ieee488:
The "button" project uses the ESP-03. What has to be modified on the ESP-01 to make it work for the project?
Removal of the header pins! That's basically it!
And maybe use of a common anode LED to comply with the boot conditions. Haven't got around to putting it together yet. The ESP-01 has four available GPIO, so it does fit the project with the right adaptations. 
ieee488:
Also, I am not sure what you mean by your comment about the "improved version with CH_PD".
The original version requires you to hold the power button while the ESP performs its negotiations. That makes it substantially less than practical. The obvious (to me at least) improvement which someone tested for me some years ago is to use the button to pull CH_PD high and hold it high with a diode from a GPIO pin until the handshake is complete. Much more sensible than switching the power supply.
I was trying to find the circuit from my previous posts. Now that you have reminded me that the "button" did not actually use an ESP-01, with some diligence I have found my previous post with the circuit: 
avanishpratap:
The most annoying thing is that the 5v and 3.3 v most common sensors like ultrasonic and Ir etc as well as Arduino is not 3.3v and the modern boards like esp32 or any esp boards are 3.3v . that makes the project even more hard than programming . The wiring and schematic creates mess and can easily destroy the boards with even little mistake.
So, get used to it! That is no reason to use an ATmega Arduino when what you really want is WiFi.
avanishpratap:
Recently I purchased a esp32 board and connected with my robot with Arduino with only rx and tx pins with 3.3 v voltage divider I don't know what happened the project runs very fine for 1 week and suddenly one week later my esp burned and I have tried everything but it didn't worked at all.
So you should now present the details here - pictures and circuit schematic - in order to learn what you did wrong. 
avanishpratap:
Now I am frustrated and not in mood to invest money on these expensive boards . First i have to learn on cheaper ones
Presently, the ESP32 is excessively expensive. But you mostly do not need it, the ESP8266 is just fine.
And the ESP8266 boards such as the minimal ESP-01 and the very practical WeMOS D1 Mini are similar in price to or possibly even cheaper than Arduino clones, so they are the "cheaper ones". 