Including look up tables in a formula

Hello

I was wondering if it is possible to link to a look up table within a formula. I have a set of constraints for maximum acceleration of a vehicle at a certian speed set in a table for example column 1 is velocity (m/s) and column 2 is maximum acceleration (m/s^2) possible at that speed

Table 1.

V A

10 9.4

20 8.1

30 6.65

40 3.9

I then have an input parameter for the vehicle that gives the actual speed at specific times

Speed{1} = 20

Speed{2} = 20

Speed{3} = 30

Speed{4} = 40

I then would like to use the max acceleration for given speed

so for

i = 1:4

ax(i) = A(i)

Where A(i) should correspond to the appropraite A from Table 1 based on the speed given. Is there a way to write this as a script so Matlab can look up the correct A for corresponding V.

Secondly if so, is it then possible for Speed{n} to be a number not listed (25 fir example) and Matlab to interpolate between the numbers given in Table 1.

Best Wishes

Kieran

Answer 1

[Adam Danz]

I propose creating an anonymous function that stores the interpolated table and receives a velocity as input and outputs the associated max acceleration. BTW, if there is a simple function that produces the max acceleration given the velocity, you should use that instead.

% Create the original table
T = table([10 20 30 40]',[9.4,8.1,6.65,3.9]','VariableNames', {'V', 'A'});

% Create an interpolated version
Vinterp = 10 : 0.01 : 40;  %Interp'd to 0.01 resolution (which you can change)
Ainterp = interp1(T.V,T.A,Vinterp);
VAmat = [Vinterp',Ainterp']; %easier to work with matrices so no table conversion

% create annonymous function that stores VAmat and does look-up
VAfcn = @(v)VAmat(abs(v-VAmat(:,1))==min(abs(v-VAmat(:,1))),2);

This function works with any precision and merely looks up the nearest value in the velocity column and returns the paired max acceleration. You can pass this anonymous function into other functions and it will retain the interpolated data.

Examples:

>> VAfcn(10.523)
ans =
       9.3324
>> VAfcn(35.03)
ans =
       5.2668
 VAfcn(22.234567)
ans =
       7.7767

[Kieran Reeves]

Thank you Adam, really appreciate you spending your time on answering my query.

[Adam Danz]

Glad I could help!

[Kieran Reeves]

Hi Adam

Is there a way to do somthing similar with 3 columns of data, whereby the VAfcn could be based on 2 of the input parameters and returns the third?

So if I had speed, long accel and lateral accel for instance. I input VAfcn with a given speed and long accel and return the lateral accel as an answer?

Best Wishes

Kieran

[Adam Danz]

Maybe. If you provide the interpolated table (VAmat in my answer) with all 3 columns, I can modify the VAfcn.

[Kieran Reeves]

Hi Adam

Thankyou for your help. Please find attached the matrix. First column is steering, 2nd is speed.

I would like to return the third column with the fcn which is lateral acceleration.

I generated from a lot of measured data but the columns in my code are named as

VAmatSteer = [VASteer, VAVx ,VAAy];

Best Wishes

Kieran

[Adam Danz]

There are NaN values in your 3rd column. Is that intended?

any(isnan(VAmatSteer))

[Adam Danz]

Here's a method that identifies the row in VAmatSteer where columns 1 and 2 are exactly equal to [a,b] and returns the value in column 3. If there is not an exactly row match for [a,b], this won't work.

m = [repmat((1:3)',2,1),repelem([1;2],3,1),(0:.1:.5)']; 

% m =
%            1            1            0
%            2            1          0.1
%            3            1          0.2
%            1            2          0.3
%            2            2          0.4
%            3            2          0.5
            
a = 1; %value in column 1
b = 2; %value in column 2

c = m(ismember(m(:,1:2),[a,b],'rows'),3);  %Value in col 3 

% c = 0.3

[Kieran Reeves]

Thanks for the answer.

OK, so it won't be possible to return a nearest match if a or b dont match?

Yes the Nan is intentional at the moment, it is because it lies outside the bounds of the vehicle dynamics model so the optimsier should move away from this, it is only to test the controller. I can easily populate as well if needed.

Thanks

Kieran

[Adam Danz]

What would the rule be if there wasn't an exact match? For example, if the nearest match of "a" is in row 140 and the nearest match of "b" is in row 141, which row do we index in column 3?

[Kieran Reeves]

Yes, I see the issue with your example. Thank-you

Is it possible to make column b the predominat search. As this is set up in groups of the same number and then find the nearest a to give the final overall answer for c.

For example from the table below if the inputs happen to be a = 1.1 and b = 2.2. It would locate the set of b results that corresponds to 2 (rows 4, 5 and 6), and then locates 1 in column a is closest for a (row 4). Then c would return 0.3, so that row 4 is the closest match to the initail inputs of 1.1. and 2.2.

% m =

% 1 1 0

% 2 1 0.1

% 3 1 0.2

% 1 2 0.3

% 2 2 0.4

% 3 2 0.5

[Adam Danz]

The 3 lines below do what you're describing.

bIdx is a logical index of column 2 values that are closest to B.

aIdx is a logical index of column1 values identifying rows where col 2 was selected and are closest to A.

c is the column 3 value of the chosen row.

bIdx = abs(m(:,2) - b) == min(abs(m(:,2) - b));
aIdx = abs(m(:,1) - a) == min(abs(m(bIdx,1) - a));
c = m(find(aIdx & bIdx, 1),3)

[Kieran Reeves]

Wow, thank-you for responding so late. i will give this a try in the morning and let you now how I get on. Really apprecaite the help Adam.

[Adam Danz]

It's 7pm where I'm at with ~2 more hours of daylight ;)

Good luck.

[Kieran Reeves]

Hi Adam

Works really well. Just though I would let you know.

Thanks once again

Kieran