# A New Foot Trajectory Planning Method for Legged Robots and Its Application in Hexopod Robots
## 1 Introduction  
With the development of AI technology, mobile robots are appearing more and more frequently in public. According to the motion mode, mobile robots can be divided into wheeled robots [1, 2], tracked robots [3], and legged robots [4, 5]. In the face of complex environments as well as rugged terrains, legged robots have incomparable flexibility and applicability compared with the other two kinds of robots. The design idea of legged robots originated from bionics. Inspired by mammals, insects, amphibians, etc., legged robots try to imitate the structure as well as movement mode of different legs [6]. Up to this point, there have been many different kinds of bionic legged robots that were designed and studied. With the support of the U.S. Department of Defense and by imitating a dog, Boston Dynamics developed the quadruped robot BigDog, which possessed strong obstacle crossing ability and could overcome rugged terrain [7]. Inspired by insects, Case Western Reserve University designed a bionic insect robot that could jump, walk, turn, and avoid obstacles in a certain space [8]. In China, also from the perspective of bionics and combining motion control analysis, different kinds of leggedrobots were designed by Shandong University [9; 10], Harbin University of Science and Technology [11], and Shanghai Jiaotong University [12]. Common legged robots include biped robots, quadruped robots, hexapod robots, and octopod robots. For biped robots, the movement balance is difficult to control [13; 14]. Even very simple walking similar to those in humans will become a big challenge for biped robots. For quadruped robots, they are able to walk steadily, but have strong dependencies on each leg [15]. When one of the four legs breaks for some reason, the quadruped robot cannot continue working anymore. In contrast, hexapod robots can still adjust in the case that one leg breaks through an adaptive fault tolerant gait [16]. Up to this point, there is very little work about octopod robots in terms of complex control [17]. All in all, hexapod robots have natural advantages in movement stability and are studied a lot. In terms of the hexapod robot's stable movement in different terrains, most research realized this by switching gait. [PERSON] et al. presented a novel CPG (center pattern generator)-based gait generation for a curved-leg hexapod robot and enabled the robot to achieve smooth and continuous mutual gait transitions [18]. [PERSON] presented an adaptive locomotion control approach for a hexapod robot by using a 3D two-layer artificial center pattern generator (CPG) network [19]. These methods all obtained promising results in some aspects, but they could not confront any complex scene because of the limited gait patterns. Our current work, from another point of view, finds a new method to help the hexapod robot improve its movement stability for all kinds of terrains, which is achieved by adaptively planning the foot's trajectory in order to stabilize the robot's attitude. With this method, the gait can remain the same. To implement the above theory on a physical robot, the robot should have the ability to sense its landing information firstly. In [20], [PERSON] et al. developed a new kind of free gait controller and applied it to a large-scale hexapod robot with heavy load, where sensory feedback signals of the foot position were employed in both the free gait planner and the gait regulator. In [21], [PERSON] and [PERSON] presented a minimalistic approach for a hexapod robot's adaptive locomotion control, which enabled traversing rough terrains with a small and affordable hexapod walking robot, and servomotor position feedback was also used to reliably detect the ground contact point. Up to this point, the problem of how to obtain landing information has not been sufficiently considered as well as studied in most legged robots. In [21], this information was obtained by comparing the joint error and the error threshold.