The most powerful is the sun
You already have the most powerful broadcast power device in the solar system available during the daytime. It's called the sun.
The sun is a big ball of flaming hot stuff that radiates power in all directions. By the time it gets to earth and filters through our atmosphere, you're left with around 300 watts per meter squared of area. So while you can't have an antenna due to the dominant wavelengths being much higher, you can have a receiving panel. If you have a 10% efficient panel of 50cm each side (0.25m2), you can get a theoretical 7.5 watts. Not really enough for a robot mobile, but if you pretend to have better solar panels you could get up to 75 watts, which is enough for some moderately energy efficient systems (a laptop charger is about 75 watts, the curiosity rover's RTG outputs about 100W).
Going through your requirements:
- No transmitting antenna
- 1 (square) foot or thereabouts.
- Safe for people to live as per normal
- A car battery is about 600Wh (45Ah, 12V), so a 100% efficient 50cm-per-side solar panel would take about 2 hours.
No, transmitting towers aren't good enough
Let's say that the sun isn't good enough for you and you have to have a transmitting tower. It's going to have to be a powerful transmitting tower. Lets say you want to get that 300W/m2 at 1km radius. The inverse square law is the killer. If you're 1 meter away and receive 1W/m2 of energy, then being 2m away gives you 0.25m2 of energy. By the time you're 1km away, you're receiving 0.000001 W/m2 of energy. Reversing this tells us that to get 300W/m2 of energy at 1km requires a power output of something like 300,000,000 W/m2 at 1m radius distance. For reference, if you switched on all the backup transmitters of the most powerful transmitter in the world while it was operating, it would only output about 3MW, still 100 times too low.
Because we've gone with the same power output as the sun at 1km range, we meed all the power requirements from your question. However we now have:
- Huge transmitting antenna (to avoid it melting)
- Enormous operation costs
- Instant burns to anyone near the transmitting tower.
So: Use solar power. Seriously. Everything else only operates at close distances or requires cancer-inducing levels of power. (Yes, the sun does output cancer-inducing levels of power, but at least its a very long way away).
The Asimo Robot draws a huge amount of power
The asimo robot has a lithium battery that weighs about 13 pounds (5.8kg). Most lithium chemistries have a power density of about 100-200 Wh/kg. This means the robot has about 600-1200 Wh of energy, which it drains in half-an-hour which results in an average power draw of 1.2-2.4kw.
So it turns out that a 100% efficient 0.25m2 square solar panel outputting 75 watts is about 20 times too low. You'd need a 100% efficient solar panel of about 5m2 surface area to power it continuously.
Powering the Asimo robot via broadcast power is not feasible. The Sun is the most powerful thing you will find that is "safe" and omnidirectional, and it's around 20 times too weak. As it turns out, there are reasons why we don't power robots via broadcast power anywhere other than micro robots on laboratory tables.
To get this to work, you'd have to handwave more efficient robots. Even 100% efficient solar panels, or 100% efficient transmitter/receiver antennas isn't enough.