I think we are connected to the world by Biochemistry first and then physical and verbal interactions. If a robot feeds a dog regularly, pampers it and cuddles it regularly, would it develop the same feeling to the dog as it would have developed with a human? A sci-fi robot like Ultron from Avenger movie.
Assuming you mean a robot "designed to be human" (that means human-like behavior patterns, human-comparable intelligence, being self-aware and able to learn), then from the dog's perspective, the only significant difference is the differing smell.
There is no scientific evidence for mystical or metaphysical "connections to the world".
From the dog's perspective, the defining factors are:
Owner's behavior (petting, feeding, walking, training, rewards for good behavior or learning tricks). In this case, the robot is no different from the human.
Owner's speech (voiceprint). There's evidence that dogs understand human speech to some extent (https://www.independent.co.uk/news/science/dogs-can-understand-human-speech-scientists-say-a7216481.html). Given how adaptable organic brains are, I assume a dog would be able to adapt to even a synthetic (digitally altered) voiceprint over time or one that spoke in a conspicuously robotic manner (for example: "Temperature alert. Please fetch an external cooling fan./Your assistance above your designated specifications continues to be noted." instead of "It's getting hot in here. Grab a soda from the fridge over there?/Good dog!"
Owner's scent. The only real difference from a dog's perspective. A robot would lack the distinctive scent cues from a human, except if the robot was designed to produce those as well. Even if those aren't present, a dog should be able to adapt to a robotic owner's distinctive smell (plastic with motor oil and a hint of ozone).