula used to determine upgrade price increase, these robots will use a different value of C, the cost coefficient, that reflect the increased difficulty of working within Type 3 limitations.

I = ( - B * C ) { ln ( cos [ ( 18 ) * [ iPS / iPSmax + 2 iPP / iPPmax + 2 iSpd / ( iSpdmax + 1 ) ] ] ) }

Exo-Type
Robotic
Power

PS
10 : +30
(+0) : +(+30)

PP
10 : +14
(+0) : +(+14)

Spd
20 : +50
(+0) : +(+50)

C
5.7708
9.2745

Base Cost
$450,000
$350,000

A sample calculation: If I want to build an exoskeleton with robotic armor attributes PS: 30, PP: 15, Spd: 50, the increase in cost would be:

I = ( - $450,000 * 5.7708 ) { ln ( cos [ ( 18 ) * [ 20 / 30 + 2 ( 5 / 14 ) + 2 ( 30 / 51 ) ] ] ) }
= ( - $2,596,860 ) { ln ( cos [ 18 * 2.5594 ] ) }= $949,418

If we assume that our pilot has the same base attributes as the robotic system, PS: 10, PP: 10, Spd: 20, and wish to build an exoskeleton with power armor attributes that give an equivalent end result as the robotic armor above:

I = ( - $350,000 * 8.2440 ) { ln ( cos [ 18 * 2.5594 ] ) }
= ( - $3,246,075 ) { ln ( cos [ ( 18 * 2.5594 ] ) }= $1,186773

The total prices for these systems are:

Robotic: $1,399,418
Power: $1,536,773

Increasing the attributes of power armor is 25% more expensive than increasing the cost of robotic armor, but that cost is offset by the higher base price of the robotic armor system. A quick calculation tells me that a maximally enhanced robotic armor system will cost $11,867,248 and a maximally enhanced power armor system will cost $14,621,560. Characters with above average physical attributes will reap greater total attributes from power armor, but the higher cost balances these advantages as enhancements are increased.