# A Bio-Inspired Control Strategy for Locomotion of a Quadruped Robot
## 1 Introduction  
Compared with wheeled robots, quadruped robots with their good environmental adaptability and motion flexibility have become a research hot spot in recent years [1; 2; 3; 4; 5; 6; 7]. Specifically, the bio-heuristic control strategy based on the CPG model is widely used in the locomotion control of legged robots due to its good simulation of the rhythmic movement of animals [8; 9; 10; 11]. At present, the typical CPG models for legged robots' locomotion control can be roughly divided into three categories: CPG model based on neuron oscillators, CPG model based on nonlinear oscillators and other kinds of CPG model. The typical CPG models based on neuron oscillators are the Matsuoka model [12], the Kimura model [13], etc. [10]. The parameters of this kind of CPG model generally have a clear biological significance. Since the equations are generally nonlinear, multi-parameter and multi-dimension, its parameter's tuning and dynamic analysis are very complex. The Kuramoto phase oscillator [14; 15; 16], Hopf oscillator [17; 18] and Van Der Pol (VDP) oscillator [19] are the typical nonlinear oscillators to constitute the second kind of CPG models. Although their parameters are not as clear as the first kind of CPG models in biological significances, this kind of CPG model is mature and fewer parameters need to be tuned. Other kinds of CPG model, such as the cosine function CPG model, hardware CPG model, etc., are seldom used. The common way to control a legged robots' locomotion using CPG-based method is that the hip joints are directly controlled by the CPG output and the knee joints are controlled by mapping the hipjoint control signals in a certain way. However, most of the previous studies focused on the CPG model and its structure and connection topological relations, while only few studies were concerned with the CPG output waveform and the inter-coordination of the joints within a leg to meet the desired foot WT [4]. Generally, for a dynamic system that has stable periodic solutions (limit cycle), the waveform of the solutions is defined by the shape of the limit cycle [11]. Universally, the limit cycle shape of the equations used as a CPG model is extremely difficult to control. Thus, it leads to the situation where it is hard to control the foot WT while using CPG output to control legged robots' locomotion directly, which leads to a series of problems, such as large mechanical shock and movement shake, high energy consumption, etc. In contrast to the CPG-based method, the WT-based method has great advantages in the foot WT arbitrarily designing and planning [4; 20; 21; 22], such as excellent capability of over-obstacle, smooth motion, smaller mechanical shock, lower energy consumption, etc. [4; 6; 23; 24]. The general operation mode while using WT-based control strategy is: firstly, planning a foot WT with a specific advantage; secondly, solving the intra-leg joints' coordinated function via inverse kinematics; finally, coupling the legs in an \"up layer\" through certain phase relationships to obtain the relative gait. Although this method solves the problem of the legged robots' foot WT, generally, gaits lack flexibility and its mutual transitions are stiff. As we analyzed above, in order to generate the desired WT, the coordination of the two joints (or more) within a leg is very important. However, the shape of periodic solution (limit cycle) of CPG is difficult to control, for cooperating with another joint (or the other joints) to generate the desired WT. Thus, it is very difficult to generate the desired WT with the CPG and inverse kinematics. Fortunately, we found that this complex problem becomes very simple with a \"NN\" layer, meanwhile, the advantages of CPG-based method in gait planning and WT-based method in foot trajectory planning can be made full use of, synchronously.