CN106475999A

CN106475999A - The acceleration control method of the Dual-Arm Coordination based on impedance model under hard conditions

Info

Publication number: CN106475999A
Application number: CN201611202256.6A
Authority: CN
Inventors: 段晋军; 甘亚辉; 戴先中
Original assignee: Southeast University
Current assignee: Southeast University
Priority date: 2016-12-23
Filing date: 2016-12-23
Publication date: 2017-03-08
Anticipated expiration: 2036-12-23
Also published as: CN106475999B

Abstract

The invention discloses under a kind of hard conditions the Dual-Arm Coordination based on impedance model acceleration control method, comprise the following steps：S1：Robot controller gathers the information of six-dimension force sensor, the information collecting is filtered processing first, then carries out gravity compensation, finally obtains the departure data with expected force or expectation moment values；S2：According to impedance model the departure transformation of data of the departure data of power or moment values is the robot end's acceleration of movement and angular acceleration of pivoting in cartesian space；S3：Try to achieve corresponding position function, velocity function, acceleration function and acceleration function；S4：According to inverse kinematics and then try to achieve the joint angles function in joint space；S5：Sent to servo-driver by the bus of controller after isochronous interpolation joint angles function being carried out joint space, and then control the action of robot.The present invention can realize real-time force tracking effect, and motion smoothing when robot follows.

Description

The acceleration control method of the Dual-Arm Coordination based on impedance model under hard conditions

Technical field

The present invention relates to the high accuracy based on impedance model is drawn under industrial robot field, more particularly to hard conditions The method for control speed of teaching robot.

Background technology

For multi-robot cooperation system is compared to single robot, in work compound ability, adapt to complex task and adaptation The aspects such as complex environment embody advantage, and are also the very important link of one of co-melting robot, are intelligent groups The basis realized.Taking multi-robot Cooperation welding as a example, in multi-robot Cooperation welding, the key scientific problems of more core are： Position power coordination problem between both arms (two transfer robots), current difficult point is embodied in the difficult control of internal force between both arms, existing It is big etc. that control algolithm realizes difficulty.Between traditional solution both arms, three kinds of intuitive solution of position power coordination are：1) foundation is double Kinetic model under robot closed chain：Set up the Coupling Dynamic Model of both arms and the object to be operated, and attempt theoretically Solve the problems such as system modelling error and external interference；2) hybrid position/power controls：Contact force to robot end and position Carry out orthogonal control, carry out power control in a direction, other directions carry out position control.3) set up mechanical arm and operated thing Internal impedance between body, solves the problems, such as the internal force in the machine human world；Set up by the external impedance between operation object and environment, solve thing Body and the external force problem of environment；Internal impedance and external impedance fused controlling.However, these three schemes suffer from the drawback that：1. it is directed to Scheme 1 and scheme 3, most of research at present rests on the theory analysis stage, and experiment also stays at simply both arms cooperation clamping Workpiece is simply moved.2. it is directed to scheme 2, hybrid position/power control is only applicable to the tight coordination of non-critical certain direction lower By the situation of force constraint, such as cooperate and the task such as carry, capture and assemble, be not appropriate for 6 DOF degree under strictly tight coordination and be all subject to The industrial applications of force constraint, such as multi-robot Cooperation welding workpiece.3. it is directed to scheme 3, do not solve strict in actual control The poor problem with the difficult control of internal force of both arms real-time under tight coordination.

Content of the invention

Goal of the invention：It is an object of the invention to provide a kind of hard conditions that can solve the problem that defect present in prior art Under Dual-Arm Coordination based on impedance model acceleration control method.

Technical scheme：For reaching this purpose, the present invention employs the following technical solutions：

The acceleration control method of the Dual-Arm Coordination based on impedance model under hard conditions of the present invention, including following Step：

S1：Robot controller gathers the information of six-dimension force sensor, the information collecting is filtered processing first, Then carry out gravity compensation, finally obtain the departure data with expected force or expectation moment values；

S2：According to impedance model by the departure transformation of data of the departure data of power or moment values be robot end The acceleration of movement and the angular acceleration pivoting in cartesian space；

S3：Smooth interpolation is carried out according to the S type speed control curve of deformation to motion, tries to achieve corresponding position function, speed Degree function, acceleration function and acceleration function；

S4：According to inverse kinematics and then try to achieve the joint angles function in joint space；

S5：Sent to watching by the bus of controller after joint angles function being carried out the isochronous interpolation of joint space Take driver, and then control the action of robot.

Further, in described step S1, the information that robot controller gathers six-dimension force sensor is in specified force control week Phase reads power and the moment information of six-dimension force sensor by UDP communication port.

Further, in described step S2, robot end's acceleration of movement and pivoting in cartesian space The matrix a of angular acceleration composition_iRepresent, a_iMatrix for 6*1, matrix a_iMiddle first three rows are that robot end is empty in Descartes Between middle movement acceleration, three row are the angular acceleration that robot end pivots in cartesian space afterwards, a_iFor：

In formula (1), F_zmaxMaximum six-dimensional force and moment information that expression can be born, a_maxRepresent that robot end allows Peak acceleration, F_dRepresent expectation follow the tracks of six-dimensional force, f be a monotonic function, S represent diagonal line function be 0 or 1 right Angular moment battle array.

Further, described step S3 comprises the following steps：

S3.1：Position function θ (t), velocity function v (t), acceleration function a (t) and acceleration are tried to achieve according to formula (2) Function j (t)：

In formula (2), θ_iFor initial position, v_iFor initial velocity, a_iFor initial acceleration, a_i+1For desired terminal velocity, t For the normalized time, T is the communication cycle of robot controller and servo-driver；

S3.2：Judge a_i+1With a_iDifference absolute value whether more than a_max, v_iAbsolute value whether more than V_max, a_maxRepresent The acceleration of the robot end's maximum allowing, V_maxRepresent the maximum speed of the robot end allowing：If a_i+1With a_iIt The absolute value of difference is more than a_max, v_iAbsolute value be not above V_max, then carry out step S3.3；If a_i+1With a_iDifference absolute value More than a_max, v_iAbsolute value also above V_max, then carry out step S3.4；

S3.3：Judge a_i+1With a_iSize：If a_i＞ a_i+1, then position function θ (t), speed are recalculated according to formula (3) Degree function v (t), acceleration function a (t) and acceleration function j (t)；If a_i＜ a_i+1, then position is recalculated according to formula (4) Put function # (t), velocity function v (t), acceleration function a (t) and acceleration function j (t)；

S3.4：Position function θ (t), velocity function v (t), acceleration function a (t) are recalculated according to formula (5) and plus adds Velocity function j (t)；

Further, in described step S5, the bus of controller is EtherCAT bus.

Further, described robot controller is divided into six levels from top to bottom, that is, client layer, six-dimensional force signals collecting and Process layer, impedance control layer, Acceleration Control layer, joint interpolation layer and EtherCAT bus communication layer；Wherein, client layer, six Dimension force signal collection and process layer, the opening of impedance control layer, Acceleration Control layer, joint interpolation layer and EtherCAT bus Communication Layer is not externally developed.

Further, described client layer provides the user mutual interface of user's secondary development, six-dimensional force Signal sampling and processing Layer provides six-dimensional force collection and the Processing Interface of user's secondary development, and impedance control layer provides the impedance control of user's secondary development Interface.

Beneficial effect：Compared with prior art, the present invention has following beneficial effect：

1) solve the problems, such as actual industrial：Dissect the problem that present actual industrial scene exists, analyze its essential characteristic, propose Corresponding solution, not only rests on theory analysis stage and the carrying application of simple both arms；

2) method versatility：Compared to traditional hybrid position power coordination approach be only applicable to non-critical tightly coordinate (only certain Individual direction or certain several direction are constrained by power) task, the scheme being carried have more versatility, tightly coordinate for non-critical simultaneously Task and strictly tight two kinds of situations of coordination of tasks (six dimensions are all by force constraint) provide solution；

3) improve following effect in real time and solving the uncontrollable problem of internal force of coordination.Compared to traditional power prosecutor case Speech, the present invention can realize real-time force tracking effect, and motion smoothing when robot follows, and efficiently solves between both arms Internal force hardly possible control problem；

4) provide open second development interface.Include for the open interface of user：The user mutual interface of task layer, The model interface of impedance layer, user oneself can change flexible parameter and modification impedance model according to demand.

Brief description

Fig. 1 is the schematic diagram of Dual-Arm Coordination control system that is directed to of method of the specific embodiment of the invention；

Fig. 2 is the Acceleration Control Organization Chart of the specific embodiment of the invention；

Fig. 3 is the flow chart in the unit force control cycle of Dual-Arm Coordination under the hard conditions of the specific embodiment of the invention；

Fig. 4 is the block diagram of the impedance control of the specific embodiment of the invention；

Fig. 5 is the corresponding relation figure of the F based on impedance model and a of the specific embodiment of the invention；

Fig. 6 is the speed controlling schematic diagram based on deformation S type curve of the specific embodiment of the invention；

Fig. 7 is the position based on speed control curve, speed, acceleration and the acceleration of the specific embodiment of the invention Schematic diagram.

Specific embodiment

With reference to specific embodiment, technical scheme is further introduced.

This specific embodiment discloses a kind of Acceleration Control of the Dual-Arm Coordination under hard conditions based on impedance model Method, comprises the following steps：

Fig. 1 is the structural representation of Dual-Arm Coordination control system.Defining wherein one robot is leading robot, clamping A part for the object to be operated, and the track of leading motion；An other robot is auxiliary robot, clamps the object to be operated Another part, in auxiliary robot end, six-dimension force sensor is installed, for preventing from leading to internal force excessive due to position and attitude error Damage force transducer, protection device is installed between robot end and six-dimension force sensor, auxiliary robot is according to end The feedback information of six-dimension force sensor follows the tracks of the movement locus of leading robot.

Robot controller is divided into six levels from top to bottom, as shown in Fig. 2 i.e. client layer, six-dimensional force signals collecting and Process layer, impedance control layer, Acceleration Control layer, joint interpolation layer and EtherCAT bus communication layer；Wherein, 1) client layer master It is used for interacting with user interface, for example, interacts with teaching box, the effect of this layer is to set correlation according to user's request Parameter, flexible parameter that such as auxiliary robot need to show in universal time coordinated etc..2) six-dimensional force Signal sampling and processing layer is mainly used In the collection of sextuple force signal, filtering, gravity compensation etc..3) impedance control layer mainly sets up six-dimensional force deviation and auxiliary machinery The relation of people's end movement, establishes power deviation F in the present invention and move in cartesian space and add in auxiliary robot end The transformation relation of speed a, the schematic diagram of specific relational expression is as shown in figure 4, the model adopting is impedance Control Model.4) accelerate Degree key-course is mainly the smooth control realized in cartesian space based on accelerating curve according to the relationship model that Fig. 4 is set up System, is that auxiliary robot draws lower end final behavior table based on impedance model in cartesian space in leading robot Existing：Real-time tracking dominates the movement locus of robot.5) when interpolation layer in joint mainly carries out to each axle waiting in joint space Interpolation synchronous planning.6) EtherCAT bus communication layer mainly completes the conversion to pulsed quantity for the joint angle angle value, and passes through This pulses switch amount is sent to servo slave station by EtherCAT main website, receives the status information from servo slave station simultaneously, including State value, present position values, velocity amplitude, accekeration etc..

In robot controller, most crucial layer is：Force signal collection and process layer, impedance layer and Acceleration Control layer, this Three layers are commonly referred to as Dual-Arm Coordination power control bag.1) force signal collection and result have impact on the precision of traction, and force signal is typically logical The method crossing filtering removes dither signal, then carries out gravity compensation under various poses to auxiliary robot.2) impedance layer Core is impedance model, linear function transformation or quadratic polynomial functional transformation that user can oneself set according to demand, but It is the requirement that need to meet monotonic function.3) Acceleration Control layer is the S type deformation acceleration planning of quintic algebra curve, specified Acceleration was carried out in the unit force control cycle with smooth interpolation, makes auxiliary robot end movement smooth and ensure to follow in real time leading Robot.

In fig. 2, " open " in open architecture controller is embodied in：Provide the user with the interface of secondary development, including The interface of three openings：User mutual interface (User Interface, UI), six-dimensional force collection and Processing Interface (Force/ Torque Acquire Interface, FTAI) and impedance control interface (Impedance Control Interface, ICI), other layers (speed controlling layer, joint interpolation layer and Communication Layer) are related to specific control realization, therefore not to external-open Put.

Fig. 3 is the unit force control cyclic flow graph of Dual-Arm Coordination under hard conditions.User (for example can show according to user interface Religion box) start auxiliary robot coordination tracing mode, and related robot flexibility tracking parameter is set, such as robot expectation The inertia (M) that shows, damping (B) and rigidity (K) coefficient etc..Robot controller in real time to six-dimensional force information, Filtering and process, obtain current six-dimensional force departure after the gravity compensation then entering line sensor, and then according to based on modulus of impedance The Acceleration Control algorithm of type tries to achieve pose departure, and final control auxiliary robot follows the tracks of leading machine according to pose side-play amount The track of people.

Fig. 4 is the structure chart of impedance control, is an introduction about the construction to Fig. 3 flow chart.

In step S2, on the basis of step S1, according to user set robot flexibility parameter and selectable impedance Types of models initializes the parameter of impedance layer, and flexible parameter can set inertia, damping and the rigidity of robot expectation performance, with When can be according to the impedance model type set such as functional relationship in Figure of description 5, generally, according to the flexibility of user Parameter can automatically select corresponding functional relationship (a certain functional relationship in Fig. 5), and general function expression is as follows：

In formula (1), a_iFor robot end in cartesian space the acceleration of movement and the angular acceleration that pivots The matrix of composition, a_iMatrix for 6*1, matrix a_iMiddle first three rows are the acceleration of robot end's movement in cartesian space, Three row are the angular acceleration that robot end pivots in cartesian space afterwards；F_zmaxIt is maximum sextuple that expression can be born Power and moment information, F_zmaxIt is a matrix being made up of three-dimensional force and three-dimensional moment, a_maxRepresent that robot end allows High acceleration, F_dRepresent the six-dimensional force that expectation is followed the tracks of, f represents the function shown in Fig. 5, and S represents that diagonal line function is 0 or 1 Diagonal matrix.

Herein choose curve 3. as a example, i.e. linear functional relation, then corresponding function expression is as follows：

S in above formula is the matrix of sextuple degree, and S is pair of horns matrix it is intended that diagonal entry is only 0 or 1.Unit Element is set to 0 expression position offset in this direction and does not stress the impact of deviation signal, and that is, the direction does not stress constraint；Element It is set to the 1 expression direction and is subject to force constraint, set herein according to actual demand.

Step S3 comprises the following steps：

S3.1：On the basis of step S2, define the power control cycle first, the principle of definition is：Controller and driving at present Communication cycle between device is 1ms or 4ms, and on the basis of 1ms or 4ms, controlling cycle defines suitable timeslice to realize The control in one power control cycle, definition unit interval piece is 20 controlling cycles, and that is, 20ms or 80ms is a timeslice, Controller bottom ensure that the power control cycle is short enough.

Known initial position θ_i, initial velocity v_i, initial acceleration a_i, initial jerk j_i=0, desired terminal speed Degree v_i+1, desired terminal acceleration a_i+1With desired terminal acceleration j_i+1=0, set up following quintic algebra curve equation：

Wherein, w₀,w₁,w₂,w₃,w₄,w₅For the coefficient of quintic algebra curve, according to " acceleration of a certain moment Mo and next Acceleration at the beginning of moment is continuous " constraints obtain to the constraint equation that should look like this.

The coefficient of quintic algebra curve can be calculated according to above-mentioned constraints, corresponding Acceleration Control curve is as said Shown in bright accompanying drawing 6.And then derive the function of corresponding position, acceleration and acceleration, expression is as follows：

In formula (5), θ_iFor initial position, v_iFor initial velocity, a_iFor initial acceleration, a_i+1For desired terminal velocity, t For the normalized time, T is the communication cycle of robot controller and servo-driver；Position function θ is tried to achieve according to formula (5) (t), velocity function v (t), acceleration function a (t) and acceleration function j (t)；

S3.3：Judge a_i+1With a_iSize：If a_i＞ a_i+1, then position function θ (t), speed are recalculated according to formula (6) Degree function v (t), acceleration function a (t) and acceleration function j (t)；If a_i＜ a_i+1, then position is recalculated according to formula (7) Put function # (t), velocity function v (t), acceleration function a (t) and acceleration function j (t)；

S3.4：Position function θ (t), velocity function v (t), acceleration function a (t) are recalculated according to formula (8) and plus adds Velocity function j (t)；

This specific embodiment is 16Kg with the artificial experimental subject of two ESTUN ER16 industrial machines, its load, and one , as leading robot, one as auxiliary robot for platform.Now only consider the situation of auxiliary robot it is assumed that initial position θ_i= 0th, initial velocity v_i=0, initial acceleration a_i=0, initial jerk j_i=0, desired terminal acceleration a_i+1=500mm/ s²With desired terminal acceleration (j_i+1=0), corresponding position, speed, acceleration and acceleration are in unit interval piece Curve chart as shown in Figure 7.

Above-mentioned accompanying drawing to specifications 1 is built dual arm system, the level in by specification accompanying drawing 2 is by above-mentioned algorithm in control It is achieved in device processed, you can robot draws the effect of robot.

Claims

1. under hard conditions the Dual-Arm Coordination based on impedance model acceleration control method it is characterised in that：Walk including following Suddenly：

S1：Robot controller gathers the information of six-dimension force sensor, the information collecting is filtered processing, then first Carry out gravity compensation, finally obtain the departure data with expected force or expectation moment values；

S2：According to impedance model by the departure transformation of data of the departure data of power or moment values be robot end in flute The acceleration of movement and the angular acceleration pivoting in karr space；

S3：Smooth interpolation is carried out according to the S type speed control curve of deformation to motion, tries to achieve corresponding position function, speed letter Number, acceleration function and acceleration function；

S5：Sent by the bus of controller after joint angles function being carried out the isochronous interpolation of joint space and drive to servo Dynamic device, and then control the action of robot.

2. under hard conditions according to claim 1 the Dual-Arm Coordination based on impedance model acceleration control method, its It is characterised by：In described step S1, the information that robot controller gathers six-dimension force sensor is to pass through in the specified force control cycle UDP communication port reads power and the moment information of six-dimension force sensor.

3. under hard conditions according to claim 1 the Dual-Arm Coordination based on impedance model acceleration control method, its It is characterised by：In described step S2, the robot end acceleration of movement and the angle pivoting in cartesian space accelerate The matrix a of degree composition_iRepresent, a_iMatrix for 6*1, matrix a_iMiddle first three rows are that robot end moves in cartesian space Dynamic acceleration, three row are the angular acceleration that robot end pivots in cartesian space afterwards, a_iFor：

a_{i} = S \cdot f (\frac{a_{m a x} \cdot (F - F_{d})}{F_{z m a x}}) - - - (1)

In formula (1), F_{z max}Maximum six-dimensional force and moment information that expression can be born, a_maxRepresent that robot end allows High acceleration, F_dRepresent the six-dimensional force that expectation is followed the tracks of, f is a monotonic function, S represents that diagonal line function is 0 or 1 to angular moment Battle array.

4. under hard conditions according to claim 1 the Dual-Arm Coordination based on impedance model acceleration control method, its It is characterised by：Described step S3 comprises the following steps：

S3.1：Position function θ (t), velocity function v (t), acceleration function a (t) and acceleration function j are tried to achieve according to formula (2) (t)：

\{\begin{matrix} θ (t) = θ_{i} + v_{i} \cdot t + \frac{a_{i}}{2} \cdot t + \frac{a_{i + 1} - a_{i}}{4 \cdot T^{2}} \cdot t^{4} - \frac{a_{i + 1} - a_{i}}{10 \cdot T^{3}} \cdot t^{5} \\ v (t) = v_{i} + a_{i} \cdot t + \frac{a_{i + 1} - a_{i}}{T^{2}} \cdot t^{3} - \frac{a_{i + 1} - a_{i}}{2 \cdot T^{3}} \cdot t^{4} \\ a (t) = a_{i} + 3 \cdot \frac{a_{i + 1} - a_{i}}{T^{2}} \cdot t^{2} - 2 \cdot \frac{a_{i + 1} - a_{i}}{T^{3}} \cdot t^{3} \\ j (t) = 6 \cdot \frac{a_{i + 1} - a_{i}}{T^{2}} \cdot t - 6 \cdot \frac{a_{i + 1} - a_{i}}{T^{3}} \cdot t^{2} \end{matrix} - - - (2)

In formula (2), θ_iFor initial position, v_iFor initial velocity, a_iFor initial acceleration, a_i+1For desired terminal velocity, t is to return The time of one change, T is the communication cycle of robot controller and servo-driver；

S3.2：Judge a_i+1With a_iDifference absolute value whether more than a_max, v_iAbsolute value whether more than V_max, a_maxRepresent and allow The maximum acceleration of robot end, V_maxRepresent the maximum speed of the robot end allowing：If a_i+1With a_iDifference Absolute value is more than a_max, v_iAbsolute value be not above V_max, then carry out step S3.3；If a_i+1With a_iThe absolute value of difference exceed a_max, v_iAbsolute value also above V_max, then carry out step S3.4；

S3.3：Judge a_i+1With a_iSize：If a_i＞ a_i+1, then position function θ (t), speed letter are recalculated according to formula (3) Number v (t), acceleration function a (t) and acceleration function j (t)；If a_i＜ a_i+1, then position letter is recalculated according to formula (4) Number θ (t), velocity function v (t), acceleration function a (t) and acceleration function j (t)；

\{\begin{matrix} θ (t) = θ_{i} + v_{i} \cdot t + \frac{a_{i}}{2} \cdot t + \frac{a_{i} - a_{m a x} - a_{i}}{4 \cdot T^{2}} \cdot t^{4} - \frac{a_{i} - a_{m a x} - a_{i}}{10 \cdot T^{3}} \cdot t^{5} \\ v (t) = v_{i} + a_{i} \cdot t + \frac{a_{i} - a_{\max} - a_{i}}{T^{2}} \cdot t^{3} - \frac{a_{i} - a_{m a x} - a_{i}}{2 \cdot T^{3}} \cdot t^{4} \\ a (t) = a_{i} + 3 \cdot \frac{a_{i} - a_{\max} - a_{i}}{T^{2}} \cdot t^{2} - 2 \cdot \frac{a_{i} - a_{\max} - a_{i}}{T^{3}} \cdot t^{3} \\ j (t) = 6 \cdot \frac{a_{i} - a_{\max} - a_{i}}{T^{2}} \cdot t - 6 \cdot \frac{a_{i} - a_{\max} - a_{i}}{T^{3}} \cdot t^{2} \end{matrix} - - - (3)

\{\begin{matrix} θ (t) = θ_{i} + v_{i} \cdot t + \frac{a_{i}}{2} \cdot t + \frac{a_{i} + a_{m a x} - a_{i}}{4 \cdot T^{2}} \cdot t^{4} - \frac{a_{i} + a_{m a x} - a_{i}}{10 \cdot T^{3}} \cdot t^{5} \\ v (t) = v_{i} + a_{i} \cdot t + \frac{a_{i} + a_{\max} - a_{i}}{T^{2}} \cdot t^{3} - \frac{a_{i} + a_{m a x} - a_{i}}{2 \cdot T^{3}} \cdot t^{4} \\ a (t) = a_{i} + 3 \cdot \frac{a_{i} + a_{\max} - a_{i}}{T^{2}} \cdot t^{2} - 2 \cdot \frac{a_{i} + a_{\max} - a_{i}}{T^{3}} \cdot t^{3} \\ j (t) = 6 \cdot \frac{a_{i} + a_{\max} - a_{i}}{T^{2}} \cdot t - 6 \cdot \frac{a_{i} + a_{\max} - a_{i}}{T^{3}} \cdot t^{2} \end{matrix} - - - (4)

S3.4：Position function θ (t), velocity function v (t), acceleration function a (t) and acceleration are recalculated according to formula (5) Function j (t)；

\{\begin{matrix} θ (t) = θ_{i} + v_{i} \cdot t + \frac{a_{i}}{2} \cdot t^{2} + \frac{V_{m a x} - v_{i} - a_{i} \cdot T}{2 \cdot T^{3}} \cdot t^{4} - \frac{V_{m a x} - v_{i} - a_{i} \cdot T}{5 \cdot T^{4}} \cdot t^{5} \\ v (t) = v_{i} + a_{i} \cdot t + 2 \cdot \frac{V_{m a x} - v_{i} - a_{i} \cdot T}{T^{3}} \cdot t^{3} - \frac{V_{m a x} - v_{i} - a_{i} \cdot T}{T^{4}} \cdot t^{4} \\ a (t) = a_{i} + 6 \cdot \frac{V_{m a x} - v_{i} - a_{i} \cdot T}{T^{3}} \cdot t^{2} - 4 \cdot \frac{V_{m a x} - v_{i} - a_{i} \cdot T}{T^{4}} \cdot t^{3} \\ j (t) = 12 \cdot \frac{V_{m a x} - v_{i} - a_{i} \cdot T}{T^{3}} \cdot t - 12 \cdot \frac{V_{m a x} - v_{i} - a_{i} \cdot T_{i}}{T^{4}} \cdot t^{2} \end{matrix} - - - (5) .

5. under hard conditions according to claim 1 the Dual-Arm Coordination based on impedance model acceleration control method, its It is characterised by：In described step S5, the bus of controller is EtherCAT bus.

6. under hard conditions according to claim 1 the Dual-Arm Coordination based on impedance model acceleration control method, its It is characterised by：Described robot controller is divided into six levels from top to bottom, i.e. client layer, six-dimensional force Signal sampling and processing Layer, impedance control layer, Acceleration Control layer, joint interpolation layer and EtherCAT bus communication layer；Wherein, client layer, six-dimensional force Signal sampling and processing layer, the opening of impedance control layer, Acceleration Control layer, joint interpolation layer and EtherCAT bus communication Layer is not externally developed.

7. under hard conditions according to claim 6 the Dual-Arm Coordination based on impedance model acceleration control method, its It is characterised by：Described client layer provides the user mutual interface of user's secondary development, and six-dimensional force Signal sampling and processing layer provides The six-dimensional force collection of user's secondary development and Processing Interface, impedance control layer provides the impedance control interface of user's secondary development.