Fig. 4: Memristive Bellman solver for path planning tasks.

a Schematic of a 5 × 5 maze path planning scene, containing 25 states. In this maze, the state_1, state_25, and state_12 is set as Start, End, and Bonus, respectively. The state_13 and state_16 is set as Trap. Each state can perform four actions, namely, up, down, left, and right. b The initial decision (weight matrix) of the probability of transitions between states. c The approximate optimal decision (weight matrix) of the probability of transitions between states. d The value evolution tendency under the four times Bellman equation solving process. e The approximate optimal decision (weight matrix) for taking appropriate action (up, down, right, or left) of each state. f The comparison of the iteration (recurrent) times of the Bellman equation precise and approximate solving process. g Schematic of a constructed road mapping scene, containing 19 states. In this road map, the state_1 and state 18 is set as Start and End, respectively. Each state can only transmit to an adjacent state without obstacles (such as lake). h The approximate optimal decision (weight matrix) of the probability of transitions between states. i The comparison of the iteration (recurrent) times of the Bellman equation precise and approximate solving process.