Collisions at high speed can damage robot hardware. Nonetheless, collisions tend to happen since robots operate increasingly in complex, unstructured environments. Research on a fundamental level is necessary to study ante-impact planning and post-impact control algorithms that allow the robots to intentionally or unintentionally collide with the environment while avoiding hardware failure. This fundamental research will be validated on three use cases: (1) industrial robots dealing with large product variability and (2) humanoid robots falling over, both characterized by unintentional collisions, and (3) robotic tasks where collisions are intentional. The goals of this project are (1) to better understand how impact results in robot hardware damage, (2) how to plan the pose of the robot prior to impact to make it more collision tolerant and (3) to mitigate the collision by impact-aware control. This project will lead to industrial robots that can be deployed in less structured environments in a robust, collision tolerant fashion. Furthermore, avoiding hardware damage each time a humanoid looses balance will allow more bold experimental work, currently hindering technological progress. Lastly, allowing robots to make contact at non-zero speeds by impacting the environment can significantly increase the speed of e.g. a picking operation.