No one was hurt in the accident in One North, a suburban research campus where the vehicle has been on a limited run since August, US software firm nuTonomy said in a statement.
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"None of the people involved was injured. The nuTonomy car, which was operating with two engineers onboard, was travelling at a low speed at the time of the incident," it said.
A company spokeswoman told AFP the damage to the car was "minimal" and the trial has not been suspended.
The cause of the accident is not yet known. The company, police and Singapore's Land Transport Authority are investigating.
The authority said in a statement the taxi was changing lanes when it collided with the lorry.
NuTonomy became the world's first company to launch driverless taxi trials in public, beating rival Uber by weeks.
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During the trial period, two nuTonomy staff will be in the car at all times -- an engineer to monitor performance, and a safety driver who takes over in emergencies, or when trips extend beyond the demarcated test area.
NuTonomy currently has six driverless cars in its fleet but is looking to expand to 12 by year-end.
Uber started a trial on public roads in Pittsburgh, Pennsylvania on September 15.
Other countries are also launching trials of autonomous vehicles.
Driverless two-passenger cars carrying passengers took to the streets of the British town of Milton Keynes on October 11 in a trial run.
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