probeset to probeset mappings between Affymetrix arrays I am interested in identifying mappings between different types of Affymetrix arrays. I am aware that mappings between gene and probeset can be extracted using Ensembl's Biomart database. 

Ensembe gene id ENSG00000181019 maps to 
1. AFFY HG-U133_Plus_2's 210519_s_at
2. AFFY HuGene-1_0-st-v1's 8002303


Is there any way to extract mappings of probeset ids between two arrays(eg: HG-U133_Plus_2, HuGene-1_0-st-v1)?

eg: 210519_s_at and 8002303
If your question is: can probeset IDs from different platforms be mapped to one another in a similar way as mapping probesets to genes, then the answer is: Yes. BioMart allows you to map almost anything that has an ID to anything else that has an ID.

You can use BioMart either via the web interface or programatically. A brief guide to using the web interface, for mapping HG U133 Plus 2 to HuGene 1.0:


Go to the start page 
Select H. sapiens Ensembl genes for your database; Human genes (GRCh38.p10) for your dataset
Click Filters in the left-hand column
Expand "REGION", scroll down to GENE and select "Input microarray probes/probesets ID list [Max 500 advised]" 
Select AFFY HG U133 PLUS 2 probe ID(s) and either copy/paste or upload a list, one per line
Click Attributes in the left-hand column
Scroll through, uncheck what you don't want to see and choose what you do, for example Gene Stable ID, AFFY HuGene 1 0 st v1 probe and AFFY HG U133 Plus 2 probe
Finally click "Results" in the menu at the top of the left-hand column


And you should see a result like this (you'll need to click the "Results" button).

You should not expect that there be a one-to-one mapping, for two reasons:


Genes have multiple transcripts and probesets are mapped to each transcript
Some transcripts have more than one probeset: in this case, the HuGene IDs 8002301 and 8002303 map to transcripts for this gene


Finally: here's a programmatic example using R/BioMart:

library(biomaRt)
mart.hs &lt;- useMart("ensembl", "hsapiens_gene_ensembl")
results &lt;- getBM(attributes = c("ensembl_gene_id", "affy_hugene_1_0_st_v1", "affy_hg_u133_plus_2"),
                 filters = "affy_hg_u133_plus_2",
                 values = c("210519_s_at"),
                 mart = mart.hs)

results
  ensembl_gene_id affy_hugene_1_0_st_v1 affy_hg_u133_plus_2
1 ENSG00000181019               8002301         210519_s_at
2 ENSG00000181019               8002303         210519_s_at