A New Proceeding of Control Strategy for a Parallel Structural Biped Robot

A New Proceeding of Control Strategy for a Parallel Structural Biped Robot Shucen Du, Josef Schlattmann Abstract In the applications of simulator, accurate machining and soldering, a parallel hexapod can usually be found. However, it is still an innovative research object to implement this structure in a personal biped walking application. This article represents a realization of a walking mechanism implying parallel hexpod as moving parts. Working principle and control structure are also described in this work. To realize a stable and riding comfortable walking mechanism, the planning and control of stability is a fatal aspect. This aspect is inevitable tightly related to the pose recognition algorithm. To solve a forward kinematic problem (FKP) is always taken as a difficulty in the recognition of pose. In this article, a new method, which integrates MEMS inertial measurement (IMU) units and lengths measurements, is designed. With the force sensors, the center of pressure (CoP) can also be confirmed. This fusion of sensory system is further to realize a steady and agile control of this biped walking robot. Instruction In this article, we represent a prototype of biped walking robot developed in the Workgroup on System Technologies and Engineering Design Methodology of Hamburg University of Technology. The position control, pose recognition and balance control strategy will also be given. The biped walking robot, CENTAUROB[1], is serially comprised of two six DOFs Gough-Stewart platforms, which are also known as Hexapods [2]. These two hexapods form the two legs of the robot and support the whole structure in turn.

Fig.1 Photo and 3D model of CENTAUROB.

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Fig.2. Coordinate system of CENTAUROB.

The mechanical structure is formed by three platforms: two as feet, one as hip. Between platforms, 12 linear actuators driven by motor units are connected to the platforms with 24 joints: 12 3-DOF-joints at hip’s side, 12 2 Cardan joints at feet’s side. As illustrated in fig. 1. To confirm the DOF of a motion mechanism, (1) is used. e

F  6n  e  1   f g   f id

(1)

g 1

In which, take one leg as example, n = 14 mean the links’ number, e = 18 is the number of joints. For 3-DOF-joints, the f = 3, and for Cardan joints, f = 2. A linear unit possesses f = 1. The sum of identical DOF Σfid =0. We can therewith confirm a 6DOF mechanism from this calculation. Inverse Kinematic The coordinate systems of the robot are defined as below: the inertial frame {W}, body-fixed frames {A}, {B}, {C} and {D}. As illustrated in fig.2. In fig.2, vectors AtA and BtB mean the displacement from corresponding coordinate centers on the hip to both feet’ s centers, Abi and Bbi mean the distribution of joints on the hip, Cpi and Dpi mean the distribution of the joints on feet, Ali and Bli indicate the vector of the linear units. The left superscripts show the reference coordinate. Ali and B li are from the joints on the hip and pointing to the joints on the feet. To convert a vector from one frame to another, a rotation matrix is needed. We define a complex angular displacement takes place in the turn of x, y and z. The angles are respectively denoted by Euler-angles: θ, ψ and φ, rotation matrix is in the form of (2).

Y X

 cos  cos  R   sin  cos   sin 

cos  sin sin   sin  cos  cos  sin cos   sin  sin    sin  sin sin   cos  cos  cos  sin  sin  sin  cos   cos sin  cos cos  

(2)

The symbol YXR implies the conversion from coordinate system X to Y. Taking the leg connected to frame {A} as an example, an expression of the position relationships among the vectors is derived in (3). A

li = AtA +

A D A DR pi- bi

(3)

And the length of each linear unit can be expressed as (4), li =||Ali||=||AtA +

2

A D A DR pi- bi

||

(4)

or expressed as

li 

t  t  ApiT A pi  AbiT A bi 2A t AT 

A T A A A



A



pi Abi 2A piT A bi

(5)

In which, Api = ADR Dpi. To drive the motors correctly, the length vary speeds of linear units are needed. These speeds are considered referred to the hip frame {A}. And a minimal coordinate system is chosen as A

y



t , A , A , A

A T A

. T

(6)

The time derivative of (3) in frame {A} is A

~ D p li A tA  DA R  A  D i

(7)

In which,

A

0 1  ~D   0 cos   0  sin  

  A     cos  sin     A    cos  cos    A  . - sin

Project the vector in (7) to the unit vector of (3), length vary speeds of the linear units are obtained, as followed equation. li  A li A li / li

(8)

In (5) and (8), “·” means the inner product computation. Now substitute the transmission ratio of the gearbox and lead screw, γ, to equation (5) and (8), a mapping from platforms’ motion in Cartesian space to the motor motion space is built in (9). qci  2000    li - li 0     n  60    li

(9)

Here, qci is the incremental encoder counting number; li0 is the initial length of lead screws; n is the rotational speed of motor, whose unit is revolution per minute. Generation of the Trajectory A normal statically walking process for the CENTAUROB could be seen as a periodic process. This process is formed of one leg supporting phase and two legs supporting 3

phase, and happens in turns on two legs. In another word, the two feet play the role of supporting foot and swing foot by turns. A whole steps process is illustrated below.

Fig.3. A whole step of the CENTAUROB.

For every step of the robot, the position trajectory, speed trajectory and acceleration trajectory should be continuous, so that the motion will be gentle and smooth. In some special cases, such as obstacles to avoid, the trajectory should be manually adjustable through setting some characteristic points. A Spline interpolation method is used to generate the Cartesian-spatial trajectory (left part of fig. 4.). The corresponding mapping in the motors motional space is given in the right lower part of fig. 4. As soon as the trajectory is generated, the balance check module will be operated. Here the foot rotation indicator is used as criteria. This choice is excessive for a static walking, but makes it accessible for the future dynamic walking pattern. The calculation of FRI is represented in the work of A. Goswami[3]. Once the calculated FRI fell out of the safe supporting area, the pattern would be modified. The definition of dangerous and safe area of supporting area can be found below in fig.5.

Fig.4. Trajectory of swing foot in Cartesian space and in motor motion space.

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Fig.5. Foot/ feet supporting area and FRI point location. (Dangerous area colored with red, safe area colored with green)

Some patterns fitting different occasions will be generated off-line, such as, normal step, stair climbing, turning and so on. These patterns will be downloaded to the PC as regular patterns. During the walking process, these regular patterns will be called and divided into segments. These segments will be online converted to motor motional space according to the mapping in (9). Eventually, the converted segments in motor motion space will be sent to the motor servo drivers one after another. The servo drivers drive 12 motors decentralized. In an accidental situation, such as unbalance is warned according to the center of pressure (CoP) sensor, a fixing value would be added to the unconsumed regular patterns. These fixed pattern segments will be converted as new trajectory. This stability control strategy will be further described in the following section. Control strategy and Sensory System The control system could be divided into two levels: online stability control in the PC; the three-closed-loop PID control in the motor servo drivers. The stability control level is formed by pose recognition sensors and CoP location sensors. The raw data will be acquired and filtered by an ATmega2560 based data acquisition board. Then, processed data will be packed and uploaded to PC for a stability control algorithm. The real time CoP location will be continuously checked. So long as the CoP is not on the boundary of the supporting area, it coincides with FRI [3]. This fact allows us to affect CoP through applying some segments of additional acceleration on the mechanical structure. An integral of these acceleration segments will form an additional speed and position trajectory in Cartesian space, this additional trajectory will be added to the regular pattern. The strategy of stability control can be found in fig.7. 12 strain gouge force sensors, 3 length sensors and 3 inertial measurement units (IMU) are used in this level. Force sensors are installed between the lead screws and Cardan joints. Length sensors are superseded by incremental encoders in present phase of project, for the sake of installation space. IMUs are placed on hip and feet. One force 5

sensor provides the absolute force value along each lead screw. The pose information acquired from the length sensors and IMUs provide the forces’ directions. These two kinds information provide the resultant force and torque applied on the ankle. For a static foot which fully contacts the ground, the counter force and torque will be known. Thus a CoP location will be obtained. Load Pattern

Start

...

Y

USB Hub PC-LabView System

CoP Generated by Sensor Unit

Unexpected Landing

In Dangerous Area?

New Ground Adaption

N

12 Incremental encoders

12 Maxon motor servo drivers

Fixing Pattern Segment generation

Perform the Pattern

Modified Trajectory

12 strain gouge force sensors

ATmega 2560 processor 54 DIN +16 AIN

Theoretical FRI & Hip-Platform Acc. Check

3 x 3D IMUs CENTAUROB

Operation

Fig.6. Structure of control system and sensory system. Fig.7. The online stability control strategy.

A barrier of sensing the real position of the end effector of a parallel structure, like Stewart-Platform, is to solve the forward kinematic problem (FKP). In this work, to avoid the complexity of FKP iterations, the real position is acquired through the combination of a three dimensional IMU and length measurement of linear units. IMU provide the orientation, combined with the feedback of three length measurements, the spatial relation between the feet and hip will be deterministic. At this level of the project, the lengths are sensed through the incremental encoders integrated in the motor units. An initial position of the encoder will be set according to end switches installed on the lead screw hub. The motor servo drivers are decentralized, a three-closed-loop PID controller, includes: position PID, speed PID and current PI loop, is utilized. Based on an averaged load level, the PID parameters are tuned in advance.

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Conclusions and Prospect In this paper, a new prototype of biped walking mechanism is represented. The uniqueness is that, the legs are formed of two hexapods, which provide high loaded and statically walking. The working principle, trajectory generation method and control strategy are also provided. The sensory system is designed and constructed in the present phase of project. With three dimensional IMU, which distributed on the hip and feet, and 3 length measurements, the real-time pose information will be calculated. This part is different from the former design provided in the [4]. For present phase of the project, the simulation of motion, mechanical and mechatronical constructions and open looped tests are finished. The close looped walking test will be accomplished. For the trajectory planning, only continuity of the speed and acceleration are concerned for now. Based on the criteria of time and energy consumption, an optimal trajectory planning strategy will be further developed. In the motor servo driver level, the PID control is done and separated from the PC. This fact blocks the developer from realizing a direct control, such pulse width modulation (PWM) of the voltage, thus a higher level of motor control is not possible. One of the control bottle-neck is the information feedback speed from servo drivers to PC. The motor information feedback obviously prolongs the control period. In the next step, motor information will be bypassing the servo drivers. As a result, direct PWM control will be achievable. This is foundation of an agile and precise stability control. Reference: [1] J. Schlattmann. Laufmaschine und Verfahren zur Steuerung einer Laufmaschine. Deutsches Patent Nr. 19637501, 07/13/2000.

[2] Merlet, J.-P.: Parallel Robots (Second Edition). Springer, Dordrecht, The Netherlands(2006) [3] Ambarish Goswami , Postural Stability of Biped Robots and the Foot-Rotation Indicator (FRI) Point [4] MEMS based Position and Motion Sensors for Controlling Complex Parallel Mechanisms

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