Mobile robots are cyber-physical systems where the cyberspace and the physical world are strongly coupled. Attacks against mobile robots can transcend cyber defenses and escalate into disastrous consequences in the physical world. In this paper, we focus on the detection of active attacks that are capable of directly influencing robot mission operation. Through leveraging physical dynamics of mobile robots, we develop RIDS, a novel robot intrusion detection system that can detect actuator attacks as well as sensor attacks for nonlinear mobile robots subject to stochastic noises. We implement and evaluate a RIDS on Khepera mobile robot against concrete attack scenarios via various attack channels including signal interference, sensor spoofing, logic bomb, and physical damage. Evaluation of 20 experiments shows that the averages of false positive rates and false negative rates are both below 1%. Average detection delay for each attack remains within 0.40s.