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Page 65 Li et al. Intell Robot 2021;1(1):58-83 I http://dx.doi.org/10.20517/ir.2021.08

Figure 5. Examples of a nonholonomic car-like robot and a manipulator robot. A: robot motion when the door is opened [15] ; B: simple planar
robot avoiding obstacles [13] .

Q-learning algorithm, which can reduce the effect of the reward function on the convergence speed.

Some researchers pointed out that if the planned path is too close to the obstacles, it is dangerous for robot nav-
igation. A dynamic risk level was incorporated to the shunting neurodynamics model to reduce the probability
of collision in the dynamic obstacle avoidance task [37] . In addition, a novel 3-D neural dynamic model was
proposed and expected to obtain the safety-enhanced trajectory in the work space considering of minimum
sweeping area [38] . A safety consideration path planning can be implemented by setting a constant value to
inhibitory inputs in Equation (2). The safety consideration shunting equation is obtained by [39,40]
( ) ( )
∑ ∑
d
−
+
= − + ( − ) [ ] + [ ] + − ( + ) [ ] + [ − ] − (10)
d
=1 =1
where parameter is the threshold of the inhibitory lateral neural connections. In Equation (2), the inhibitory

input is only from the obstacles. However, in the safety consideration model, the inhibitory input is

consisted of two parts: [ ] and ∑ [ − ] .The ∑ [ − ] term guarantees that the negative
−
−
−
=1 =1
activity propagates to a small region due to the threshold of the inhibitory lateral neural connections. Thus,
there is a small negative neural activity region surrounding the obstacles, and the robot is able to keep a safe
distance from obstacles to avoid possible collisions.
Many variants of the bio-inspired neurodynamics models have been developed to deal with different situa-
tions. The additive model generates the real-time collision-free robot paths under most conditions [13] . Even
the computation of the additive model is simpler, the real-time performance of the additive model could be
saturated in many situations. A similar neural network model was proposed by Glasius et al. [41] for real-time
trajectory generation. Even Glasius’s model had limitations with fast dynamic systems, Glasius bio-inspired
neural network models have been used in underwater robots [42–44] . Inspired by the bio-inspired neural net-
work model, a distance-propagating dynamic system was proposed that can efficiently propagate the distance
instead of the neural activity from the target to the entire robot work space [45] . After that, Willms and Yang
designed the safety margins around obstacles. The robots not only avoid obstacles but also keep a safe distance
between the obstacles [46] . Based on Willms and Yang’s previous work, a shortest path neural networks model