I built my own using a ESP8266 and servo motors. I essentially retrofitted my current blinds. I used a servo motor and a custom designed 3D Printed gearbox to attach to the rod which turns to open and close them. Since it moves approx 90°, this was easy to do. I then programmed the ESP microcontroller to move the servo.
I have the ESP setup hosting a small web server and can send them commands via HTTP to open, close, and partially open them. I then use webcore to send the commands.
If you already have motorized blinds, I assume it would be fairly easy to use the ESP board to control them to move one direction or another. If their not motorized, you just have to assess the blind type and decide what motor would be best to do the job.
I would also recommend hardwiring them, even if you have to run a cable up to them. I tried some tests with batteries and small solar panels to charge the batteries, and even if they only moved two times a day, at less than 1A draw for a couple seconds, they would be dead in a couple weeks. Even with the solar panels, as you would need a pretty large one, and a lot of sunlight to keep it charged. I just have a 6V source plugged into an outlet nearby, and used a cable hider ran up the side of the window. Blends right in, and if the blinds are down, you can't tell its there unless you really look for it.