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A swarm of randomly moving miniature robots is an effective solution for the exploration of unknown terrains. However, the deployment of a swarm of miniature robots poses two challenges: finding an adequate locomotion strategy for fast exploration and obstacles negotiation; and implementing simple design and control solutions suited for mass manufacturing. Here, we tackle these challenges by developing a new soft robot with a minimalistic design and a simple control strategy that can randomly propel itself above obstacles and roll on the ground upon landing. The robot is equipped with two propellers that are periodically activated to jump, a soft cage that protects the robot from impacts and allows to passively roll on the ground, and a passive self-righting mechanism for repetitive jumps. The minimalistic control and design reduce the complexity of the mechanics and electronics and are instrumental to the production of a large number of robots. In the paper, the key design aspects of the robot are discussed, the locomotion of a single prototype is experimentally characterized, and improvements of the system for future swarm operations are discussed.