CN103197671A - Humanoid robot gait planning and synthesizing method - Google Patents

Abstract

The invention discloses a humanoid robot gait planning and synthesizing method, and belongs to the technical field of humanoid robot motion planning. The humanoid robot gait planning and synthesizing method comprises the following steps that a polynomial function is adopted to represent tracks of hip joints and the tail ends of swing legs of a robot, a one-foot support period gait and a double-feet support period gait are respectively planned when the robot walks according to constraint conditions including geometric constraints, maximum stride height of the tail end of each swing leg, gait periodicity, impact effect, hip joint motions and the like when the humanoid robot walks, then the planned gaits are synthesized, and whether obtained gait tracks are stable is judged according to a zero moment point criterion. According to the humanoid robot gait planning and synthesizing method, the one-foot support period gait and the double-feet support period gait of the robot are planned and synthesized into a complete gait, the problem that collisions between legs of the robot and ground affect walking stability when the robot walks is solved, walking stability of the robot is improved, and an important effect, of the double-feet support period gait of the robot, on a complete gait period is explained at the same time.

Description

A kind of anthropomorphic robot gait planning and synthetic method

Technical field

The present invention relates to anthropomorphic robot motion planning field, particularly anthropomorphic robot gait planning and synthetic method.

Background technology

The anthropomorphic robot gait planning refers in order to finish the walking of robot, sequential and phase propetry to each joint angle motion in the robot ambulation process are determined, make robot can finish some simple job tasks, target as upper limbs grasps and moves, the operation that cooperates with the people simply, the necessary walking that can be stable of robot.The method of present anthropomorphic robot gait planning mainly contains off-line planning, online planning and off-line planning and adds three kinds of methods of online correction.Yet no matter be which kind of planing method, the gait that obtains must have stability and periodicity.

In the prior art before the present invention, a complete gait cycle during the anthropomorphic robot walking generally comprises a single pin and supports phase and a double support phase, wherein double support phase only account for wherein 20%.But for the stabilized walking of robot, double support phase plays a part very important, must consider the gait of double support phase.

After prior art was analyzed, the inventor found: when the robot walking, though shared time of robot double support phase is very short, for the stability of whole gait cycle very big influence is arranged.If according to existing technology, just the gait of a complete walking period of robot walking is planned that so the moment of robot before single pin support phase finishes, pin and ground bump, and might cause robot walking unstability, influence the stability of robot walking.

Summary of the invention

At above-mentioned prior art situation, the embodiment of the invention provides a kind of gait planning and synthetic method that can obtain apery robot stabilized gait.

Now the technology of the present invention solution is described below:

Anthropomorphic robot gait planning and synthetic method may further comprise the steps:

Step 1: adopt polynomial function to represent the robot hip joint and the track of the end of leading leg; Described polynomial function refers to:

$X_a=\left\{\begin{array}{c}{x}_a\left(t\right)=a_0+a_{1}t+a_2{\mathrm{<figure-callout\; id="2"\; label="t"\; filenames="HSA00000648853700022.png"\; state="\{\{state\}\}">t</figure-callout>}}^2+a_3{t}^3\\ z_a\left(t\right)=b_0+b_{1}t+b_2{\mathrm{<figure-callout\; id="2"\; label="t"\; filenames="HSA00000648853700022.png"\; state="\{\{state\}\}">t</figure-callout>}}^2+b_3{\mathrm{<figure-callout\; id="3"\; label="t"\; filenames="HSA00000648853700022.png"\; state="\{\{state\}\}">t</figure-callout>}}^3+b_4{\mathrm{<figure-callout\; id="4"\; label="t"\; filenames="HSA00000648853700022.png"\; state="\{\{state\}\}">t</figure-callout>}}^4+b_5{\mathrm{<figure-callout\; id="5"\; label="t"\; filenames="HSA00000648853700022.png"\; state="\{\{state\}\}">\; <figure-callout\; id="0"\; label="t"\; filenames="HSA00000648853700011.png,HSA00000648853700012.png"\; state="\{\{state\}\}">t</figure-callout>\; </figure-callout>}}^5\end{array}\right.,0\&le;t\&le;T_s---\left(1\right)$

Wherein, be illustrated in figure 1 as a complete walking period of robot ambulation, establish the terminal true origin O (0,0) of being of robot supporting leg, (x _a(t), z _a(t)) be the terminal position coordinates with respect to true origin of leading leg, it is terminal at forward direction x to lead leg _a(t) and normal direction z _a(t) track is represented a with a cubic polynomial and five order polynomials respectively ₀, a ₁, a ₂, a ₃, b ₀, b ₁, b ₂, b ₃, b ₄, b ₅It is undetermined coefficient.

x _hs(t)＝c ₀+c ₁t+c ₂t ²+c ₃t ³；0≤t≤T _s (2)

x _hd(t)＝d ₀+d ₁t+d ₂t ²+d ₃t ³；0≤t≤T _d (3)

z _hs(t)＝z _h(t)，0≤t≤T _s (4)

z _hd(t)＝z _h(t)，0≤t≤T _d (5)

Wherein, hip joint is used vectorial X respectively at the track that single pin supports phase and double support phase _Hs(x _Hs(t), z _HsAnd X (t)) _Hd(x _Hd(t), z _Hd(t)) represent, represent the propulsion track x of hip joint with two cubic polynomial functions respectively _Hs(t) and z _Hd(t), the movement locus z of normal direction _Hs(t) and z _Hd(t) represent with a linear function;

Step 2: the constraint condition during according to the anthropomorphic robot walking, obtain the coefficient of track polynomial function, single, double pin supports the track of phase when obtaining the robot walking thus; Constraint condition during described anthropomorphic robot walking refers to:

Step 2.1: geometrical constraint

The built on stilts when starting of leading leg of robot, kiss the earth when halting according to the coordinate system definition, can get so:

z _a(0)＝0 (6)

z _a(T _s)＝0 (7)

Step 2.2: the terminal maximum of leading leg is striden height

After robot starting to the end of leading leg contact with ground during this period of time in, be in single leg support phase, for fear of leading leg and the unexpected collision on ground, lead leg with the distance that a bit of buffering is arranged before ground contact, the maximum that this segment distance is defined as the end of leading leg is striden height.In some researchs, with x _a(t) and z _a(t) regard as and have parabolical relation.Stride high form though this disposal route can be simplified the maximum of describing step-length and leading leg end, the gait that this method obtains does not have periodically.Among the present invention, define the terminal maximum of leading leg by following equation and stride height.

x _a(T _m)＝S _m (8)

z _a(T _m)＝H _m (9)

${\stackrel{\&CenterDot;}{z}}_a\left(T_m\right)=0---\left(10\right)$

In the formula (5), H _mBe that the terminal maximum of leading leg is striden height, S _mBe to lead leg end with respect to H _mThe coordinate on directions X, as shown in Figure 1.T _mThen be that the end of leading leg reaches maximum and strides the high used time.

Step 2.3: the periodicity of gait

Obtain periodic gait, must guarantee that the attitude when each step begins with end is identical with speed.And at double support phase, the end of two legs all contacts with ground, and is static, so the speed when single pin support phase begins is zero.Therefore have:

x _a(0)＝-D/2 (11)

x _a(T _s)＝D/2 (12)

${\stackrel{\&CenterDot;}{x}}_a\left(0\right)=0---\left(13\right)$

${\stackrel{\&CenterDot;}{z}}_a\left(0\right)=0---\left(14\right)$

Step 2.4: reduce the collision influence

In the robot ambulation process, lead leg when contacting with ground, just and ground collision has taken place.Collision can cause the joint angle speed of robot to be undergone mutation, in order to reduce to collide the sudden change of the joint angle speed of bringing, can suppose to lead leg and collision on the ground after can not upspring, by make lead leg terminal with collision on the ground before speed remain zero, so just can eliminate the sudden change of the joint angle speed of being brought by collision.Can get thus:

${\stackrel{\&CenterDot;}{x}}_a\left(T_m\right)=0---\left(15\right)$

${\stackrel{\&CenterDot;}{z}}_a\left(T_m\right)=0---\left(16\right)$

Utilize formula (6)-(16), can be in the hope of the coefficient in the formula (1) and parameter T _mThrough type (1) so just can not collided influence and the track of leading leg that satisfies planning requirement of gait parameter according to the rules.

Step 2.5: hip joint motion has very significant effects for the walking stability of robot system.Be designated as:

x _hs(t)＝c ₀+c ₁t+c ₂t ²+c ₃t ³；0≤t≤T _s (17)

x _hd(t)＝d ₀+d ₁t+d ₂t ²+d ₃t ³；0≤t≤T _d (18)

z _hs(t)＝z _h(t)，0≤t≤T _s (19)

z _hd(t)＝z _h(t)，0≤t≤T _d (20)

Step 2.6: in order to obtain the track of hip joint, need the coefficient in definite formula (17) and the formula (18).Be located at single pin when supporting phase and double support phase and beginning, the position coordinates of hip joint on directions X is respectively S _S0And S _D0, the position coordinates on the Z direction is H _hExcept considering that periodically gait also will be considered the walking stability of robot double support phase with reducing the collision influence.When planning hip joint track, following restriction relation is arranged:

The hip joint motion of step 2.6.1:Z direction

Robot in the process of walking, the center of gravity of robot is constantly changing, can stabilized walking in order to make robot, on the Z direction, the center of gravity of robot changes should be as far as possible little, just the motion amplitude of hip joint on the Z direction is very little.Suppose that hip joint remains unchanged in the Z direction motion that single pin supports phase and double support phase, in whole walking period, has so:

z _hs(t)＝H _h (21)

z _hd(t)＝H _h (22)

H _hBe the body construction according to robot, a given constant.

Step 2.6.2: the periodicity of gait

In order to guarantee that the robot walking has periodically, the pose of robot and angular velocity are necessary identical when finishing with double support phase when single pin support phase begins.Therefore, following restriction relation is arranged:

x _hs(0)＝-S _s0 (23)

$x_{\mathrm{hd}}\left(T_d\right)=\frac{1}{2}D-S_{s0}---\left(24\right)$

${\stackrel{\&CenterDot;}{x}}_{\mathrm{hs}}\left(0\right)=V_{h1}---\left(25\right)$

${\stackrel{\&CenterDot;}{x}}_{\mathrm{hd}}\left(T_d\right)=V_{h1}---\left(26\right)$

In the formula (25), V _H1Be the speed of hip joint when each goes on foot starting.

Step 2.6.3: the continuity of gait

The continuity of gait also is to need to consider in the robot gait planning, meet this requirement, the hip joint motion track must be continuous in whole gait cycle so, just the displacement at directions X must be identical with speed when single pin support phase finishes to begin with double support phase constantly for hip joint, that is:

x _hd(0)＝S _d0 (27)

x _hs(T _s)＝S _d0 (28)

${\stackrel{\&CenterDot;}{x}}_{\mathrm{hs}}\left(T_s\right)=V_{h2}---\left(29\right)$

${\stackrel{\&CenterDot;}{x}}_{\mathrm{hd}}\left(0\right)=V_{h2}---\left(30\right)$

Step 3: single, double pin supports the track of phase and synthesizes the complete gait track when obtaining the robot walking at last during with the robot walking that obtains;

Step 4: according to zero point the moment criterion judge whether the gait track that obtains stable.Described zero point, the moment criterion was: refer on robot foot and the ground contact surface a bit, the reacting force on ground is zero in the equivalent moment horizontal component of this point.

$x_{\mathrm{zmp}}=\frac{\underset{i=1}{\overset{5}{\mathrm{\&Sigma;}}}{m}_i({\stackrel{\&CenterDot;\&CenterDot;}{z}}_i+g)x_i-\underset{i=1}{\overset{5}{\mathrm{\&Sigma;}}}{m}_i{\stackrel{\&CenterDot;\&CenterDot;}{x}}_i{z}_i}{\underset{i=1}{\overset{5}{\mathrm{\&Sigma;}}}{m}_i({\stackrel{\&CenterDot;\&CenterDot;}{z}}_i+g)}---\left(31\right)$

$y_{\mathrm{zmp}}=\frac{\underset{i=1}{\overset{5}{\mathrm{\&Sigma;}}}{m}_i({\stackrel{\&CenterDot;\&CenterDot;}{z}}_i+g)y_i-\underset{i=1}{\overset{5}{\mathrm{\&Sigma;}}}{m}_i{\stackrel{\&CenterDot;\&CenterDot;}{y}}_i{z}_i}{\underset{i=1}{\overset{5}{\mathrm{\&Sigma;}}}{m}_i({\stackrel{\&CenterDot;\&CenterDot;}{z}}_i+g)}---\left(32\right)$

z _zmp＝0 (33)

According to formula (31) and formula (32), just can obtain zmp trajectory figure at zero point, thereby whether the walking of judging robot is stable.

Description of drawings

A complete cycle gait synoptic diagram when Fig. 1 is the robot propulsion;

Fig. 2 is hip joint forward direction track synoptic diagram;

Fig. 3 is robot ambulation rod shape synoptic diagram;

When Fig. 4 is the anthropomorphic robot walking zero point zmp trajectory figure;

Embodiment

In order more clearly to set forth purpose of the present invention and technical scheme, below in conjunction with accompanying drawing embodiments of the present invention are described in further detail.

In order to obtain leading leg terminal track, need to determine below the coefficient in the formula (1) to determine coefficient in the formula (1) according to the constraint condition in the robot ambulation process.

At first provide known parameter, D=0.72m, T _s=0.6s, T _d=0.1s, T _c=T _s+ T _d=0.7s, T _m=0.3s, H _m=0.05m, H _h=1.2m, S _m=0m, S _S0=0.18m, S _D0=0.12m, V _H1=0.42m/s, V _H2=0.39m/s.

1, finds the solution the lopcus function of leading leg

The rewriting lopcus function of leading leg is following formula:

$X_a=\left\{\begin{array}{c}{x}_a\left(t\right)=a_0+a_{1}t+a_2{\mathrm{<figure-callout\; id="2"\; label="t"\; filenames="HSA00000648853700022.png"\; state="\{\{state\}\}">t</figure-callout>}}^2+a_3{t}^3\\ z_a\left(t\right)={\mathrm{<figure-callout\; id="0"\; label="b"\; filenames="HSA00000648853700011.png,HSA00000648853700012.png"\; state="\{\{state\}\}">b</figure-callout>}}_0+b_{1}t+b_2{\mathrm{<figure-callout\; id="2"\; label="t"\; filenames="HSA00000648853700022.png"\; state="\{\{state\}\}">t</figure-callout>}}^2+b_3{\mathrm{<figure-callout\; id="3"\; label="t"\; filenames="HSA00000648853700022.png"\; state="\{\{state\}\}">t</figure-callout>}}^3+b_4{\mathrm{<figure-callout\; id="4"\; label="t"\; filenames="HSA00000648853700022.png"\; state="\{\{state\}\}">t</figure-callout>}}^4+b_5{\mathrm{<figure-callout\; id="5"\; label="t"\; filenames="HSA00000648853700022.png"\; state="\{\{state\}\}">\; <figure-callout\; id="0"\; label="t"\; filenames="HSA00000648853700011.png,HSA00000648853700012.png"\; state="\{\{state\}\}">t</figure-callout>\; </figure-callout>}}^5\end{array}\right.,$ 0≤t≤T _s

With formula (8), (10), (11), (12) and (13) simultaneous, that is:

$\left\{\begin{array}{c}{x}_a\left(T_m\right)=S_m\\ x_a\left(0\right)=-D/2\\ x_a\left(T_s\right)=D/2\\ {\stackrel{\&CenterDot;}{x}}_a\left(0\right)=0\\ {\stackrel{\&CenterDot;}{x}}_a\left(T_m\right)=0\end{array}\right.$

By this five equations and known parameter, just can obtain the coefficient a in the formula (1) _i(i=0,1 ..., 3), be respectively: a ₀=-0.36, a ₁=0, a ₂=6.0, a ₃=-6.67, with coefficient substitution formula (1), with regard to the lopcus function that has obtained leading leg on directions X be:

x _a(t)＝-0.36+6t ²-6.67t ³，0≤t≤0.6s (34)

Again with formula (6), (7), (9), (16), (14) and (16) simultaneous, that is:

$\left\{\begin{array}{c}{z}_a\left(0\right)=0\\ z_a\left(T_s\right)=0\\ z_a\left(T_m\right)=H_m\\ {\stackrel{\&CenterDot;}{z}}_a\left(T_m\right)=0\\ {\stackrel{\&CenterDot;}{z}}_a\left(0\right)=0\\ {\stackrel{\&CenterDot;}{z}}_a\left(T_m\right)=0\end{array}\right.$

By this six equations and known parameter, just can obtain the coefficient b in the formula (1) _i(i=0,1 ..., 5), be respectively: b ₀=0, b ₁=0, b ₂=2.22, b ₃=-7.41, b ₄=6.17, b ₅=0, with coefficient substitution formula (1), with regard to the lopcus function that has obtained leading leg on the Z direction be:

z _a(t)＝2.22t ²-7.41t ³+6.17t ⁴，0≤t≤0.6s (35)

By formula (34) and formula (35), the lopcus function that can obtain leading leg just, that is:

$X_a=\left\{\begin{array}{c}{x}_a\left(t\right)=-0.36+{6t}^2-{6.67t}^3\\ z_a\left(t\right)={2.22t}^2-7.41{\mathrm{<figure-callout\; id="3"\; label="t"\; filenames="HSA00000648853700022.png"\; state="\{\{state\}\}">t</figure-callout>}}^3+{6.17\mathrm{<figure-callout\; id="4"\; label="t"\; filenames="HSA00000648853700022.png"\; state="\{\{state\}\}">\; <figure-callout\; id="0"\; label="t"\; filenames="HSA00000648853700011.png,HSA00000648853700012.png"\; state="\{\{state\}\}">t</figure-callout>\; </figure-callout>}}^4\end{array}\right.,$ 0≤t≤0.6s (36)

Because the gait during robot ambulation has periodically and symmetry, therefore obtained just can the be supported track of leg of the track of leading leg.

2, find the solution the hip joint lopcus function

Rewriteeing the hip joint lopcus function is following formula:

x _hs(t)＝c ₀+c ₁t+c ₂t ²+c ₃t ³，0≤t≤T _s

x _hd(t)＝d ₀+d ₁t+d ₂t ²+d ₃t ³，T _s≤t≤T _d

z _hs(t)＝z _h(t)，0≤t≤T _s

z _hd(t)＝z _h(t)，T _s≤t≤T _d

At first ask hip joint to support the track of phase at single pin.Equation of constraint is:

$\left\{\begin{array}{c}{z}_{\mathrm{hs}}\left(t\right)=H_h\\ x_{\mathrm{hs}}\left(0\right)=-S_{s0}\\ {\stackrel{\&CenterDot;}{x}}_{\mathrm{hs}}\left(0\right)=V_{h1}\\ x_{\mathrm{hs}}\left(T_s\right)=S_{d0}\\ {\stackrel{\&CenterDot;}{x}}_{\mathrm{hs}}\left(T_s\right)={\mathrm{<figure-callout\; id="2"\; label="V\; h"\; filenames="HSA00000648853700022.png"\; state="\{\{state\}\}">V</figure-callout>}}_h\end{array}\right.$

According to known parameters and equation of constraint, be easy to the coefficient c in the formula of trying to achieve (2) _i(i=0,1 ..., 3) be: c ₀=-0.18, c ₁=0.42, c ₂=-0.049, c ₃=0.325, then can obtain hip joint and at the lopcus function that single pin supports the phase be:

x _hs(t)＝-0.18+0.42t-0.049t ²+0.325t ³，0≤t≤0.6s (37)

z _hs(t)＝1.2，0≤t≤0.6s (38)

By formula (37) and formula (38), just can obtain hip joint and support the lopcus function of phase at single leg, that is:

$X_{\mathrm{hs}}=\left\{\begin{array}{c}{x}_{\mathrm{hs}}\left(t\right)=-0.18+0.42t-0.049{\mathrm{<figure-callout\; id="2"\; label="t"\; filenames="HSA00000648853700022.png"\; state="\{\{state\}\}">t</figure-callout>}}^2+{0.325t}^3\\ z_{\mathrm{hs}}\left(t\right)=1.2\end{array}\right.,$ 0≤t≤0.6s (39)

3, find the solution hip joint and support the track of phase at both legs, equation of constraint is:

$\left\{\begin{array}{c}{z}_{\mathrm{hd}}\left(t\right)=H_h\\ x_{\mathrm{hd}}\left(T_d\right)=\frac{1}{2}D-S_{s0}\\ {\stackrel{\&CenterDot;}{x}}_{\mathrm{hd}}\left(T_d\right)=V_{h1}\\ x_{\mathrm{hd}}\left(0\right)=S_{d0}\\ {\stackrel{\&CenterDot;}{x}}_{\mathrm{hd}}\left(0\right)={\mathrm{<figure-callout\; id="2"\; label="V\; h"\; filenames="HSA00000648853700022.png"\; state="\{\{state\}\}">V</figure-callout>}}_h\end{array}\right.$

According to known parameters and equation of constraint, be easy to the coefficient d in the formula of trying to achieve (3) _i(i=0,1 ..., 3) be: d ₀=0.12, d ₁=0.39, d ₂=-0.194, d ₃=2.293, then can obtain hip joint and at the lopcus function of double support phase be:

x _hd(t)＝0.12+0.39t-0.194t ²+2.293t ³，0.6s≤t≤0.7s (40)

z _hd(t)＝1.2，0.6s≤t≤0.7s (41)

By formula (40) and formula (41), just can obtain hip joint and support the lopcus function of phase at single leg, that is:

$X_{\mathrm{hd}}=\left\{\begin{array}{c}{x}_{\mathrm{hd}}\left(t\right)=0.12+0.39t-{0.194\mathrm{<figure-callout\; id="2"\; label="t"\; filenames="HSA00000648853700022.png"\; state="\{\{state\}\}">t</figure-callout>}}^2+{2.293t}^3\\ z_{\mathrm{hd}}\left(t\right)=1.2\end{array}\right.,$ 0.6s≤t≤0.7s (42)

What Fig. 2 represented is the track of hip joint, owing to when planning hip joint track, respectively the hip joint track of single pin support phase and double support phase is planned that as can be seen from the figure, the track that single pin supports phase and double support phase is continuous.

Fig. 3 is the plane walking rod shape figure of five link robots, and robot supports the entire motion of phase and double support phase at single pin as we can see from the figure.Robot when each EOS attitude and the attitude of beginning be identical substantially, the deformation trace of robot center of gravity almost is level, illustrate robot in the process of walking center of gravity change not quite, the walking that proves robot is stable.

Fig. 4 is forward direction zmp trajectory at zero point figure, and as can be seen from the figure zero point, zmp trajectory was substantially at the center of stabilized zone, and the robot walking is stable.

The present invention is directed to the problem of seldom considering the double support phase gait in the present gait planning, proposed to support based on the single pin under the constraint condition the synthetic method of gait of phase and double support phase, leg and collision on the ground are to the problem of the influence of walking stability when having solved the robot walking, and adopt polynomial function to cook up the lead leg track of terminal and hip joint of robot, illustrate that robot can not ignore in the gait of double support phase, the gait track that planning simultaneously obtains has continuity, stability and periodicity.

Claims (10)

1. an anthropomorphic robot gait planning and synthetic method is characterized in that: may further comprise the steps:

Step 1: adopt polynomial function to represent the robot hip joint and the track of the end of leading leg;

Step 2: the constraint condition during according to the anthropomorphic robot walking, obtain the coefficient of track polynomial function, single, double pin supports the track of phase when obtaining the robot walking thus;

Step 3: single, double pin supports the track of phase and synthesizes the complete gait track when obtaining the robot walking at last during with the robot walking that obtains;

Step 4: according to zero point the moment criterion judge whether the gait track that obtains stable; Described zero point, the moment criterion was: on robot foot and the ground contact surface a bit, the reacting force on ground is zero in the equivalent moment horizontal component of this point;

z _zmp＝0 (33)

According to formula (31) and formula (32), just can obtain zmp trajectory figure at zero point, thereby whether the walking of judging robot is stable.

2. a kind of anthropomorphic robot gait planning according to claim 1 and synthetic method, it is characterized in that: the polynomial function described in the step 1 refers to:

Wherein, a complete walking period of robot ambulation is established the terminal true origin O (0,0) of being of robot supporting leg, (x _a(t), z _a(t)) be the terminal position coordinates with respect to true origin of leading leg, it is terminal at forward direction x to lead leg _a(t) and normal direction z _a(t) track is represented a with a cubic polynomial and five order polynomials respectively ₀, a ₁, a ₂, a ₃, b ₀, b ₁, b ₂, b ₃, b ₄, b ₅It is undetermined coefficient.

x _hs(t)＝c ₀+c ₁t+c ₂t ²+c ₃t ³；0≤t≤T _s (2)

x _hd(t)＝d ₀+d ₁t+d ₂t ²+d ₃t ³；0≤t≤T _d (3)

z _hs(t)＝z _h(t)，0≤t≤T _s (4)

z _hd(t)＝z _h(t)，0≤t≤T _d (5)

Wherein, hip joint is used vectorial X respectively at the track that single pin supports phase and double support phase _Hs(x _Hs(t), z _HsAnd X (t)) _Hd(x _Hd(t), z _Hd(t)) represent, represent the propulsion track x of hip joint with two cubic polynomial functions respectively _Hs(t) and z _Hd(t), the movement locus z of normal direction _Hs(t) and z _Hd(t) represent with a linear function.

3. a kind of anthropomorphic robot gait planning according to claim 1 and synthetic method is characterized in that: the constraint condition during anthropomorphic robot walking described in the step 2 refers to: geometrical constraint, the terminal maximum of leading leg stride high constraint, gait the periodicity constraint, reduce to collide influence constraint, hip joint motion for the walking stability constraint of robot system.

4. a kind of anthropomorphic robot gait planning according to claim 3 and synthetic method is characterized in that: the concrete of described geometrical constraint determines that method is:

Robot leads leg at when starting built on stilts, kiss the earth when halting, define according to coordinate system:

z _a(0)＝0 (6)

z _a(T _s)＝0 (7)

5. a kind of anthropomorphic robot gait planning according to claim 3 and synthetic method is characterized in that: the described terminal maximum of leading leg is striden high constraint and is determined by following equation:

x _a(T _m)＝S _m (8)

z _a(T _m)＝H _m (9)

In the formula (5), H _mBe that the terminal maximum of leading leg is striden height, S _mBe to lead leg end with respect to H _mThe coordinate on directions X, T _mBe that the end of leading leg reaches maximum and strides the high used time.

6. a kind of anthropomorphic robot gait planning according to claim 3 and synthetic method is characterized in that: the periodic constraint of described gait must guarantee in each step beginning and the attitude when finishing is identical with speed.And at double support phase, the end of two legs all contacts with ground, and is static, so the speed when single pin support phase begins is zero, therefore has:

x _a(0)＝-D/2 (11)

x _a(T _s)＝D/2 (12)

7. a kind of anthropomorphic robot gait planning according to claim 3 and synthetic method, it is characterized in that: the described constraint that reduces to collide influence by make lead leg terminal with collision on the ground before speed remain zero, to eliminate the sudden change of the joint angle speed of being brought by collision, thus:

Utilize formula (6)-(16), can be in the hope of the coefficient in the formula (1) and parameter T _m, through type (1) just can not collided influence and the track of leading leg that satisfies planning requirement of gait parameter according to the rules.

8. a kind of anthropomorphic robot gait planning according to claim 3 and synthetic method is characterized in that: described hip joint motion is designated as for the walking stability constraint of robot system:

x _hs(t)＝c ₀+c ₁t+c ₂t ²+c ₃t ³；0≤t≤T _s (17)

x _hd(t)＝d ₀+d ₁t+d ₂t ²+d ₃t ³；0≤t≤T _d (18)

z _hs(t)＝z _h(t)，0≤t≤T _s (19)

z _hd(t)＝z _h(t)，0≤t≤T _d (20)

9. a kind of anthropomorphic robot gait planning according to claim 8 and synthetic method is characterized in that: described hip joint motion need obtain the track of hip joint for the walking stability constraint of robot system and determine coefficient in formula (17) and the formula (18); The restriction relation of the track of hip joint comprises: the hip joint motion of Z direction, the periodicity of gait, the continuity of gait.

10. a kind of anthropomorphic robot gait planning according to claim 8 and synthetic method, it is characterized in that: the periodicity of described gait has following restriction relation:

x _hs(0)＝-S _s0 (23)

In the formula (25), V _H1Be the speed of hip joint when each goes on foot starting;

The continuity of described gait has following restriction relation:

x _hd(0)＝S _d0 (27)

x _hs(T _s)＝S _d0 (28)

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