Fig. 5: Figure reproduced with permission from ref. 17—spatial and temporal dynamics of fragile and antifragile behaviors of a robot in uncertain environments.
The spatial dynamics (inset left) describe the robot’s trajectory, in Cartesian (x,y) space, in the presence of uncertainty (i.e., several types of unexpected faults in the robot’s motion). Red describes the strong (i.e., fragile) deviation from the goal of moving as fast as possible from point P1 to point P2 in the presence of faults. Green marks the antifragile trajectory which absorbs the uncertainty and gains a smoother trajectory. The temporal dynamics (inset right) describe the robot’s trajectory tracking in the presence of uncertainty from the perspective of travel time. Travel time is implicit in the relation between the control signal sent to the robot’s actuators and the curvature of the trajectory of the robot given that signal. In this case, the fragile behavior is characterized by longer executions away from the prescribed dynamics whereas the antifragile behavior has a more straight convergence in the presence of faults. Closed-loop dynamics in the presence of stressors and volatility. The planes describe possible system dynamics motions from various initial conditions in the presence of stressors and volatility and the convergence to antifragile behavior. The redundant overcompensation refers to geometrically longer paths to reach the antifragile region (i.e., the green curve between the planes). These longer paths ensure that the system’s response can cope with jitter in reaching prescribed dynamics in the presence of faults.
