- Research
- Open Access
Robot body self-modeling algorithm: a collision-free motion planning approach for humanoids
- Ali Leylavi Shoushtari^{1}Email author
- Received: 2 October 2015
- Accepted: 15 April 2016
- Published: 27 April 2016
Abstract
Motion planning for humanoid robots is one of the critical issues due to the high redundancy and theoretical and technical considerations e.g. stability, motion feasibility and collision avoidance. The strategies which central nervous system employs to plan, signal and control the human movements are a source of inspiration to deal with the mentioned problems. Self-modeling is a concept inspired by body self-awareness in human. In this research it is integrated in an optimal motion planning framework in order to detect and avoid collision of the manipulated object with the humanoid body during performing a dynamic task. Twelve parametric functions are designed as self-models to determine the boundary of humanoid’s body. Later, the boundaries which mathematically defined by the self-models are employed to calculate the safe region for box to avoid the collision with the robot. Four different objective functions are employed in motion simulation to validate the robustness of algorithm under different dynamics. The results also confirm the collision avoidance, reality and stability of the predicted motion.
Keywords
- Motion Planning
- Collision Avoidance
- Humanoid Robot
- Artificial Potential Field
- Lift Motion
Background
Central nervous system (CNS) manages the human posture and gesture by driving and control the musculoskeletal system in a way that not only resolves the kinematic and kinetic redundancies but also takes advantage of those to reach high maneuverability (Rashedi et al. 2010). From engineering point of view the redundancy both in kinematic and kinetic levels is considered as a problem in terms of system analysis while at the same time, it is a privilege in sense of design (to create a high maneuverable system). Evaluation and studying the human CNS’s strategy in performing dynamic tasks such as lifting (Ayoub 1998; Hsiang and Ayoub 1994; Xiang et al. 2010a; Sitoh et al. 1993; Leylavi Shoushtari 2013), walking (Anderson and Pandy 2001a, b; Xiang et al. 2009), jumping (Babič et al. 2006), somersault (Blajer et al. 2007) and standing up (Mistry et al. 2010; Lord et al. 2002; Janssen et al. 2002) is considered as a source of inspiration to control, motion planning (Abedi and Leylavi Shoushtari 2012) and motion learning (Oztop et al. 2008) of humanoids. The main idea is that human CNS considers several dynamic and static criteria to perform those tasks. Therefore, if we can define the dynamic/static constraints appropriately and sufficiently, the generated motion would be as same as human movement. Optimal motion planning framework is considered as an appropriate solution since numerous physiologically meaningful terms such as postural stability, physiological energy consumed and body physical capability can be included in as constraints and/or cost functions (Ivaldi et al. 2012). Accordingly, Ivaldi et al. (2010) proposed an online motion planning and control method for reaching movement for humanoid robots and Lord et al. (2002) and Janssend et al. (2002) evaluate sit-to stand movement and Mistry et al. (2010) proposed an optimization-based solution for human-like motion planning for this task.
Manual human lifting task is an important operation in many industrial processes which subjected to motion simulation in this research. It could be performed by different techniques (Anderson and Chaffin 1986) where “squat” and “back lift” are most common ones which can be characterized based on kinematical data of lifter (Zhang et al. 2000). Space time optimization (Chang et al. 2001) and predictive dynamics (Xiang et al. 2010b) are efficient optimization-based strategies and were used to human posture prediction of this task (Ayoub 1998; Hsiang and Ayoub 1994; Xiang et al. 2010a; Sitoh et al. 1993; Chang et al. 2001; Cheng and Lee 2005). Collision-Avoidance is one of the key features for realization of simulated motion. Numerous methods are presented in order to avoid the collision in simulation process. Wang and Hamam (1992) take advantage of an optimization-based solution to solve the collision-avoidance problem while Sezgin et al. (1997) implement the same strategy (optimal motion planning) to propose a collision resolution for set of redundant robots. The former approach was about object collision while later method was subjected to robot–robot collision. Later on, Yang and Meng took different approach and proposed an artificial neural network (ANN)-based solution to reduce the computation burden and made the resolution appropriate for implementing in real-time process (Yang and Meng 2000).
To deal with self-collision issue for hyper redundant robots such as humanoids, researchers are executed the artificial potential field (APF) based approaches which result smooth trajectories (Sahara et al. 2004; Sugiura et al. 2006; Khatib 1986). Ohashi et al. (2007) implemented this strategy to recognize dynamic/static obstacles by feeding back the distance from the robot’s hand and obstacle and Dietrich et al. (2012) proposed a reactive, torque-based self-collision free algorithm could be integrated into a task hierarchy for mobile two hands robot. Guan et al. (2006) evaluated the feasibility of stepping over the barriers by humanoids and represented an adaptive motion planning approach. The result of feasibility analysis is integrated in an algorithm for motion planning of feet and waist of humanoid. In the same research, the procedure of walking over the barriers was investigated in a case that the projection of the total center of mass (CoM) of the humanoid was kept within the base of the support (BOS) (Stasse et al. 2009). Yoshida et al. (2008) represent an iterative method for 3D collision-free motion planning where in each iteration, the kinematics of collision and dynamic feasibility of generated posture were checked by the algorithm. Dalibard et al. (2009) solved this problem using a randomized method and under stability and physical capability and task constraints. While Khansari-Zadeh and Billard (2012) proposed a unified framework based on Dynamical System to guarantee the collision-free motion planning of robotic manipulator with convex shaped obstacles.
A short summary of relevant research studies together with highlighted features in columns
Study | Motion generation approach | Collision avoidance algorithm | Self-modeling method | Target task | Application |
---|---|---|---|---|---|
Ayoub (1998) | Optimization | Checking the collision of box with knee | – | Human manual lifting | Occupational biomechanics |
Multi-objective optimization approach | Virtual body spheres (located at joints) | – | Human manual lifting | Human biomechanics | |
Dynamic/Static computational optimization | – | – | Human normal walking | Human kinesiology | |
Xiang et al. (2009) | Optimization (incorporation of recursive Lagrangian dynamics with analytical Gradients) | A sphere filling algorithm is applied to avoid the collision of wrist with hip | – | Human walking (under external loads i.e. backpack) | Human motion prediction |
Blajer et al. (2007) | optimization | – | – | Jumping | Humanoid robot |
Mistry et al. (2010) | Mimicking kinematics of human movement | – | – | Sit-to-stand | Humanoid robots |
Wang and Hamam (1992) | optimization | A computational geometry algorithm to compute the distance between the robot segments and object | – | Robotic manipulation | Motion planning of robotic manipulator |
Sugiura et al. (2006) | Null-space optimization criteria | Artificial potential field method | – | Walking | Humanoid robots |
Ohashi et al. (2007) | Linear Inverted Pendulum Mode (LIPM) | Arm force feedback (which acts as a function of the distance from robot to obstacle) | – | Walking | Humanoid robots |
Gold and Scassellati (2007) | Mapping from motor activity to motion | – | Dynamic Bayesian model | Self-recognition | Social robotics |
Martinez-Cantin et al. (2010) | Active learning algorithm | – | Recursive Least Squares (RLS) estimation | Estimating the kinematic model of a serial robot | Social robotics |
Bongard et al. (2006) | Forward locomotion generation through self-model algorithm | – | Continuous dynamics Self-Modeling | Damage recovery | Autonomous robots |
Table 1 represents a summary of the relevant works addressed before and highlights the main features of each study in columns. The columns 2, 3 and 4 are allocated to novelty points of each work which are as follow: (1) Motion generation approach, (2) Collision avoidance algorithm and (3) Self-modeling method. The works presented in first four rows (Ayoub 1998; Xiang et al. 2009, 2010a; Anderson and Pandy 2001a, b) show that the optimal motion planning approaches are capable to predict human movements and so, these methods are appropriate for motion planning and control of humanoids too (fifth and sixth rows). Nevertheless, collision avoidance is another issue to be considered in motion planning of humanoid robots which is addressed in rows 7, 8 and 9. However, the applied collision avoidance algorithms have two major problems to be implemented in optimization-based motion planning approaches: (1) These algorithms are not consistent with optimization frameworks i.e. artificial potential field (APF) (Sugiura et al. 2006; Khatib 1986) and arm force feedback (Ohashi et al. 2007), (2) Even though there exist collision avoidance algorithms fitted into these frameworks i.e. virtual body sphere (Xiang et al. 2009, 2010a; Anderson and Pandy 2001a, b), these are not feasible (since don’t consider the geometry of whole body). In this research study we are taking advantage of the bio-inspired concept of “self-modeling” to present a feasible collision avoidance algorithm which is consistent with optimization based motion generation framework.
This paper presents a self-modeling-based approach to be implemented in a standard optimal motion planning algorithm. The proposed scenario works based on a set of 12 predefined kinematical self-models of human body that covers all of the feasible postures in manual lifting task. The models actually are parametric mathematical functions which represent a “virtual boundary” of human body. Then, the self-modeling algorithm is integrated in an optimal dynamic motion planning of manual lifting task to avoid object collision/self-collision (Xiang et al. 2010b). The algorithm uses the Cartesian position of the joints to calculate minimum horizontal distance required to move the hand back to avoid penetration of the box to the “virtual boundary”. In fact, the collision avoidance is defined as an inequality constraint and is implemented in optimization-framework together with the other constraints such as range of motion of joint, initial and final position of hand, lifting constraint to enhance the realization of the predicted motion. The lifting task is simulated for four different objective functions subjected to be minimized.
Kinematics and dynamics of the system
Optimization-based motion simulation
Objective functions
Collision checking through self-modeling scenario
Results
It shows the 12 possible conditions due to the vertical position of the joints and relevant 12 candidates self-models
No. candidate self-model | Conditions according to relative positions of joints |
---|---|
1 | y _{ k } ≥ y _{ h } & y _{ e } ≥ y _{ s } |
2 | y _{ k } ≥ y _{ h } & y _{ e } < y _{ s } & y _{ e } ≤ y _{ k } |
3 | y _{ k } ≥ y _{ h } & y _{ e } < y _{ s } & y _{ e } > y _{ k } |
4 | y _{ k } ≥ y _{ h } & y _{ e } = y _{ s } & y _{ e } > y _{ h } |
5 | y _{ k } < y _{ h } & y _{ e } ≥ y _{ s } & y _{ e } ≥ y _{ h } |
6 | y _{ k } < y _{ h } & y _{ e } < y _{ s } & y _{ e } ≥ y _{ h } |
7 | y _{ k } < y _{ h } & y _{ e } < y _{ s } & y _{ e } < y _{ h } |
8 | y _{ k } < y _{ h } & y _{ e } < y _{ s } & y _{ e } < y _{ k } |
9 | y _{ k } < y _{ h } & y _{ e } = y _{ s } & y _{ e } > y _{ h } |
10 | y _{ k } < y _{ h } & y _{ k } ≤ y _{ s } < y _{ h } & y _{ k } < y _{ e } ≤ y _{ hd } |
11 | y _{ k } < y _{ h } & y _{ s } < y _{ h } & y _{ hd } < y _{ e } ≤ y _{ h } |
12 | y _{ k } < y _{ h } & y _{ s } < y _{ h } & y _{ e } < y _{ hd } ≤ y _{ k } |
The “task parameters” i.e. lifting time, weight and dimension of the manipulated object, initial and final position of the object and “body segments properties” i.e. length, mass, inertial properties and position of the center of mass of each body segment are used as inputs for this optimization algorithm. Then the kinematical and dynamical model of human body is employed as two main set of constraints using the mentioned input parameters. These two sets of constraints are responsible for checking the kinematic and dynamic consistency of the predicted movement. The designed objective functions are aimed to impose different dynamic on the predicted movement to check the efficiency of the collision avoidance algorithm under different dynamics.
Lifting task parameters and values
Lifting parameters | Values |
---|---|
Box depth | 0.370 m |
Box height | 0.365 m |
Box weight | 9 kg |
Initial height | 0.365 m |
Final height | 1.37 m |
Initial horizontal position | 0.490 m |
Final horizontal position | 0.460 m |
Lifting time duration | 1.2 s |
Discussion
In this research, the dynamic motion simulation of human lifting was planned as an optimization-based problem with 100 variables. Total lifting time was divided in 10 evenly distributed sequences. The first and last sequences are designed to be coincided with starting and finishing lifting time, so the initial and final postures are optimized by the algorithm and there’s no need to pre define these postures anymore. The novel body collision avoidance algorithm inspired from body self-awareness ability of human was implemented successfully in optimal motion planning framework. The basic idea is based on the automatic selection of body models with the respect to the posture predicted by the algorithm. Later, the model will be implemented in calculation of the desired position of robot’s wrist where box would not collide with the body. The lifting motion was generated using four biologically meaningful objective functions to evaluate the performance of the collision avoidance algorithm for motions with different dynamics. Finally the stability index TMA was measured for all of the four simulation result to demonstrate the stability of predicted motions.
Comparison between predicted and experimental results shows good compatibility in joint angle profile in Fig. 7 in terms of joint profile’s trends. In particular, the predicted profiles for joint angles have the same trend as the experimental profiles while their amplitudes are higher. Based on Fig. 7, the predicted profiles for the shoulder is not even have same curvature as experimental results which the un-modeled DOFs of the shoulder (this joint has 3DOFs) would be a reasonable explain for that. The predicted angles for three of objective functions \({\text{F}}_{\text{TMA}}\), \({\text{F}}_{\uptau}\), \({\text{F}}_{\text{ank}}\) almost are the same while for \({\text{F}}_{\Updelta \uptheta}\) it differs. Since the \(F_{\Updelta \uptheta}\) is a kinematical-based defined function so it directly effects on the kinematics of the system (joint angles). So the kinematical nature of this objective function would be the reason of this difference. It is also recognizable in Fig. 6 by comparing posters set C with the other three sets. In particular, in posture set C the body starts motion with a completely squatted posture due to the foot dorsiflexion (\(\theta_{ankle} = 45{^\circ }\)) and knee flexion (\(\theta_{knee} = 120{^\circ }\)). While, the predicted motion for the other three objective functions initiate while the shank is almost vertical (\(\theta_{ankle} \approx 45{^\circ }\)) and knee is in extension mode (\(\theta_{knee} \approx 70{^\circ }\)). Consequently, the body requires to a forward bending in order to reach to the box. These two predicted modes of the lifting motion resemble two well-known lifting techniques i.e. leg lift or squat and back lift. In particular, the posture set C in Fig. 7 is similar to leg lift method since the body starts with the squatted posture and the rest of the posture sets (especially B and D since their initial postures of shank are quite vertical) looks like back lift technique due to the forward bending of the initial body postures.
According to the predicted angle profiles of joint, the lifting motion can be divided in two main portions: the primer starts from first to fifth time sequences and secondary is from the sixth to last one. The joints of lower body activate more (rather than lower one) within the former section while in second section the joints contributed to the upper body (specially elbow) activate more than the lower joints. This fact is clearly demonstrate by torque profiles of the ankle for three objective functions i.e. \(F_{\Updelta \uptheta}\), F _{ τ } and F _{ ankle } in Fig. 8 where the torque deviation in first part of the motion (−20 to 15 N.m) is quite greater than the second part (−20 to −10 N m). Likewise, the forth torque profile in the first portion has a deviation of −20 to −20 N m while in the second part it is reduced to [5 N m 15 N m]. In the first section of motion of Fig. 7, the angle profiles of knee predicted for three objective functions i.e. F _{ TMA }, F _{ τ } and F _{ ankle } varies from 25° to 85° while in the second section it deviates from 0° to 25° Similarly, the forth angle profile in the first portion has a deviation from 25° to 120° while this amplitude reduces to 0° to 30° in the last part. In contract to the lower joints, the torque profiles of elbow presented in Fig. 8 have inverse trend where the predicted torque of the elbow in the first section is almost constant (−15 N m) while in the last part, it varies from −15 to 15 N m. In summary, the lower joints (ankle and knee) are active more in the first section of the motion rather than second portion. While, elbow has an inverse trend and it activates more in the second section of lifting time.
At the beginning of the second portion of movement (sequence 5), the body is in upright posture and the box has a distance from body which will move the system to an unstable region. This fact is demonstrated in Fig. 9 where the TMA value (≈0.15 m) is close to the margin of stability (0.20 m). Consequently, the shoulder extends in order to pull the box toward body and increase the stability of the system. The shoulder extension starts from 5th time sequence and finishes to sequence 8. Likewise, in Fig. 9, we see that during the same time interval the stability increases (by decreasing TMA value from 0.15 to 0.08 m). In the next step (sequence 8–10) the shoulder flexion lifts the box up to the final position. However, the final positioning of box is also assisted by continues flexion of the elbow from sequence 5 to 10 (Fig. 7).
Conclusion
Using different objective functions has enabled algorithm to simulate lifting motion with different dynamics. The presented results in Fig. 6 prove that there’s no collision for all predicted motions. So, the algorithm is robust to changes in dynamics of motion. The outcomes can be categorized as two distinguished lifting techniques i.e. squat lift and leg lift. It means algorithm is capable to generate two different motions which verify the generalization capability. The analysis carried out on the predicted angles and torques profiles of the joints shows that the kinematical results are consistent with the dynamical results. The outcome motions of the algorithm also were kinematically validated with the experimental results which demonstrate the result’s feasibility. What the collision avoidance algorithm does practically is to move the wrist away from the body in order to avoid the collision. While the wrist displacement could endangered the stability of the system, but all of the four predicted motions are stable (Fig. 9). In other words, the self-modeling approach successfully prevents the collision of the box with the body disregarding the dynamics of the movement while also guarantees its stability and reality. It also shows its kinematic and dynamic consistency with the optimal motion planning framework. Briefly, the design of the self-modeling algorithm and its integration in optimal motion planning framework has successfully represented through proving the robustness and generalization capability of the algorithm together with the stability and feasibility of the outcomes.
Declarations
Acknowledgements
Author would like to thanks R. Rahmatollahpoor for his helpful comments.
Competing interests
The author declares that he has no competing interests.
Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
Authors’ Affiliations
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