how to obtain the ip address of the connected wifi router in android programmatically?

What you want is DhcpInfo....

final WifiManager manager = (WifiManager) super.getSystemService(WIFI_SERVICE);
final DhcpInfo dhcp = manager.getDhcpInfo();
final String address = Formatter.formatIpAddress(dhcp.gateway);

This will determine the formatted gateway IP address, which should be what you're looking for.

Since formatIpAddress is Deprecatted, here is the alternative :

public String getHotspotAdress(){
    final WifiManager manager = (WifiManager)super.getSystemService(WIFI_SERVICE);
    final DhcpInfo dhcp = manager.getDhcpInfo();
    int ipAddress = dhcp.gateway;
    ipAddress = (ByteOrder.nativeOrder().equals(ByteOrder.LITTLE_ENDIAN)) ?
            Integer.reverseBytes(ipAddress) : ipAddress;
    byte[] ipAddressByte = BigInteger.valueOf(ipAddress).toByteArray();
    try {
        InetAddress myAddr = InetAddress.getByAddress(ipAddressByte);
        return myAddr.getHostAddress();
    } catch (UnknownHostException e) {
        // TODO Auto-generated catch block
        Log.e("Wifi Class", "Error getting Hotspot IP address ", e);
    }
    return "null"
}