New Developments on Online Generation of Trajectories in Quadruped Robots

Carla M.A. Pinto2 *,Cristina P. Santos**, Diana Rocha*, Vitor Matos**
* Instituto Superior de Engenharia do Porto
and Centro de Matematica da Universidade do Porto
Rua Dr Antonio Bernardino de Almeida, 431,
4200-072 Porto, Portugal
** Dept. Electronica Industrial
and Centro Algoritmi Universidade do Minho
Campus de Azurem
4800-058 Guimaraes, Portugal
Received 30 January, 2011; accepted in revised form 19 June, 2012
Abstract: There has been considerable development in the design of efficient controllers for trajectory follow-
ing in articulated robots with many degrees-of-freedom. Nevertheless generating trajectories online is still a
complex and unsatisfactorily solved problem.
In this paper we present a new architecture for a Central Pattern Generator (CPG), for online generation of
trajectories in quadruped robots. Our model is based on a CPG model for locomotor rhythms of quadruped
animals, proposed by Golubitsky, Stewart, Buono, and Collins. Their model consists of eight coupled cells
(CPG units) and each CPG unit is modeled as an oscillator by a system of ordinary differential equations
We generalize their CPG model, considering that each cell or CPG unit is divided in rhythmic and discrete motor
primitives, modeled by simple nonlinear systems of ODEs. Superposition of discrete and rhythmic primitives
may allow for more complex motor behaviours, namely locomotion in irregular terrain and obstacle avoidance.
In this paper, the discrete primitive is inserted into the rhythmic one (i) as an offset of the solution, (ii) summed to
the solution of the rhythmic primitive. We also consider three types of couplings between CPG units: synaptic,
diffusive and mixed.
In this article we try to tackle the impact that these discrete corrections may have in the achieved system solu-
tions. Numerical results show that amplitude and frequency of the periodic solutions are almost constant for all
couplings in cases (i) and (ii). The larger variation occurs in the values of amplitude and frequency for case (i)
in the synaptic coupling.
Results are also obtained in a robotic experiment using a simulated AIBO robot that walks over a ramp. Am-
plitude and frequency may be identified, respectively, with the range of motion and the velocity of the robots’


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