Kinematics model-free trajectory tracking method for robotic arms and robotic arm system

A kinematics model-free trajectory tracking method for a robotic arm, wherein the method comprises steps of:

• obtaining an actual trajectory equation ra(t) of the robotic arm at time t according to a sensor, and combining the actual trajectory equation ra(t) with a predetermined target trajectory equation rd(t) to obtain a first error function e(t);
• passing the first error function e(t) through a gradient neural network to obtain a driver rate {dot over (θ)}(t) of the robotic arm;
• obtaining a second error function ε(t) according to an actual speed {dot over (r)}a of an end effector of the robotic arm obtained from the sensor and a product Ĵ(θ(t)){dot over (θ)} (t) of a Jacobian matrix and a driver rate;
• passing the second error function ε(t) through the gradient neural network to obtain Ĵ(θ(t));
• jointly solving {dot over (θ)}(t) and Ĵ(θ(t)) to obtain a joint state vector θ(t) of the robotic arm;
• driving a motion of the robotic arm by a controller according to the joint state vector θ(t) of the robotic arm to complete trajectory tracking;
• the e(t) is expressed by the following formula:
• e(t)=∥rd(t)−ra(t)∥22
• wherein, the rd(t) represents a predetermined target trajectory equation at time t, and ∥·∥2 represents a 2-norm of a vector;
• the {dot over (θ)} (t) is expressed by the following formula:
• {dot over (θ)}(t)=γĴ(θ(t))T(rd(t)−ra(t))
• wherein, the shown {dot over (θ)}(t) represents a first derivative of θ(t) at time t, the Ĵ(θ(t)) represents the Jacobian matrix, and the γ represents a preset positive convergence parameter.