I have WiFi mesh network with more than one AP. So I want to see the clients' RSSI level for each APs to steer them to AP with better RSSI. I am curious whether I can check the RSSI by forcing them to broadcast some packets. In other words, I dont want to wait for the clients to send Broadcast packets, I want to make them send it, whenever I want. Lets say, I have full control over AP's software.
You could probably force your peers to send ARP or ND packets by sending a gratuitious ARP with their address.
This, however, is not the approach usually taken — most mesh networking daemons send broadcast or multicast packets periodically (these are typically known as "Hello" packets, and are compulsory in OLSR(v2) and Babel, and optional in DYMO/AODVv2).
Note further that RSSI is a poor predictor of link quality, at least for 802.11. You'll find a good discussion of related issues in the Minstrel litterature.